The sum of the equation is = 5494000.
What does summation mean in math?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
Briefing:Distribute 2j to (j+3).
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used.
The sum is 5,494,000.
Calculation according to the statement:[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]
simplifying them we get:
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]
Split the summation into smaller summations that fit the summation rules.
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]
[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]
The formula for the summation of a polynomial with degree 2
is:
[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]
Substitute the values into the formula and make sure to multiply by the front term.
[tex](2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$[/tex]
we get: 5373400
Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]
we get: 120600
Add the results of the summations.
5373400 + 120600
= 5494000
The sum of the equation is = 5494000.
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Points A, B, and C are located on a circle, and chords exist between all three points. If the measure of ∠BAC is 88°, what is the measure of BC?
The measure of the central angle of the circle BC = 176°
What is Central Angle?The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.
The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Given data ,
Let the three points be represented as A, B and C
Now , the measure of angle ∠BAC = 88°
And , the measure of the central angle is given by
Central Angle = 2 x Angle in other segment
On simplifying the equation , we get
The measure of central angle BC = 2 x 88°
The measure of central angle BC = 176°
Hence , the measure of central angle is 176°
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The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
The length of rectangle is 25 feet and the width of rectangle is 135 feet.
According to the question,
The perimeter of a rectangle is 320 feet. The length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
Odd integers that follow each other and they differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers. The perimeter of a rectangle is 320 feet. Let the length of a rectangle is x. The next consecutive odd integer is x+2.width = 5(x+2)
=5x+10.
Let, Length - l:Width - w; l = 5w and the perimeter of a rectangle is 320 feet. Formula for perimeter of rectangle is 2(Length + Breadth). Perimeter of a rectangle is the sum of the length of all sides of the rectangle. The perimeter of a rectangle formula is,
P = 2(l + b)
In words, it is equal to the sum of two times the length and two times the breadth of the rectangle. Perimeter for any figure is defined as the length of its boundary.
2(length + width) = 320
Length+ width=160
x+5x+10=160
6x=150
x=25
Length = 25 feet
width = 5(25+2)=135 feet.
Hence, the length of rectangle is 25 feet and the width of rectangle is 135 feet..
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if i get 6 gems every 2 minutes and 30 seconds how many gems will i have after one hour?
Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.
How many gems will I have after one hour?Given that;
6 gems are gotten every 2 minutes and 30 secondsLets convert 2min to second; 2min = ( 60 × 2 )sec = 120secHence 6 gems are gotten every 120sec and 30 seconds
Hence 6 gems are gotten every 150seconds
Next we convert 1 hour to seconds
1 hour = ( 60 × 60 × 1 )sec = 3600sec
Now,
6 gems can be gotten every 150seconds
x gems can be gotten every 3600 seconds
x = ( 6 × 3600 ) / 150
x = 21600 / 150
x = 144 gems
Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.
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The number of students from there sections of class 6 are 32,3640. find minimum number of books required for their class library . so, that they can be equally distributed among the students of three sections?
The minimum number of books required to be equally distributed among the students are 1,440 books.
What is LCM?The smallest feasible multiple of two or more numbers is found using the LCM method. LCM is an abbreviation for least common multiple. The LCM of two numbers is divisible by both of them. The LCM of 6 and 8 is 24, for example. As a result, 24 is divisible by both 6 and 8.To find the minimum required books so that they can be equally distributed:
The number of students in three sections of class 6th are 32, 36, and 40.
Now, find the LCM od 32, 36, and 40.
The LCM od 32, 36, and 40 will be 1,440.
Therefore, the minimum number of books required to be equally distributed among the students are 1,440 books.
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What is NOT another name for Q?
A. line LQ←→
B. line RG←→
C. line LG←→
D. line RL←→
The line that is not another name for Q is RL
How to determine the line that is not another name for Q?For a line to represent the point Q, the following must be true:
The line must start from any pointAnd the line must go through point QUsing the above highlights,
The line LQ starts from L and extends through QThe line RG starts from R and extends through QThe line LG starts from L and extends through QThe line RL starts from R and does not extend through QHence, the line that is not another name for Q is RL
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ratio and proportion
1. there are 24 green cars and 48 white cars in a parking lot.
i) find the ratio of green cars to white cars.
ii) what can you say about them?
