Answer:
1/2.x+3(x-1)-5=30
1/2.x+3x-3-5=30
(1/2+3)x-8=30
7/2.x-8=30
7/2.x=38
7x=76
x=76/7
CMIIW
Answer each question and tell your reasoning.
a. Is 60% of 400 equal to 87?
b. Is 60% of 200 equal to 87?
c. Is 60% of 120 equal to 87?
2. 60% of x
is equal to 87. Write an equation that expresses the relationship between 60%, x
, and 87. Solve your equation.
Equation:
x=
3. Write an equation to help you find the value of each variable. Solve the equation.
60% of c
is 43.2.
Equation:
c=
38% of e
is 190.
Equation:
e=
Answer:
Step-by-step explanation:
400*60% can be rewriten as 400×0.6 which is 240, so a is false.
the same steps can be repeated for b and c
b) 200*0.6=120, therefore is false
c) 120*0.6=72, therefore is false
2)
[tex]60 percent * x=87\\0.6x=87\\x=\frac{87}{0.6} \\\\x=145[/tex]
Now we check the answer by using the same steps in problems a,b,c
[tex]145*0.6=87\\87=87[/tex]
3)
[tex]0.6c=43.2\\c=\frac{43.2}{0.6} \\c=72[/tex]
and finally
[tex]0.38e=190\\e=\frac{190}{0.38} \\e=500[/tex]
What angle of descent ( depression) should the pilot use to safely bring the plane to the airport runway? The plane is 10,000 feet above the ground and is a little more than 30 miles ( approximately 160,000 feet) from the airport. Write an equation and show work . Round the angle measure to the nearest whole degree. ( Picture is not drawn to scale )
Answer:
4 degrees ( to nearest degree).
Step-by-step explanation:
The trig ratio you want is the tangent.
tan x = 10,000 / 160,000 where x is the angle of depression.
tan x = 0.0625
x = 3.576 degrees.
can someone help me please?
Answer:
the answer to the question is answer C
Answer:
Step-by-step explanation:
B is your answer
Hey guys please help? Trigonometry
So, the task is: find cos a, if:
1) sin a = (3√11)/10, a ∈ (0; π/2)
2) sin a = (3√11)/10, a ∈ (π/2; π)
Could someone please explain how to solve it? I can't figure out what difference a ∈ (0; π/2) and a ∈ (π/2; π) make in the way I have to solve it mmh... I'll pin my attempt to do the first one (failed for some reason)
Step-by-step explanation:
a ∈ (0; π/2) here means that our angle, a must lie between 0 and pi/2, exclusive.
So this mean our angle must be in between 0 and pi/2, but can not be neither 0 and pi/2.
Here we have
[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]
We must find cos.
Using the Pythagorean theorem
[tex]( \sin( \alpha ) ) {}^{2} + ( \cos( \alpha ) ) {}^{2} = 1[/tex]
It is mostly notated as this,
[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]
But they mean the same thing, we know
[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]
So we plug that in for sin a.
[tex]( \frac{3 \sqrt{11} }{10} ) {}^{2} + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex] \frac{99}{100} + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex] \cos {}^{2} ( \alpha ) = \frac{100}{100} - \frac{99}{100} [/tex]
[tex] \cos {}^{2} ( \alpha ) = \frac{1}{100} [/tex]
Since cos is Positve over the interval (0; π/2), we take the positive or principal square root.
[tex] \cos( \alpha ) = \frac{1}{10} [/tex]
2. We would get the same work for the second part, the only difference is that cosine is negative over the interval
(π/2, π)
So the answer for 2 is
[tex] \cos( \alpha ) = - \frac{1}{10} [/tex]
Disclaimer: Your work you did was correct, just remember for fractions like
[tex]1 - \frac{99}{100} [/tex]
Convert 1 into a fraction that has a denominator of 100.
[tex] \frac{100}{100} - \frac{99}{100} = \frac{1}{100} [/tex]
There is 1 pint of liquid in this container. if another pint were added, how much liquid would there be? a) 2 cups b) 1 pint c) 1 quart d) 2 gallons
Answer:
C: 1 Quart
Step-by-step explanation:
2 pints are the equivalent of 1 quart
Answer:1 Quart
Step-by-step explanation: Because 2 pints equals=1 quart
From the top of a 6m house, the angle of elvation to the top of a flappole is across the street is 9 degrees. the angle of depression is 22 degrees to the base of the flapole. Redraw the diagram below and label all the angles. How tall is the flagpole? Round naswer to one decimal place.
