Answers
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.
Related Questions
Volume=
Help me please! Thank u so much I appreciate it
Answers
the volume of the oblique pyramid is 16 cubic units
How to determine the volumeThe formula for finding the volume of a oblique pyramid is given as;
Volume = [tex]\frac{1}{3}[/tex] × base area/ height
Where
base area = area of a right triangle
From the lengths of the triangle given, we can deduce that the opposite side is 24unit and the adjacent side or the base is 10 unit
let's put in the values to the formula
Base area = 10 × 24
Base area = 240 units
height = 5 units
Since we have both the height and the base area, let's find the volume
Volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{240}{5}[/tex]
Volume = [tex]\frac{1}{3}[/tex] × [tex]48[/tex]
Find the division
Volume = 16 cubic units
Thus, the volume of the oblique pyramid is 16 cubic units
Learn more about an oblique pyramid here:
https://brainly.com/question/24249430
#SPJ1
Find the area of the shaded region
Answers
∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.
Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².
∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find
[tex]\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm[/tex]
where [tex]h[/tex] is the length of the altitude originating from vertex O, and so
[tex]\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm[/tex]
where [tex]b[/tex] is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².
So, the total area of the shaded region is
(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²
Find a power series representation for the function. (center your power series representation at x = 0. ) f(x) = 1 9 x f(x) = [infinity] n = 0
Answers
The power series representation for the function, so the interval of convergence is (-9,9).
The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.
Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.
The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.
We have given f(x)=1/(9+x)
f(x)=(1/9)*(1/(1-(-x/9))
f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]
=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
Let an=(-1)n*(xn/9n+1)
using the Ratio Test
L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|
=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|
=lim n-->infinity|(-1)*(x)/9)|
=|-x/9|<1
x/9<1 and x>9>-1
x<9 and x>-9
x is -9<x<9
for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)n]
By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges
=1/9*diverges
the series diverges for x=9
for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)2n]
which is diverges
so the interval of convergence is (-9,9)
Learn more about convergence here https://brainly.com/question/21089324
#SPJ4
Mrs. wright made 92 cups of fruit punch for a party. how many gallons of punch did she make?
Answers
Answer:
5.75 - 5 3/4
Step-by-step explanation:
1 Cup = 0.0625 gallons
92 cups = 5.75 gallons
If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?
Answers
The value of the functions f(x) and g(x) will be √(4x + 3) and √2. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
If (f g)(x) = h(x) such that h(x) = √(8x + 6). Then we have
(f g)(x) = h(x)
f(x) · g(x) = h(x)
Then put the value of h(x), then we have
f(x) · g(x) = √(8x + 6)
f(x) · g(x) = √2(4x + 3)
f(x) · g(x) = √(4x + 3) × √2
Thus, the value of the functions f(x) and g(x) will be √(4x + 3) and √2.
Then the correct option is B.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
Use the standard deviation to identify any outliers in the given data set.
{35, 31, 29, 34, 6, 31, 32, 30}
Answers
Considering the standard deviation, the data-set has no outliers.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For the given data-set, the mean is:
(35+31+29+34+6+31+32+30)/8 = 28.5.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(35-28.5)^2+(31-28.5)^2+(29-28.5)^2+(34-28.5)^2+(6-28.5)^2+(31-28.5)^2+(32-28.5)^2+(30-28.5)^2}{8}} = 8.7[/tex]
A measure is said to be an outlier if it is more than 3 standard deviations for the mean. Hence the thresholds are:
Less than 28.5 - 3 x 8.7 = 2.4.More than 28.5 + 3 x 8.7 = 54.6.Since all values are between 2.4 and 54.6, the data-set has no outliers.
More can be learned about the standard deviation of a data-set at https://brainly.com/question/24754716
#SPJ1
Which if the following rational functions is graphed below?
A.F(x)=1/x+4
B.F(x)=1/4x
C.F(x)=1/x-4
D.F(x)=4/x
Answers
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Take note that there is a vertical asymptote at x = -4. This means that our function has the form:
▪ [tex]\longrightarrow \sf{F (x)=\dfrac{A}{x + 4} }[/tex]
[tex]\leadsto[/tex] By comparing it with the given options, the correct option is A.
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{A. \: \: F(x)= \dfrac{1}{x + 4} }[/tex]
A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.