Based on the given tast content; the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars.
Ratio and proportionNumber of green cars = 24Number of white cars = 48Ratio of green cars to white cars = 24 : 48
= 24 / 48
= 1 / 2
Ratio of green cars to white cars = 1 : 2
Therefore, the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars
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Need help with my math please. Determine the most probable next term in each list of numbers.
Answer:
23. 216
24. 56
25. 52
26. -7
27. 5
Step-by-step explanation:
Question 23Work out the differences between the terms until the differences are the same:
[tex]1 \underset{+7}{\longrightarrow} 8 \underset{+19}{\longrightarrow} 27 \underset{+37}{\longrightarrow} 64 \underset{+61}{\longrightarrow} 125[/tex]
[tex]7 \underset{+12}{\longrightarrow} 19 \underset{+18}{\longrightarrow} 37 \underset{+24}{\longrightarrow} 61[/tex]
[tex]12 \underset{+6}{\longrightarrow} 18 \underset{+6}{\longrightarrow} 24[/tex]
As the third differences are the same, the sequence is cubic and will contain an n³ term. The coefficient of n³ is always a sixth of the third difference. Therefore, the coefficient of n³ = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n³ and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} n&1 & 2 & 3&4&5 \\\cline{1-6} n^3 & 1 & 8 & 27 & 64 & 125 \\\cline{1-6} \sf sequence & 1 & 8 & 27 & 64 & 125 \\\cline{1-6}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^3[/tex]
So the next term in the sequence is:
[tex]\implies a_6=6^3=216[/tex]
Question 24Work out the differences between the terms until the differences are the same:
[tex]2 \underset{+4}{\longrightarrow} 6 \underset{+6}{\longrightarrow} 12 \underset{+8}{\longrightarrow} 20 \underset{+10}{\longrightarrow} 30 \underset{+12}{\longrightarrow} 42[/tex]
[tex]4 \underset{+2}{\longrightarrow} 6 \underset{+2}{\longrightarrow} 8 \underset{+2}{\longrightarrow} 10 \underset{+2}{\longrightarrow} 12[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +1 & +2 & +3 & +4 & +5 & +6 \\\cline{1-7} \sf sequence & 2 & 6 & 12 & 20 & 30 & 42 \\\cline{1-7}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^2+n[/tex]
So the next term in the sequence is:
[tex]\implies a_7=7^2+7=56[/tex]
Question 25Work out the differences between the terms until the differences are the same:
[tex]4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19 \underset{+9}{\longrightarrow} 28 \underset{+11}{\longrightarrow} 39[/tex]
[tex]3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7 \underset{+2}{\longrightarrow} 9 \underset{+2}{\longrightarrow} 11[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +3 & +3 & +3 & +3 & +3 & +3 \\\cline{1-7} \sf sequence & 4&7&12&19&28&39 \\\cline{1-7}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^2+3[/tex]
So the next term in the sequence is:
[tex]\implies a_7=7^2+3=52[/tex]
Question 26Given numbers:
-1, 2, -3, 4, -5, 6
As the list of numbers does not increase or decrease, we cannot apply the same method as the previous questions.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} \sf list & -1 & 2 & -3 & 4 & -5 & 6 \\\cline{1-7}\end{array}[/tex]
From comparing the position of the term to its number in the list, we can see that the nth term is the same as n, but the odd numbers are negative and the even numbers are positive.
Therefore, the rule is:
[tex]\implies a_n=n \quad \textsf{where }n \textsf{ is an even natural number}[/tex]
[tex]\implies a_n=-n \quad \textsf{where }n \textsf{ is an odd natural number}[/tex]
So the next term in the sequence is:
[tex]\implies a_7=-7[/tex]
(since 7 is an odd natural number)
Question 27Given numbers:
5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5, 5, 5, 5
The pattern of these numbers appears to be an ascending number of 5s with a 3 in between:
One 5, followed by a 3Two 5s, followed by a 3Three 5s, followed by a 3Four 5s, followed by a 3Therefore, the next number of 5s will be five. This means the next number in the list will be 5, since there are only four 5s after the last 3.
