The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-[tex]x^{2}[/tex]
Find the integration of 16-[tex]x^{2}[/tex].
=16x-[tex]x^{3}/3[/tex]
Now find the value of integration from x=-1 to x=1.
=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
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Find the midpoint of the line segment joining the points (-1,-3) and (-11,10).
Answer: Midpoint=(−6 ,3.5)
Step-by-step explanation:
=(1+22,1+22)M=(x1+x22,y1+y22)=(−1+−112,−3+102)M=(−1+−112,−3+102)=(−122,72)M=(−122,72)=(−6,312)
Answer:
(-6,3.5)
Step-by-step explanation:
x = [tex]\frac{-1-11}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = -6
y = [tex]\frac{-3+10}{2}[/tex] = [tex]\frac{7}{2}[/tex] = 3.5
Given the angles inscribed in the circle, find m ∠ DBC.
Answer:
m∠DBC = 51°
Step-by-step explanation:
Circle Theorem vocabulary
Chord: A straight line joining two points on the circle.Inscribed angle: The angle formed when two chords meet at one point on a circle.Intercepted arc: The arc that is between the endpoints of the chords that form the inscribed angle.Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of the intercepted arc.
Therefore:
[tex]\sf \implies \angle DBC=\dfrac{1}{2}\:\overset{\frown}{BC}[/tex]
[tex]\sf \implies \angle DBC=\dfrac{1}{2}\:(102^{\circ})[/tex]
[tex]\sf \implies \angle DBC=51^{\circ}[/tex]
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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
To determine ∠DBC, we will apply the theorem relating the inscribed angle to the intercepted arc:
[tex]\longrightarrow \sf{Intercepted \: arc= (inscribe \: angle)}[/tex]
[tex]\longrightarrow \sf{Intercept \: arc= 102^\circ}[/tex]
[tex]\longrightarrow \sf{Inscribed \: angle= \angle DBC }[/tex]
[tex]\longrightarrow \sf{102=2( \angle DBC)}[/tex]
[tex]\longrightarrow \sf{\angle DBC= \dfrac{102}{2} }[/tex]
▪ [tex]\longrightarrow \sf{\angle DBC = 51^\circ}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\boxed{\bf{\large m \: \angle DBC= 51^\circ}}[/tex]
two buildings are built 10m apart. *the angle of depression from the top of the shorter building (y) to the foot of the taller building (p) is 53. *the angle of elevation from the top of the shorter building to the top of the taller building (x) is 28. *calculate the height (xp) of the taller building. page 262 trigonometry topic 11 of text book
The height of the taller building is 18.6 meters
How to find the side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Therefore, the height of the taller building is the sum of the height of the smaller building and upper part of the taller building.
tan 53 = opposite / adjacent
tan 53 = x / 10
cross multiply
x = 10 tan 53
x = 10 × 1.32704482162
x = 13.2704482162
x = 13.3 m
tan 28 = y / 10
y = 10 tan 28
y = 5.31709431661
y = 5.3
Therefore, the height of the taller building is 13.3 + 5.3 = 18.6 meters.
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Find the area of a circle whose radius is 14 inches. (Use π = 3.1416.)
Question
Answer:
615.7536
Step-by-step explanation:
Remember the equation for finding the area of a circle is:
A=π[tex]r^2[/tex]
Just substitute in your radius for r and solve:
A=3.1416*[tex]14^2[/tex]
A=3.1416*196
A=615.7536
8 out of 10 people saw the show
Answer: 80% of the 10 people saw the show.
Step-by-step explanation:
8/10 = 0.8, which is 80%.
I hope this helped!
Find the value of x if m2 = 4x - 2.
68⁰
2
The value of x is 11 1/2 OR 11.5
Calculating the measure of anglesFrom the question, we are to determine the value of x
In the given diagram, we have two isosceles triangles
Since base angles of isosceles triangles are equal,
Then, each of the base angles of the isosceles triangle is 68°
Then, we can write that
m ∠2 + 68° + 68° = 180° (Sum of angles in a triangle)
From the given information,
m ∠2 = 4x - 2
Then,
4x -2 + 68° + 68° = 180°
4x = 180 - 68 - 68 +2
4x = 46
x = 46/4
x = 11 1/2 OR 11.5
Hence, the value of x is 11 1/2 OR 11.5
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How many fruits did Anna get?
Answer: Anna got 30
Step-by-step explanation: 2x+3y=25
15+10=25
Given △BAD AB = 3x - 4 ED = 24 CA = 12 BE = 3x Find x to the nearest hundredth.
Answer:
x = 10.67
Step-by-step explanation:
The triangles shown are similar, so corresponding sides are proportional. This lets us write a relation that can be solved for x.
SetupFor the given figure, we can write the proportion ...
