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2 years ago

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Antoine has a solid, spherical ball of clay with a radius of 5 cm. If he shapes it into a solid, cone–shaped figure with a radiu

s of 2 cm, what will the height of the cone be?

1 answer:

weqwewe [10]2 years ago

3 0

Answer:

Step-by-step explanation:

We'll call height h.

The equations of a cone and sphere are:

Cones: 1/3 * base area * h

Spheres: 4/3 π * r³

The base area of a cone would be the area of a circle equation:

π * r² = π * 2² = 4π.

Because you're converting from sphere to cone, you would set their equations equal to each other.

1/3 * 4π * h = 4/3 π * 5³

Next, isolate h.

h = (4/3 π * 5³)/(1/3 * 4π)

h = 125

Hope this helps!

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I WILL AWARD BRAINLIEST!! PLEASE HELP!!

bezimeni [28]

Answer:

Part 1) $A(57/7,9),B(4,16/5), m=7/5$

Part 2) $A(-7,6),B(9,-6/7), m=-3/7$

Part 3) $A(80/3,9),B(5,2.5), m=0.3$

Part 4) $A(-10/63,1/3),B(2/3,-22/90), m=-0.7$

Part 5) $A(-1/5,7),B(8,48), m=5$

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

Part 1) we have

$7x-5y=12$

step 1

Find the slope

$7x-5y=12$

isolate the variable y

$y=(7/5)x-(12/5)$

so

the slope is $m=(7/5)$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$9=(7/5)x-(12/5)$

$(7/5)x=9+(12/5)$

$(7/5)x=(57/5)$

$x=(57/7)$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=(7/5)(4)-(12/5)$

$y=(28/5)-(12/5)$

$y=(16/5)$

Part 2) we have

$y=-(3/7)x+3$

step 1

Find the slope

the slope is $m=-(3/7)$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$6=-(3/7)x+3$

$(3/7)x=3-6$

$(3/7)x=-3$

$x=-7$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=-(3/7)(9)+3$

$y=-(27/7)+3$

$y=-(6/7)$

Part 3) we have

$y=0.3x+1$

step 1

Find the slope

the slope is $m=0.3$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$9=0.3x+1$

$0.3x=9-1$

$0.3x=8$

$x=80/3$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=0.3(5)+1$

$y=2.5$

Part 4) we have

$6.3x+9y=2$

step 1

Find the slope

$6.3x+9y=2$

isolate the variable y

$y=-(0.7)x+(2/9)$

so

the slope is $m=-0.7$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$(1/3)=-(0.7)x+(2/9)$

$(0.7)x=(2/9)-(1/3)$

$(0.7)x=(2/9)-(1/3)$

$(0.7)x=-(1/9)$

$x=-(10/63)$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=-(0.7)(2/3)+(2/9)$

$y=-(14/30)+(2/9)$

$y=-(22/90)$

Part 5) we have

$y-5x=8$

step 1

Find the slope

$y-5x=8$ -------> $y=5x+8$

the slope is $m=5$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$7=5x+8$

$5x=7-8$

$x=-1/5$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=5(8)+8$

$y=48$

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2 years ago

Diane has a hospital appointment. When she arrives at the hospital, the car park is nearly full. There are a total of 534 car pa

nevsk [136]

Hiii

all you do is subtract...
534-476=58

58 spots are left.

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2 years ago

The Office of Student Services at UNC would like to estimate the proportion of UNC's 34,000 students who are foreign students. I

Pachacha [2.7K]

Answer:

Mean is 3.05

Standard deviation is 1.69.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are foreign, or they are not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The probability of x sucesses on n repeated trials, with p probability.

In this problem, we have a sample of 50 students, so $n = 50$ . The proportion of all UNC students that are foreign students is 0.061, so $p = 0.061$ .

The mean is given by the following formula:

$E(X) = np = 50*0.061 = 3.05$

The standard deviation is given by the following formula:

$\sigma = \sqrt{n*p*(1-p)} = \sqrt{50*0.061*(1-0.061))} = 1.69$

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1 year ago

Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.

lawyer [7]

Simplifying the given expressions we proceed as follows:
(5sqrt3)^x
=5^x*(3^1/2)^x
=5^x*3^x/2
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(1/2)^(x-3)
=1/2^(x-3)
=2^-(3-x)
=2^u
where u=-(3-x)

9/3sqrt(3)
=3/(3)^(1/2)
=3(3)^(-1/2)

16/(3sqrt (2^x))
=1/3*(2^4*2^(-x/2))
=1/3*2^(4-x/2)
=1/3*2^u
where:
u=4-x/2

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2 years ago

Read 2 more answers

Julie is a math tutor. She charges each student $210 for the first 7 hours of tutoring and $20 for each additional hour. When th

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I'm sorry I do not know how to set up the equation but I do know it's 17 hours because 7(30)= 210 and 10(20)= 200 and 200+210=410

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2 years ago