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Identify the meaning of the variables in the point-slope form of a line.
m
(X1. Y1)
(x,y)
000
the slope of the line
any point on the line
a given point on the line
In the point-slope form of a line, (y-y1)=m(x-x1)
'm' represents the slope of the line.
(x1,y1) represents a given point on the line.
(x,y) represents any point on the line.
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
A straight line is represented using its slope and a point on the line using point slope form. This means that the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1,y1).
The point slope form's equation is (y-y1)=m(x-x1), where (x, y) is a randomly chosen point on the line and m is the slope.
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Answer:
1) (x1,y1)= a given point on the line
2)(x,y) = any given point on the line
3)m= a slope of a line
2. Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary
f(x)=-0.5x+2
g(x)=x³-5x² + 3
The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
How to solve the system of equations?Given:
f(x) = -0.5x+2
g(x) = x³ - 5x² + 3
The point of intersection exists the point where f(x) = g(x)
x³ - 5x² + 3 = - 0.5x + 2
x³ - 5x² + 3 + 0.5x - 2 = 0
x³ - 5x² + 0.5x + 1 = 0
Factorize and estimate the value of x
Let x = 0.53 and 4.85
substitute the value of x = 0.53
f(0.53) = -0.5(0.53) + 2
f(0.53) = -0.265 + 2
f(0.53) = 1.375
If x = 4.85
f(4.85) = -0.5(4.85) + 2
f(4.85) = -2.425 + 2
f(4.85) = -0.245
Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
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HELP ME ASAP!!! I WILL GIVE MANY POINTS and
The 8 cm circle radius and the location of the circle X gives the following values;
(a) tan(<XAB) = -(r - 8)/(2•r + 4) = (8 - r)/8
Which gives;
r = (8 - 4)÷2 = 2(b) <XAB is approximately 0.644 radians
(c) The area of the shaded region is approximately 3.107 cm²
Which method can be used to analyze the figure?8 × (8 - r) = 0.5 × 16 × (8 + r) × sin(A)
(8 - r) = (8 + r) × sin(A)
sin(A) = (8 - r)÷(8 + r)
(8 - r)² = 8² + (8 + r)² - 2×8×(8 + r)×cos(A)
16×(8 + r)×cos(A) = (8² + (8 + r)²) - (8 - r)²
Which gives;
cos(A) = ((8² + (8 + r)²) - (8 - r)²) ÷ (16×(8 + r))
cos(A) = (2•r + 4)/(r + 8)
tan(A) = ((8 - r)÷(8 + r))/( (2•r + 4)/(r + 8))
tan(A) = -(r - 8)/(2•r + 4) = (8 - r)/8
(8 - r)/(2•r + 4) = (8 - r)/8
8 = 2•r + 4
2•r + 4 = 8
Therefore;
r = (8 - 4)÷2 = 2(b) sin(A) = (8 - r)÷(8 + r)
sin(A) = (8 - 2)÷(8 + 2) = 0.6
Therefore;
<XAB = <A = arcsin(0.6) ≈ 0.644 rad
<XAB in degrees ≈ 36.87°
Angle at sector PXQ = 180° - 2 × (36.87°) ≈ 106.26°
Area of sector PXQ ≈ (106.26°/(360°)) × π × 2²
(106.26°/(360°)) × π × 2² ≈ 3.71
Area of sector APO ≈ (36.87°/(360°)) × π × 8² ≈ 20.59
Area of triangle AXB = 8 × (8-2) = 48
The shaded area is therefore;
48 - (2×20.59 + 3.71) ≈ 3.107
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a) The radius of the small circle is 2 centimeters.
b) The measure of the angle XAB is approximately equal to 51.340°.
c) The area of the shaded region is approximately equal to 2.423 square centimeters.
How to analyze a system formed by three semicircles and a circle
In this question we must analyze a geometrical system formed by three semicircles and a circle. The small circle touches the two side semicircles tangentially at points P and Q and the uppermost section of it also tangent to the central semicircle (point R).