AB/CA = DB/ED . . . . . . where DB = ED +BE
(3x-4)/12 = (24 +3x)/24 . . . . . . substitute given values
SolutionMultiplying by 24 gives ...
2(3x -4) = 3x +24
6x -8 = 3x +24 . . . . . eliminate parentheses
3x = 32 . . . . . . . . add 8-3x
x = 32/3 = 10 2/3 ≈ 10.67 . . . . . divide by 3 and convert to decimal
The value of x to the nearest hundredth is 10.67.
28 grams of seeds cost $100 , and 14 grams of seeds cost $60. If you only have $70 and someone gives you $30 to buy 28 grams, how many grams of seeds would you give the person that gave you $30 if you paid $70?
Answer:
8.4 grams
Step-by-step explanation:
We have $70 to start and someone us another $30 for a total of $100. We pay $100 for 28 grams of seeds. If we assume the peron giving us $30 wants a fair share of the seeds, we would calculate an average cost per gram and use that to determine the grams of seeds that the $30 would have covered.
($100/28 grams) = $3.57/gram
($30/$3.57/gram) = 8.4 grams
Answer:
28 grams of seeds
Step-by-step explanation:
(This question is a little tricky)
Note that:
{28 grams of seeds = $100}
----------------------------------------
You have $70 already, and then someone gives you $30.
It means $70 + $30 = $100
So you have $100 now, you can buy 28 grams of seeds and give the person that gave you $30.
Hope this helps :)
I'm thinking of a number. If I add 4 to the number and then multiply the result by 3,the answer is the same as subtracting 5 from the number and then multiplying the result by 2.
(a) in terms of x?
(b) solve the equation n find the number what I'm thinking of
Answer:
x=-22
Step-by-step explanation:
Let's substitute the number you are thinking of with x
(x+4)*3=(x-5)*2
3x+12=2x-10
x+12=-10
x=-22
A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 18 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.04 ounces and 0.17 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge,u, differs from ounces? Perform a two-tailed test. Then fill in the table below. I need the two critical values at the 0.1 level of significace. Also need the answers to al other questions and whether we accpe for reject.
Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 7 ounces, that is:
[tex]H_0: \mu = 7[/tex]
At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:
[tex]H_1: \mu \neq 7[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given by:
[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]
Hence the value of the test statistic is found as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]
t = 1
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]
Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
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If a sample mean is 32, which of the following is most likely the range of
possible values that best describes an estimate for the population mean?
Answer:
(28.36)
Step-by-step explanation:
Pls help
Write the equation for a parabola with a focus at (-4,3) and a directrix at y=5
Answer:
y=(1/-4)(x+4)^2 +4
Step-by-step explanation:
Don't ask
Use the slope formula to find the slope of the line in the graph shown above.
Question 19 options:
A)
–2
B)
2
C)
–1∕2
D)
1∕2
According to the slope formula, the slope of the line shown in the picture is equal to - 1 / 2. (Correct choice: C)
How to find the slope of a line shown in a graph
In this problem we should determine the slope associated to a line described on a Cartesian plane. This information can be found by knowing the coordinates of two points and substituting on the secant line formula:
m = Δy / Δx (1)
Where:
m - SlopeΔx - Change in the independent variable.Δy - Change in the dependent variable.After a quick inspection, we find that the points (0, 3) and (6, 0) lie on the line and the slope according to the secant line formula is:
m = (0 - 3) / (6 - 0)
m = - 3 / 6
m = - 1 / 2
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Kiran was trying to solve the equation 3x 8 = 7x - 8. She said, "The equation has no
solutions because the constant is the same." Do you agree with Kiran? Explain your
reasoning
The statement that the equation has no solutions because the constant is the same is true
How to determine the true statement?The equation is given as:
3x - 8 = 7x- 8
Add 8 to both sides
3x - 8 + 8= 7x- 8 + 8
Evaluate the like terms
3x = 7x
Divide both sides by x
3 = 7
The above equation is false, because 3 and 7 are not equal
This means that the statement that the equation has no solutions because the constant is the same is true
Hence, I agree with Kiran
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Can the sides of a triangle have lengths 6, 20, and 20?
Answer:
Yes.
Step-by-step explanation:
This would be an isosceles triangle - with 2 equal sides both 20 long with a base of length 6.
A triangle can be formed from 3 line segments as long as the sum of the length of any 2 sides exceeds the length of the third side.
Elijah has a flower box in shape of a rectangular prism with injector dimensions that are 15 inches in length, 8 inches in width height. elijah will flower box 3/4 full of soil. how many cubic inches of soil will be in flower box?
720 cubic inches of soil will be in the flower box.