Answers
The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336
How to find probability combinations?We are given;
Total number of objective questions = 5 questions
Number of choices of first 2 questions = 3 choices
Number of choices of last 3 questions = 4 choices
Number of ways of answering the first 2 questions = 3 * 3 = 9 ways
Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways
Total number of ways of answering the five questions = 9 * 64 = 576 ways
Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.
Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144
Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192
The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336
Read more about Probability Combinations at; https://brainly.com/question/11732255
#SPJ1
If a = 1,b=2 and c=-3 find
a^b-c b^c-a c^a-b
Answers
Answer:
The value of
[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b \: [/tex]
is
[tex] \frac { 19}{8} [/tex]
Step-by-step explanation:
Greetings ![tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b[/tex]
where,
a=1b=2c=-3Thus, substitute these values to the given equation to find the values.
[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b ... \: substitute \: \\ given \: values \\ (1) {}^{2} - ( - 3)(2) {}^{ - 3} - 1( - 3) {}^{1} - 2 \\ 1 + 3 \: ( \frac{1}{8} ) - 1( - 3) - 2 \\ 1 + \frac{3}{8} + 3 - 2 \\ \frac{11}{8} + 3 - 2 \\ \frac{35}{8} - 2 \\ \frac{19}{8} = 2 \frac{3}{8} [/tex]
Hope it helps
What is the area of parallegram ABCD
Answers
Answer:
c
Step-by-step explanation:
if you take the triangle off of the left side and attach it to the left side then you would have a 6 by 4 rectangle that has an area of 24 units squared.
How old is David
please help me
Answers
Answer: 25 ?
Step-by-step explanation:
what is - 4x +7 > x -13
Answers
Answer:
[tex]\huge\boxed{\sf x < 4}[/tex]
Step-by-step explanation:
Given inequality:-4x + 7 > x - 13
Subtract x to both sides
-4x - x + 7 > -13
-5x + 7 > -13
Subtract 7 to both sides
-5x > -13 - 7
-5x > -20
Divide -5 to both sides
x < -20/-5
x < 4[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]x < \bf 4[/tex]
Step-by-step explanation:
[tex]-4x + 7 > x -13[/tex]
We have to make [tex]x[/tex] the subject of the equation:
• Subtract [tex]x[/tex] from both sides:
[tex]-4x - x + 7 > -13[/tex]
⇒ [tex]-5x + 7 > -13[/tex]
• Now subtract 7 from both sides:
[tex]-5x > -13 - 7[/tex]
⇒ [tex]-5x > -20[/tex]
• Next divide both sides by -5, and remember that dividing an inequality by a negative number reverses the inequality symbol:
[tex]x < \frac{-20}{-5}[/tex]
⇒ [tex]x < \frac{20}{5}[/tex]
⇒ [tex]x < \bf 4[/tex]
Find the shaded area. Round to the nearest 10th, if necessary.
Answers
Answers:
16 cm²
24 cm²
40 cm²
Step-by-step explanation:
The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.
[1] First shaded area
A = L * W
A = (4 cm) * (12 cm - 5 cm - 3 cm)
A = (4 cm) * (4 cm)
A = 16 cm²
[2] Second shaded area
A = L * W
A = (2 cm) * (12 cm)
A = 24 cm²
Lastly, we add them together.
16 cm² + 24 cm² = 40 cm²
how do you find the length of a rectangle if the diagonal is 10 inches long and the width is 8 inches
Answers
Answer:
Step-by-step explanation:
Use pythagorean theorem (a^2+b^2=c^2). The diagonal represents c and the width represents b or a. 8^2+b^2=10^2->64+b^2=100->b^2=36->b=6. So your height would be 6.
find the average rate of change of the function in the interval 6,13
Answers
Using it's concept, the average rate of change of the function on the interval [6,13] is given by:
[tex]r = \frac{f(13) - f(6)}{7}[/tex]
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In this problem, we want to find the rate in the interval [6, 13], which is given as follows:
[tex]r = \frac{f(13) - f(6)}{13 - 6} = \frac{f(13) - f(6)}{7}[/tex]
More can be learned about the average rate of change of a function at https://brainly.com/question/24313700
#SPJ1
Look at the diagram below
Answers
Answer:
TRUE
Since , Angle ABD is congruent or equal to Angle CBD
we know that sides opposite to equal angles are also equal.
i.e AD and CD are opposite sides to angles ABD and CBD respectively.