(a) Therefore, we have to solve the following system of equations:
8² + h² = (8 + r)² (1)
h + r = 8 (2)
By (2) in (1):
8² + (8 - r)² = (8 + r)²
32 · r = 64
r = 2
The radius of the small circle is 2 centimeters.
(b) The measure of the angle XAB is found by trigonometric functions:
tan m ∠ XAB = OX / AO
tan m ∠ XAB = 10 / 8
m ∠ XAB ≈ 51.340°
The measure of the angle XAB is approximately equal to 51.340°.
(c) The area of the shaded region if the area of the triangle AXB minus the areas of the three circular sections, that is:
A = 0.5 · (16 cm) · (10 cm) · sin 51.340° - (51.340° / 180°) · π · (8 cm)² - 0.5 · (77.320° / 180°) · π · (2 cm)²
A ≈ 2.423 cm²
The area of the shaded region is approximately equal to 2.423 square centimeters.
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A trapezoid has bases with lengths of 1.5 yards and 4 yards. The height is 12 yards. What is the area of the trapezoid?
A) 24 square yards
B) 27 square yards
C) 33 square yards
D) 66 square yards
If f(x) = x/3 and g(x)=1/x find f(x)-g(x)
A.
x-1/3-x
C. 1/3
B. x²-3/3x
D. 3-x²/3x
Please select the best answer from the choices provided
Answer:
x^2-3/3x
Step-by-step explanation:
x/3-1/x=x*x-1*3/3*x
=x^2-3/3x
How can you make iot clear that a measured value of 980 inches actually has 3 significant figures?
The figure 980 inches can be written as 980.0 inches. It contains two non-zero digits and a zero trailing before the decimal point. Hence, it has three significant figures.
Rules to Determine Number of Significant Figures:
There are three fundamental rules that one can use to determine the significant figures in any given number or value. These rules go as follows:
Digits that are not zero are always counted among significant figures.Any zeros in the range of two significant digits are to be counted.The zeroes at the end of any number are significant unless they have been used after a decimal point.For the portion followed by a decimal point, zeroes at the end are not counted, but zero between two non-zero digits and zero in the initial portion of the floating point are counted while taking note of the significant figures in a decimal value.
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Use the root test to determine the convergence or divergence of the series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] 1 nn n = 1
The root test is Divergent, for given [infinity] 1 nn n = 1.
The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.
The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate
Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.
explanation:
If tan is series
if Lim n root (1) = l
if l =<1 than it is convergent
if l = > 1 than it is divergent
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HELPPPPP: An ipod cost $200. Ivy is going to save money for the ipod by babysitting for $15 per week. Ivy already has $32 saved. Write an inequality that can be used to find the minimum number of weeks Ivy must babysit to earn enough to buy an ipod.
To form an equation from a word problem, we can recognize variables and operations from keywords.
Solving the QuestionLet the number of weeks be a.
We're given:
Goal amount is $200 at minimumMoney earned is $15aCurrent amount is $32Because $200 is the minimum account required, we know that the amount earned must be greater than or equal to 200.
[tex]200\leq[/tex]
Our current savings and money can be calculated by adding 15a and 32:
[tex]200\leq15a+32[/tex]
Answer[tex]200\leq15a+32[/tex]
Does anyone know the last two? Match the correct property to the equation showing that property.
Explanation: The 4th one is the distributive property because it shows an equal sign and the 5th one is the inverse property of addition because it uses more than addition.
Answer: 4th one is distributive property 5th one is inverse property of addition
P.S. I am sure 95% sure that I am correct.
factor this:
18x^2+39x-15
Steps for Factoring:
1) Find CM (common factor) for the expression: 3
Factor out 3 =>
[tex]3(6x^{2}+13x-5)[/tex]
2)Factor the above expression by grouping:
The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]
a and b should add up to 13 and multiply up to -30 (6 × -5)
By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)
3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]
Factor out 2x in the first group and 5 in the second group:
[tex]2x(3x-1)+5(3x-1)\\[/tex]
As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)
(3x-1) (2x+5)
The answer is 3(3x-1) (2x+5)
Hope it helps!