Cuboid Definition: Cuboid shaped objects surround us in our day-to-day life. From television sets, books, carton boxes to bricks, mattresses, and shoeboxes, cuboid objects are all around us. In Geometry, a cuboid is a three-dimensional figure with six rectangular faces, twelve edges, and eight vertices.
Volume of Cuboid = Length x Width x Height
∴ The volume of the soil box = 15 x 8 x 8 = 960 inch³
Since 3/4 is occupied by the soil, the volume of the soil becomes
= 3/4 x 960
= 720 inch³
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How many natural numbers between $150$ and $300$ are divisible by $9$?
Answer:
There are 17 natural numbers divisible.
There are 17 natural numbers between 150 and 300 that are divisible by 9.
To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.
The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).
Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):
Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1
Number of multiples of 9 = (297 - 153) / 9 + 1
Number of multiples of 9 = 144 / 9 + 1
Number of multiples of 9 = 16 + 1
Number of multiples of 9 = 17
So, there are 17 natural numbers between 150 and 300 that are divisible by 9.
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Consider the line 4x + 2y = 8.
What is the slope of a line perpendicular to this line?
m1 x m2 = - 1
Rearrange 4x + 2y = 8.
4x + 2y = 8
-4x, then ÷ 2
y = - 4x + 8 / 2
y = - 2x + 4
m1 = - 2, find reciprocal of - 2, by placing 1 over the 2
So, - 2 will become - 1/2, but multiplying this gives us a positive 1. Thus, m2 = 1/2
m1 x m2 = - 1
-2 x 1/2 = - 1
That means slope perpendicular to the line
4x + 2y = 8 is y = 1/2x, where a half is the gradient/slope.
Ans: 1/2
Hope this helps!
In a certain company, there were five candidates running for President. After the vots were tallied, it turned out that Victor, like in the election, finished in thir place, and david beat him. Greg said that he didn't come in first, but he also didn't come in last. Mac in an interview, said that in this election he wasn't able to win, but at least he was one place hight than his old rival Bill. What place did each candidate come in?
Considering the situation described, the classification of the elections is given as follows, according to their order of finish:
David, Greg, Victor, Mac, Bill.
How to find the classification of the elections?We take the situation that is described, and build the classification from it. The classification has the following format:
P1 - P2 - P3 - P4 - P5
With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.
From the text given in this problem, we have that:
Victor finished in third place, and David beat him, hence P3 = Victor, David = P1 or P2.Greg didn't come in first nor in last, hence, considering that Victor is P3, Greg = P2 or P4.Mac didn't win, but he finished higher than Bill, hence, considering that Mac didn't win and that Victor is P3, Mac = P4, Bill = P5.From the bullet points above, we can conclude that David = P1, Greg = P2.Hence the classification of the election is given by:
David, Greg, Victor, Mac, Bill.
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A photo below is being enlarged you a 24 negative by 30 inches current what is the scale factor being used to enlarge it
If a photo below is being enlarged you a 24 negative by 30 inches current. The scale factor being used to enlarge it is: 6.
Scale factorGiven:
Enlarged size=24 negative by 30 inches
Original size=4 in, 5 in
Using this formula
Let k represent the (ratio) scale factor being used to enlarge it
Scale factor/Enlarged size/Original size
Let plug in the formula
K=24/4
K=6
K=30/5
K=6
Therefore if a photo below is being enlarged you a 24 negative by 30 inches current. The scale factor being used to enlarge it is: 6.
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An empty box is shaped like a rectangular prism. the box has a base area of square foot and a height of foot. how much packing material is required to fill the box?
3 /10 foot³ packing material is required to fill the box.
What is meant by volume of prism?
The volume of a prism is defined as the total space occupied by the three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length. Therefore, The volume of a Prism = Base Area × Length.The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.Volume = base area × height
= 9/10 × 1/3
= 3 /10 foot³
Therefore, 3/10 foot³ packing material is required to fill the box.
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The complete question is-
An empty box is shaped like a rectangular prism. The box has a base area of 9/10 square foot and a height of 1/3 foot. How much packing material is required to fill the box?
Can someone please check this?
What is the solution of square root 1-3x = x+3?
O x = -8 or x = -1
O x=-8
O x=-1
O no solution
Answer: x = -1
Step-by-step explanation:
To remove the radical on the left side of the equation, square both sides of the equation.
√1−3x2=(x+3)2
Simplify each side of the equation.
1−3x=x2+6x+9
Solve for x
x=−1−8
Exclude the solutions that do not make true
√1−3x=x+3
x=−1
Which algebraic expression represents the phrase below? five times the sum of a number and eleven, divided by three times the sum of the number and eight 5(x 11) 3(x 8) startfraction 5 x 11 over 3 x 8 endfraction start fraction 5 (x 11) over 3 (x 8) endfraction 5x 11 3x 8
The overall algebraic expression will be: [tex]\frac{5(x+11)}{3(x+8)}[/tex]
Definition of algebraic expression -
An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
Five times the sum of a number and eleven, divided by three times the sum of the number and eight.