The height of the flag pole which is described as in the task content is; 8.2m.
What is the height of the flagpole as described from the top of the 6m house?The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;
tan 22° = 6/x
x = 6/tan 22 = 14.9m.
Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;
tan 9° = y/14.9
y = 14.9 tan 9° = 2.2m
Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.
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Does anybody know this? The quotient of -45 and -5 is
Dagogo uploads 333 videos on his channel every month. each video averages 151515 minutes in length and gets an average of 150{,}000150,000150, comma, 000 new views. the average ratio of likes-to-views of dagogo's videos is 1:51:51, colon, 5. dagogo wants to reach a total of 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel. assuming these rates continue, for how many months does dagogo need to upload videos to get to 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel?
To acquire 90000000 views on his channel, he has to upload 20 videos every month.
According to the given information:Every month, he posts 3 videos to his channel. An average number of people watch each video. = 1500000
In search of:
How many months must pass before he begins to receive 90,000,000 views on his channel?
Step 1
On his channel, he posts three videos each month.
The average number of views per video is.
3 Videos Receive Views
= 3 * 1500000
= 4,500,000 Views
Number of 4,500,000 views each month
Complete 90000000 Views
Step 2
Total Views/Months = Total Views/Total Views
Days in a month = 90000000/4500000
= 20
20 Monthly months in the number
To acquire 90000000 views on his channel, he has to upload 20 videos every month.
20 Months is the right response, so.
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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!
The equivalent expression of the radical expression ∛1080 is 6∛5
How to evaluate the radical expression?The radical expression is given as
∛1080
Express 1080 as 216 * 5
∛1080 = ∛(216 * 5)
Split the factors
∛1080 = ∛216 * ∛5
Evaluate the cube root of 216
∛1080 = 6 * ∛5
Evaluate the product
∛1080 = 6∛5
Hence, the equivalent expression of the radical expression ∛1080 is 6∛5
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What is the following simplified product? Assume x 20.
(√6x² +4√8x³)(√9x-x√5x^5)
O 3x√√6x+x²√30x+24x²2x+8x³10x
O 3x√6x+x√30x+24x²√2+8x5/10
O 3x√√6x-x+√30x+24x² √2-8x² 10
O3x6x-x30x+24x²2x-8x510x
The simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
How to determine the simplified product?The product expression is given as:
(√6x² +4√8x³)(√9x-x√5x^5)
Evaluate the exponents
(√6x² +4√8x³)(√9x-x√5x^5) = (x√6 +8x√2x)(3√x - x^3√5x)
Expand the brackets
(√6x² +4√8x³)(√9x-x√5x^5) = x√6 * 3√x + 8x√2x * 3√x - x√6 * x^3√5x - 8x√2x * x^3√5x
This gives
(√6x² +4√8x³)(√9x-x√5x^5) = 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
Hence, the simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
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Which of these is a simplified form of the equation 7p 4 = − p 9 2p 3p? 13p = 13 3p = 5 7 = 4 11 = 15
Answer:
[tex]\boxed{\sf{3p=5}}[/tex]Step-by-step explanation:
To find:
The value of pGiven:
7p + 4 = −p + 9 + 2p + 3p[tex]\sf{7p+4=-p+9+2p+3p}[/tex]
Isolate the term of p, from one side of the equation.
Combine like terms.
[tex]\rightarrow \sf{7p+4=-p+2p+3p+9}[/tex]
Add the numbers from left to right.
-p+2p+3p=4p
7p+4=4p+9
Then, you subtract by 4 from both sides.
[tex]\sf{7p+4-4=4p+9-4}[/tex]
Solve.
7p=4p+5
Subtract by 4p from both sides.
7p-4p=4p+5-4p
Solve.
[tex]\boxed{\sf{3p=5}}[/tex]
Divide by 3 from both sides.
3p/3=5/3
Solve.
p=5/3
Divide is another option.
5/3=1.6666
So, the final answer is 3p=5.
I hope this helps, let me know if you have any questions.
Jessica is a Custodian at an oracle Arena. She waxes 20m^2 of the floor in 3/5 of an hour. Jessica waxes the floor at a constant rate. How many square metres can she wax per hour?
Answer:
Step-by-step explanation:
Just multiply how much she waxes in 3/5 hour by 5/3. Answer is 100/3 or 33.33 sq. meters per hour
A private grassland has an area of 2/5km squared. The owner of the garden buys an extra of 1/3km squared of land from the neighbour to make his grassland bigger. What is the new size of the grassland?