So, AD = CD
Can you please answer this question
Answers
Answer:
look above
Step-by-step explanation:
hope it helps
808, 408, 208,108, 68 find out wrong number.
Answers
68 is the wrong number in the sequence 808, 408, 208,108, 68
What is Number system?A number system is defined as a system of writing to express numbers.
Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequence is 808, 408, 208,108, 68
Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.
808, 408, 208,108, 68
Let us find the difference between the consecutive numbers
400, 200, 100, 40
As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.
Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
201
5. One flight took a total of 4.6 hours. Write this number as a mixed number
and as an improper fraction. Show your work in the space below. Remember
to check your solution.
Answers
The improper fraction is 25 / 6 hours
The mixed fraction is [tex]4\frac{1}{6}[/tex] hours.
What is the mixed fraction and the improper fraction?The time is written as a decimal. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.
A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is greater than the denominator.
In order to convert 4.6 hours to a mixed fraction, the proper fraction has to be determined. To determine this value, multiply 0.6 by the minutes in an hour
0.6 x 60 minutes = 10 minutes
The decimal becomes : [tex]4\frac{10}{60}[/tex] hours
[tex]4\frac{1}{6}[/tex] hours
To convert the mixed fraction to an improper fraction, multiply the denominator by the whole number and add the numerator, then divide by the denominator
The improper fraction is : 25 / 6 hours
To learn more about decimals, please check: https://brainly.com/question/15287678
#SPJ1
Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance from balloon a to the ground is 1,000 feet, how far is balloon b from balloon a? round your answer to the nearest whole number.
Answers
The distance from Balloon A to Balloon B, d ≈ 1,052 feet
What is distance ?
Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.The given parameters are;
The angle at which Balloon A rises, x° = 50° above horizontal
The angle at which Balloon B rises, y° = 78° above horizontal
The (vertical) distance of Balloon A to the ground, h = 1,000 ft.
The required parameter;
The distance from Balloon A to Balloon B, d
We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule
Let,
The height of the balloon strings are equal
The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.
The distance of the Balloon A from Charlie, l₁, is given as follows;
l₁ × sin(x°) = h₁
∴ l₁ = h₁/(sin(x°))
Which gives;
l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.
l₁ ≈ 1,305.41 ft.
For Balloon B, we get;
h₁ = h₂ = 1,000 ft.
∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.
l₂ ≈ 1,022.34 ft
The angle between the balloon strings, θ = 180° - (x° + y°)
∴ θ = 180° - (50° + 78°) = 52°
The angle between the balloon strings, θ = 52°
By cosine rule, we have;
d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))
∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet
Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet
Learn more about distance
brainly.com/question/15172156
#SPJ4
Enduro solved -4x > 120 by adding 4 to each side of the inequality. What mistake did he make?
Answers
The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
What are inequalities?Inequalities are expressions that have unequal values, when compared
How to determine Enduro's mistake?The inequality is given as
-4x > 120
When 4 is added to both sides, the inequality becomes
4 - 4x > 120 + 4
The above is not the solution to the inequality.
The solution is as follows:
We have:
-4x > 120
Divide both sides inequality by -4
x < -30
Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
Read more about inequality at:
https://brainly.com/question/24372553
#SPJ1
What is the period of y=−5 cos( 8 π x)+3? Give an exact value. units PLEASE MAKE IT QUICK
Answers
Answer:
Maximum/Minimum Value: (0,−2) is a local minima (1/8,8) is a local maxima
Explanation: Use the derivative to find the maximum and minimum
Answer:
Period = ¹/₄
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven function:
[tex]y=-5 \cos (8 \pi x)+3[/tex]
Comparing the given function with the standard form:
A = 5B = 8πC = 0D = 3[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]
Therefore, the period of the given function is ¹/₄.
Learn more about cosine functions here:
https://brainly.com/question/27818219
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]
It has to be the last line in the second picture since it intersects the x axis at approximately x=-1.333[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{Last \: option \: (D.)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Write the equation in slope-intercept form. Then solve y.
▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]
▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]
Identify the x-intercept,
[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]
[tex]\small\longrightarrow \sf{3x=-4}[/tex]
[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]
[tex]\small\longrightarrow \sf{x = -1.33}[/tex]
The graph has the next properties:
[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]
[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]
[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]
Half of the children in a library group like pets, one fourth don't like pets and seven children do not have any
preference. How many students in the library group like pets?
Answers
Answer:
14 children
Step-by-step explanation:
Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.
0.25x = 7
x = 28
Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.
Magda utilizó una cuadrícula de 1 cm de lado para dibujar la figura sombreada, usando triángulos
rectángulos.
Answers
The area of the figure Magda shaded with side lengths of 1 and √2 centimeter is equal to 1.21 cm².
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b represents the base area.h represents the height.In order to calculate the area of the figure Magda shaded with side lengths of 1 and √2 centimeter, we would determine the area of each triangle as follows:
For triangle 1, we have:
Area = 1/2 × b × h
Area = 1/2 × 1 × 1
Area = 0.5 cm².
For triangle 2, we have:
Area = 1/2 × b × h
Area = 1/2 × √2 × 1
Area = 0.71 cm².
Total area = Area of triangle 1 + Area of triangle 2
Total area = 0.5 + 0.7
Total area = 1.21 cm².
Read more on area of triangle here: brainly.com/question/2391510
#SPJ1
Complete Question:
Magda used a 1 cm square grid to draw the shaded figure, using right triangles. 1 cm 3 cm √2 cm 1 cm 1 cm what is the area of the figure Magda shaded?
What is the radius of the sector of the circle below, if the area is 30.39 m^2 and the central angle < AOB measures 43 °. (round answer to the nearest whole meter)
Answers
Answer:
a. 9m
Step-by-step explanation:
Pi = 3.14 = 22/7
formula :
Area of a Sector of a Circle = (central angle)/360 * πr² =
(central angle)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r^2 = 30.39
r^2 = (30.39 * 360) / (Pi * 43)
r^2 = (30.39 * 360) / (22/7 * 43)
r = √ (30.39 * 360 * 7) / (22 * 43)
r = √76582.8/946
r = √80.9543340381
8.99746264444 which is roughly
9
The radius of the sector will be 9m. The correct option is A.
What is the arc length of the circle?The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.
The radius will be calculated as below:-
Area of a Sector of a Circle = (central angle)/360 * πr² =
(Ф)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r²= 30.39
r² = (30.39 * 360) / (Pi x 43)
r²= (30.39 x 360) / (22/7 x 43)
r = √ (30.39 x 360 x 7) / (22 x 43)
r = √76582.8/946
r = √80.9543340381
r = 9
Therefore, the radius of the sector will be 9m. The correct option is A.
To know more about the arc length of the circle follow
https://brainly.com/question/26235466
#SPJ5
20 points !!!
help me please !!
Answers
Minimum: 59
Lower Quartile: 67
Median: 76
Upper Quartile: 86
Maximum: 92
Interquartile Range: 19
#6 pls quick answer!!!
Answers
Answer:
ANSWER: mix 120 ml of 35% acid solution with 60 ml of 65% acid solution to obtain 180 ml 0f 45% acid solution
Step-by-step explanation:
If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.
Acid content of first ingredient + acid content of second ingredient = acid content of the mixture
So, 0.35x + 0.65(60) = 0.45(x + 60)
0.35x + 39 = 0.45x + 27
12 = 0.10x
120 = x
Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?
90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
Translation of 0 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Translation of negative 2 units x, 0 units y composition 90 degree rotation about point 0
Answers
A rule which describes the transformations that maps ΔJKL to ΔJ"K"L" is: D. translation of -2 units x, 0 units y composition 90 degree rotation about point 0.
What is a transformation?A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on the diagram (see attachment), we can infer and logically deduce that a rule which describes the transformations that maps triangle JKL to triangle J"K"L" is a rotation of 90 degrees about the origin and then translated 2 units left.
Read more on transformations here: https://brainly.com/question/27939466
#SPJ1
what is the value of sin30°+cos60°
Answers
The answer is 1.
Here, we need to know the trigonometric values of sin 30° and cos 60°, which are :
sin 30° = 0.5cos 60° = 0.5Hence, sin 30° and cos 60° :
0.5 + 0.51