A computer store decides to increase the prices of all the items it sells by 15%. the store manager uses matrices to prepare the new price list. matrix a contains the unit price of each product in each category. matrix b contains the revised price of each item in each category. how can the manager obtain the entries for matrix b? a. by adding 15 to each entry of matrix a b. by multiplying each entry of matrix a by 15 c. by multiplying each entry of matrix a by 1.15 d. by multiplying each entry of matrix a by 0.15
The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The manager could achieve scalar multiplication on Matrix A, utilizing the scalar 1.15.
What is the matrix?The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix. Matrices contain wide applications in engineering, physics, economics, and statistics as well as in different branches of mathematics.
Increasing the price by 15% would mean we exist taking 100% of the value + another 15%
100 + 15 = 115%
115% = 115/100 = 1.15.
Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.
Therefore, the correct answer is option c. by multiplying each entry of matrix a by 1.15.
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Answer:
C - by multiplying each entry by 1.15
Step-by-step explanation:
Edmentum.
The measure of central angle qrs is startfraction 8 pi over 9 endfraction radians. what is the area of the shaded sector?
The area of the shaded sector is 144π units squared.
What is a sector?A circular sector, also known as a circle sector or disk sector, is a piece of a disk bounded by two radii and an arc, with the smaller area known as the minor sector and the larger area known as the major sector.To find the area of the shaded sector:
Given - The central angle of the sector is, θ [tex]=\frac{8\pi }{9} rad[/tex].
The radius of the circle is, [tex]R=18 units[/tex].
We know that the area of a sector of a circle of radius 'R' and central angle θ is given as:
[tex]A=\frac{1}{2} R^{2}[/tex]θ
Insert, θ [tex]=\frac{8\pi }{9} ,R=18[/tex] and obtain:
[tex]A=\frac{1}{2} *18^{2} *\frac{8\pi }{9} \\A=\frac{(324*4)}{9} \pi \\A=(36*4)\pi \\A=144\pi units^{2}[/tex]
Therefore, the area of the shaded sector is 144π units squared.
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The complete question is given below:
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
In the figure, ABCDEF is a regular hexagon. △ BDF is drawn by joining the
alternate vertices. Show that △ BDF is equilateral
Answer:
Step-by-step explanation:
Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.
ProofAB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon
∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon
ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence
FB ≅ BD ≅ DF . . . . CPCTC
ΔBDF is equilateral . . . . definition of equilateral triangle
Bernie owns Bernie’s Bike Shop and is advertising his company by
taking his logo and placing it around town on different sized signs. After creating a few signs, he
noticed a relationship between the amount of ink he needs for his logo and the size of the sign.
1. The table below represents some of the signs Bernie has created and the relationship
between the amount of ink needed versus the size of the sign. Complete the information
below to help Bernie see this relationship
From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:
f(x) = x²Domain = 2, 3, 4, 15 and x.Range = 4, 9, 16, 225 and x².What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:
f(x) = x²
From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:
Domain = 2, 3, 4, 15 and x.Range = 4, 9, 16, 225 and x².Read more on domain here: brainly.com/question/17003159
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Select the correct answer what are the solutions of this quadratic equation x^2+8x+3=0
Answer:
x= -4 + radical 13
Step-by-step explanation:
Can someone explain step by step how to do this problem? Thanks! Calculus 2
Answer:
1.314 MJ
Step-by-step explanation:
As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.
There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.
The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.
Mass of waterThe mass of the water being raised is the product of the volume of the cone and the density of water.
The cone volume is ...
V = 1/3πr²h . . . . . . for radius 2 m and height 8 m
V = 1/3π(2 m)²(8 m) = 32π/3 m³
The mass of water in the cone is then ...
M = density × volume
M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg
Center of massThe center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.
Easy WayThe discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...
W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J
Hard Way
As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.
V(y) = (32π/3)(y/8)³
The differential volume at height y is the derivative of this:
dV = π/16y²
The work done to raise this volume of water to a height of 10 m is ...
(9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J
The total work done is the integral over all heights:
[tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]
It takes about 1.31 MJ of work to empty the tank.
Mya has ballet lessons every sixth day and swimming lessons every fourth day. Today she has both lessons. In how many days will Mya have both lessons on the same day again?