Answer:
11/15 km
Step-by-step explanation:
Simply sum the areas:
2/5 + 1/3 = (6 + 5)/15 = 11/15
Select the correct answer. which function has a phase shift of to the right? a. b. c. d.
The function y = 2sin has a phase shift of pi/2 to the right (2x - pi).
What is a trigonometric function?An angle or angle function (such as the sine, cosine, tangent, cotangent, secant, or cosecant) is most simply defined in terms of the ratios of pairs of sides of a right-angled triangle.The inverse of a trigonometric function (such as arcsine, arccosine, or arctangent).To find the function which has a phase shift to the right:
The function has a phase shift of pi/2 to the right.
By definition, you have the phase shift is:
asin(bx+c)Phase shift = -c/bWhen you substitute the values from the function [tex]y=2sin(2x-\pi )[/tex], where [tex]c=-\pi[/tex] and [tex]b=2[/tex], you obtain:
Phase shift = [tex]-(-\pi )/2[/tex]Phase shift = [tex]\pi /2[/tex]Therefore, the function y = 2sin has a phase shift of pi/2 to the right (2x-pi).
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The complete question is given below:
Which function has a phase shift of pi/2 to the right?
Brayden has 24 feet of fence available to build a rectangular fenced in area. If the width of the rectangle is xx feet, then the length would be \frac{1}{2}(24-2x). 2 1 (24−2x). A function to find the area, in square feet, of the fenced in rectangle with width xx is given by f(x)=\frac{1}{2}x(24-2x).f(x)= 2 1 x(24−2x). Find and interpret the given function values and determine an appropriate domain for the function.
The maximum area is achieved when the rectangle is a square of side 6 feet, with a domain, 0 < x < 12.
The perimeter available with Brayden is 24 feet.
The width of the rectangle is assumed to be x feet.
The length can be calculated using the formula:
2(length + width) = perimeter,
or, 2length + 2width = perimeter,
or, 2length = perimeter - 2width,
or, length = (1/2)(perimeter - 2 width).
Substituting the values, we get:
length = (1/2)(24 - 2x).
The area can be calculated using the formula:
Area = length*width.
Substituting the values, we get:
Area = (1/2)(24 - 2x)x = (1/2)x(24 - 2x).
Now, we need to maximize the area for the given perimeter.
For that, we differentiate the area function, with respect to its width x.
d(Area)/dx = (1/2)(24 - 2x) + (1/2)x(-2),
or, d(Area)/dx = 12 - x - x = 12 - 2x ... (i).
To check for the point of inflection, we equate this to zero, to get:
12 - 2x = 0,
or, 2x = 12,
or, x = 6.
To check whether this is maximum or minimum, we differentiate (i) with respect to x to get:
d²(Area)/dx² = -2 which is less than 0, implying area is maximum at x = 6.
Thus, the maximum area is achieved when the width is 6 feet.
Length = (1/2)(24 - 2x) = (1/2)(24 - 2*6) = (1/2)12 = 6.
Thus, the maximum area is achieved when the length is 6 feet.
The area function is, area = (1/2)x(24 - 2x).
We know that the area is always greater than 0, thus, we can show that:
(1/2)x(24-2x) > 0,
or, x(24 - 2x) > 0,
or, x(12 - x) > 0, which is true when 0 < x < 12.
Thus, the domain of the area function is 0 < x < 12.
Thus, the maximum area is achieved when the rectangle is a square of side 6 feet, with a domain, 0 < x < 12.
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use substitution to solve the system 3x+8y = -56 2x-y = 7
Answer: x = 0 ; y = -7
Step-by-step explanation:
Given equation:
1) 3x + 8y = -56
2) 2x - y = 7
Subtract 2x on both sides of 2) equation to isolate y-value
2x - y - 2x = 7 -2x
-y = 7 - 2x
Divide -1 on both sides of 2) equation
-y / -1 = (7 - 2x) / -1
y = 2x - 7
Current system
1) 3x + 8y = -56
2) y = 2x - 7
Substitute 2) equation into the y-value of 1) equation
3x + 8 (2x - 7) = -56
Simplify by distributive property
3x + 8 × 2x - 8 × 7 = -56
3x + 16x - 56 = -56
Combine like terms
19x - 56 = -56
Add 56 on both sides
19x - 56 + 56 = -56 + 56
19x = 0
Divide 19 on both sides
19x / 19 = 0 / 19
[tex]\Large\boxed{x=0}[/tex]
Substitute the x-value into one of the equations to find the y-value
2x - y = 7
2 (0) - y = 7
0 - y = 7
-y = 7
[tex]\Large\boxed{y=-7}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
can you please help me with the question the link is down below
Answer:
output = 9
Step-by-step explanation:
add 5 to the input to obtain output
output = 4 + 5 = 9
what is the volume of a triangular pyramid that is 12 feet tall and has a base area of 5 square feet
The volume of the triangular prism as described is; 20 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid refers to pyramid which has a triangular base
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism = (1/3) ×5 × 12
Volume = 20 cubic foot
Therefore, volume of the triangular prism as described is; 20 cubic foot.