Let the number be x.
Five times the sum of a number and eleven means 5 multiplied to the sum of x and 11. In expression this will be written as:
5(x + 11)
Three times the sum of the number and eight means 3 multiplied to the sum of x and 8. In expression this will be written as:
3(x + 8)
So, the overall algebraic expression will be: [tex]\frac{5(x+11)}{3(x+8)}[/tex]
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In a mixed school, the number of girls is 375. if the boys to girls is 4:5.how many boys are in the school
Answer:
300
Step-by-step explanation:
375 divided by 5=75
Each “1”=75
4x75=300
There are 300 boys.
Hope this makes sense
Answer:
300 boys
Step-by-step explanation:
Let the number of boys = x
Girls: 375
boys : girls = 4 : 5
total in the ratio is 9
girls are 5/9 of total, and are 375
boys are 4/9 of total
5/9 x = 375
x = 375 × 9/5
x = 675
Boys are 4/9 of total.
4/9 × 675 = 300
is the identity for addition for rational number a) 1 b) 0 c) -1 d) 1/2
The identity for addition for rational numbers is zero which is the option b.
Given addition of rational numbers.
We are required to find the identity for the addition of rational numbers.
Rational numbers are those numbers which can be written in the form of p/q and q cannot be equal to zero because if q is equal to zero the whole fraction will become infinity. The numbers whih cannot be written as p/q are known as irrational numbers.
From the all option zero is the identity for addition for rational numbers. This means if a is a rational number. Then a+0=0+a=a.
Hence the identity for addition for rational numbers is zero which is the option b.
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i need this solven within the next hour please. Diego made these notes about ABC. Determine whether each answer is correct. I f an answer is incorrect, explain any errors, and provide the correct solution.
Answer:
Okay, so:
sinA = 22.5/25.5
<A = 62* (correct)
cos C = 22.5/25.5 (correct)
tanA = 22.5/12.0 = 1.875 (correct)
sinC = 12.0/25.5
tan C = 12.0/22.5 = 0.53 (correct)
Step-by-step explanation:
I'll explain the wrong ones in the comments hold on-
P (-7, 1) T(x,y)= (x+9, y - 3) find the image of the given point under the given translation
[tex](-7+9, 1-3)=\boxed{(2, -2)}[/tex]
The answer is (2,-2).
What do we mean by translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.A transformation known as a translation involves shifting each point in a figure by the same amount and in the same direction. For instance, this transformation shifts the parallelogram 3 units upward and 5 units to the right.A transformation in geometry is an action that moves, flips, or modifies a shape (referred to as the preimage) to produce a new shape (called the image). An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction.Find the image of the given point under the given translation:
The rule of translation is (x+9, y - 3), P (-7, 1).
Here we need to add 9 from
x value is -7+9=2
y We need to subtract -3 from
y value is (1-3)=-2
So, P’=( 2,-2)
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Find a b, 6a 9b, |a|, and |a − b|. (simplify your vectors completely. ) a = −9, 12 , b = 6, 4
The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.
Find the values of a + b, 6a + 9b, |a|, and |a − b|:Given that,
a = <−9, 12> , b = <6, 4>
These vectors can be rewritten as,
a = <−9, 12> = −9i + 12j
b = <6, 4> = 6i + 4j
To find a + b,we add both vectors a and b together,a + b = −9i + 12j + 6i + 4j
a + b = −9i + 6i + 12j + 4j
a + b = (−9 + 6)i + (12 + 4)j
a + b = −3i + 16j
To find 6a + 9b, we first find 6a and 9b then add them both together,
6a = 6 (−9i + 12j )
6a = −54i + 72j
9b = 9(6i + 4j)
9b = 54i + 36j
Now add 6a and 9b together,
6a + 9b = −54i + 72j + 54i + 36j
6a + 9b = −54i + 54i + 72j + 36j
6a + 9b = 0i + 108j
To find |a|, use the formula to find the magnitude of a vector,If a = a₁i + a₂j, |a| = √a₁² + a₂²
Here, a = −9i + 12j
|a| = √(−9)² + (12)²
|a| = √81 + 144 = √225
|a| = 15
To find |a − b|, first subtract b from a and find the magnitude of the resultant,a - b = −9i + 12j - (6i + 4j)
a - b = −9i - 6i + 12j - 4j
a - b = −15i + 8j
Now use the formula to find the magnitude of a vector,
|a − b| = √(-15)² + (8)²
|a − b| = √225 + 64 = √289
|a − b| = 17
Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.
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