Mya would have both lessons on the same day again on the 12th day.
In how many days would they have the classes on the same day again?In order to determine when they would have the both lessons on the same day, the common multiple of 6 and 4 has to be determined. A multiple of a number is the product of an integer and that number. A common multiple is the multiple that is common to two or more numbers.
Multiple of 6 = 6, 12, 28, 24, 30, 36,
Multiple of 4 = 4, 8, 12, 16, 20, 24, 28
Common multiple = 12
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Find the area of a circle if i) radius is 21cm ") diameter is 28cm
Answer:
i) 441π cm² ≈ 1385.4 cm²
ii) 196π cm² ≈ 615.8 cm²
Step-by-step explanation:
The areas of circles with radius 21 cm or diameter 28 cm can be found using the appropriate area formula.
i)The formula for the area of a circle based on its radius is ...
A = πr²
When the radius is 21 cm, the area is ...
A = π(21 cm)² = 441π cm² ≈ 1385.4 cm²
ii)The formula for the area of a circle based on its diameter is ...
A = (π/4)d²
When the diameter is 28 cm, the area is ...
A = (π/4)(28 cm)² = 196π cm² ≈ 615.8 cm²
Answer:
Before multiplying by pi. 441π cm²
After multiplying by pi. 1384.74 cm²
Step-by-step explanation:
The formula for area of a circle is πr².
r=radius
Square the radius.
21²=441
If they want the answer in this form: 441π cm². If not, then use 3.14 for π.
441*3.14=1384.74
The answer is 1384.74 cm².
Hope this helps!
What is 3.172 rounded to the nearest tenth?
3.2
3.3
3.7
3.8
Answer: 3.2
Step-by-step explanation: 3.2 is the answer because the number 7 is higher than 5. so the number 1 goes up by one, which that equals 3.2
Algebra 3, in the excercise size the graphs to determine the functions domain and range, x and y intercepts if any, and the functions values indicated below the graphs
Answer:
Read explanation
Step-by-step explanation:
I answered another one of your questions just like this in detail so I'll keep this one shorter.
Domain: (-∞, 0]
Range: (-3,∞)
x-intercept: Approximately -3.75
y=intercept: -3
For what value of x is 3 − x equal to x − 3?
Answer:
x = 3
Step-by-step explanation:
Given the information from the question, we can deduce that:
3 - x = x - 3
Now our goal here is to find x.
3 - x = x -3
3 - x - 3 = x - 3 - 3
- x = x - 6
- x - x = x - 6 - x
- 2x = - 6
x = [tex]\frac{-6}{-2}[/tex] = 3
Answer: 3
Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.
x - 3 = 3 - x
Adding 3 to both sides, we have
x = 6 - x
Adding x to both sides we have
2x = 6
Dividing by 2 from both sides, we get
x = 3
Lauren has an above-ground pool. to keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. when the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? use π = 3.14
1885.5 m^3 of water will fill the container.
To find how many cubic feet of water will it contain:
Given -
Lauren has an above-ground swimming pool. The water level in the pool must be 4 inches above the pool's surface in order for the skimmer to function properly. π = 3.14The pool comprises a 12-foot-radius cylinder with a height of 4.5 feet.
Height of pool = 4.5 ftRadius of pool = 12 ftThe height of the water is 4 inches below the pool top12 inches make 1 ft4 inches = 4/12 ft = 0.33 ftTherefore, height of water = 4.5 - 0.33 = 4.17 ftThe volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed.
The volume of the cylinder formed by the water = volume of water = [tex]\pi r^{2} h[/tex]volume = 3.14 x [tex]12^{2}[/tex] x 4.17 = 1885.5 m^3 of waterTherefore, 1885.5 m^3 of water will fill the container.
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The complete question is given below:
Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14
A cylinder with a radius of 12 feet and a height of 4.5 feet.
a section of a circle has both endpoints on the circle. what is the section of the circle called
Answer:
ChordStep-by-step explanation:
What is chord?A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.
A section of a circle has both endpoints on the circle. Chords are the sections of a circle.
Therefore, the final answer is "chords".
I hope this helps, let me know if you have any questions.
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