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If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3 startroot 11 endroot, what must also be a root of f(x)? 3 i startroot 11 endroot negative 3 i startroot 11 endroot 3 minus startroot 11 endroot negative 3 minus startroot 11 endroot
Answer:
C
Step-by-step explanation:
C
Answer:
Step-by-step explanation:
its c
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!
[tex]denote \: by \: s \: the \: cost \: of \: a \: sweatshirt \\ denote \: by \: t \: the \: cost \: of \: a \: t \: shirt[/tex]
[tex]3t + 7s = 240.5 \\ 6t + 5s = 220[/tex]
[tex] - 6t - 14s = - 481 \\ 6t + 5s = 220[/tex]
[tex] - 9s = - 261 \\ s = \frac{ - 261}{ - 9} = 29 \: dollars[/tex]
[tex]3t + 7(29) = 240.5 \\ [/tex]
3t + 203 = 240.5
3t = 37.5
t = 12.5 dollars
Assume that adults have iq scores that are normally distributed with a mean of μ=100 and a standard deviation σ=15. find the probability that a randomly selected adult has an iq less than 130
The probability that a randomly selected adult has an IQ less than 130 is 0.9332
For given question,
We have been given adults IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15.
We need to find the probability that a randomly selected adult has an IQ less than 130
Sketch the curve.
The probability that X < 130 is equal to the area under the curve which is less than X = 130
Since μ = 100 and σ = 15 we have:
⇒ P ( X < 130 ) = P ( X- μ < 130 - 100 )
⇒ P ( X < 130 ) = P((X− μ)/ σ < 130 - 100/20 )
Since (X-μ)/σ = Z and (130 - 100)/20 = 1.5 we have:
P (X < 130) = P (Z < 1.5)
Now, we use the standard normal table to conclude that:
P (Z < 1.5) = 0.9332
Therefore, the probability that a randomly selected adult has an IQ less than 130 is 0.9332
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Circle T is shown. Line segment Q S is a diameters. Point R is opposite of point T. Lines are drawn from points Q and S to point R to form a right triangle. Angle Q R S is a right angle.
The measure of arc QS is (4x – 18)°.
What is the value of x?
40.5
49.5
94.5
180
The value of angle x of the given cyclic segment is; 49.5°
How to find the angle of an arc?We are given the measure of the angle of arc QS as (4x – 18)°
Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;
Thus;
(4x – 18)° = 180°
4x - 18 = 180
4x = 180 + 18
4x = 198
x = 198/4
x = 49.5°
The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.
The formula to measure the length of the arc is;
Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)
Arc Length Formula (if θ is in radians) s = ϴ × r.
Thus, the value of x of the given cyclic segment is; 49.5°
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Eduro solved -4x > 120 by adding 4 to each side lf the inequality what mistake did he make?
Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4
Inequalityminus four x greater than 120
-4x > 120
divide both sides by -4x < 120/-4
There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4
x < -30
Check:
-4x > 120
-4(-30) > 120
120 > 120
Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4
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Some randomly selected high school students were asked to name their favorite sport to watch. The table displays the distribution of results. A 2-column table with 5 rows. Column 1 is labeled sport with entries football, basketball, baseball, soccer, none. Column 2 is labeled probability with entries 0.23, 0.18, 0.26, 0.17, 0.16. What is the probability that a student chose football given that they like watching sports? 0.16 0.23 0.27 0.77
The probability that a student chose football given that they like watching sports is: c. 0.27.
Conditional ProbabilityUsing this formula
P[Like (Football)/Like (Sport)]
Where:
P=Probability
Like (Football)=0.23
Like (Sport)=0.23+0.18+0.26+0.17=0.84
Let plug in the formula
P[Like (Football)/Like (Sport)]=0.23/0.84
P[Like (Football)/Like (Sport)]=0.27
Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.
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Answer:
C.
Step-by-step explanation:
Someone please help me with Graph!!
(My answers keep coming wrong)
Topic= Solving systems of equations by Graphing
See below for the solution to the systems of equations
How to solve the systems of equations?System of equations 1
Here, we have
y = -5x/3 + 3
y = x/3 -3
We start by plotting the graph of both equations
Next, we write out the point of intersection of the equations
See attachment for the equation of the system
From the attached graph, the point of intersection of the equations is (3, -2)
Hence, the solution to the system is (3, -2)
System of equations 2
Here, we have
y = 4x + 3
y = -x -2
We start by plotting the graph of both equations
Next, we write out the point of intersection of the equations
See attachment for the equation of the system
From the attached graph, the point of intersection of the equations is (-1, -1)
Hence, the solution to the system is (-1, -1)
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A fruit basket contains only apples and bananas. If there are 8 apples and 13 bananas, what is the ratio of bananas to fruit? Select all that apply.
13:8
13:21
StartFraction 8 Over 13 EndFraction
21 to 13
StartFraction 13 Over 21 EndFraction
The ratio of bananas to fruit is 13 : 21
How to determine the ratio of bananas to fruit?The given parameters are
Banana = 13
Apple = 8
The total number of fruits is
Fruit = Banana + Apple
Substitute the known values in the above equation
Fruit = 13 + 8
Evaluate the sum
Fruit = 21
The ratio of bananas to fruit is then represented as:
Ratio = Banana : Fruit
Substitute the known values in the above equation
Ratio = 13 : 21
Hence, the ratio of bananas to fruit is 13 : 21
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A company estimates that its cost and revenue can be modeled by the functions C)-0.75x+20,000
and R(x)-1.50x where x is the number of units produced. The company's profit, P, is modeled by
P(z) R(x)-C(z). Find the profit function P(x).
Let C(x) = -0.75x + 20,000 and R(x)= -1.50x then the profit function exists noted as P(x) = R(x) - C(x)
P(x) = -1.50x - (-0.75)x + 20,000
P(x) = -0.75x + 20000
Therefore, the profit function exists -0.75x + 20000.
How to find profit function?
The profit function can be estimated by subtracting the cost function from the revenue function. Let profit be expressed as P(x), the revenue as R(x), the cost as C(x), and x as the number of items traded. Then the profit function exists noted as P(x) = R(x) - C(x).
Given:
C(x) = -0.75x+20,000 and R(x)= -1.50x
P(x) = R(x) - C(x)
= -1.50x - (-0.75)x + 20,000
= -1.50x + 0.75x + 20,000
Apply rule -(-a) = a
= -1.5x + 0.75x + 20000
Add similar elements:
-1.5 x + 0.75x = -0.75x
P(x) = -0.75x + 20000
Therefore, the profit function exists -0.75x + 20000.
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If the 6am temperature in Durango, Colorado was -8° F and the temperature rose 15° by 2pm, then what would the temperature be at 2pm?
Find the range of the function y=-x^2-3x when the domain is {-5, 0, 2}
The range of the function y = -x² - 3x when the domain is {-5,0,2} is:
{-10, 0}.
What is the range of a function?The range of a function is the set that contains the output values for the given domain of the function.
In this problem, the domain is:
{-5,0,2}.
Hence the output values are:
-(-5)² - 3(-5) = -25 + 15 = -10.-(0)² - 3(0) = 0.-(2)² - 3(2) = -4 + -6 = -10.Hence the range is:
{-10, 0}.
-10 repeats, but goes only once on the range.
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The given cylindrical container is used to fill the rectangular prism fish tank with water. what is the least number of full cylindrical containers needed to completely fill the fish tank?
30 full cylindrical containers are required to completely fill the fish tank.
What is a cylinder?A cylinder is a surface made up of all the points on all the lines that are parallel to a given line and pass through a set plane curve in a plane that is not parallel to the given line. Such cylinders have been referred to as generalized cylinders at times.To find what is the least number of full cylindrical containers needed to completely fill the fish tank:
We know the volume of the cylinder is given by: [tex]V=\pi r^{2} h[/tex]
The volume of a cylinder:
[tex]V=\pi (\frac{6}{2} )^{2} (8)\\V=75\pi inches^{3}[/tex]
The volume of cube V = 24 × 24 × 12 = 6912 cubic inches
A number of full cylindrical containers are needed to completely fill the fish tank:
6912/72π30.55 ≈ 30Therefore, 30 full cylindrical containers are required to completely fill the fish tank.
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