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3 years ago

What is the volume of a sphere with a diameter of 4 meters? (Use 3.14 for π.)

Mathematics

1 answer:

mixer [17]3 years ago

6 0

Answer:

volume of the sphere = $33.493m^3$

Step-by-step explanation:

Given:

$Diameter= 4 m$ , $Radius = 4/2 =2 m$

Volume of a sphere= $\frac{4}{3} *\pi* r^3$

= $\frac{4}{3} *\pi* 2*2*2$ : $\pi =3.14$

= $\frac{4}{3} *3.14*2*2*2$

= $1.33*3.14*2*2*2$

= $33.493m^3$

The volume of the sphere with the radius of 2 m is $33.493m^3$

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3 years ago

A square park with sides 15 meters in length has a diagonal walkway as shown.

Alexxandr [17]

Answer:

The approximate length of the diagonal walkway is 21.21 meters

Step-by-step explanation:

we know that

Applying the Pythagorean Theorem in the square park, find out the the approximate length of the diagonal walkway

$c^2=a^2+b^2$

where

c is the diagonal of the square

a and b are the length sides of the square

we have

$a=15\ m\\b=15\ m$

substitute

$c^2=15^2+15^2\\c^2=450\\c=21.21\ m$

therefore

The approximate length of the diagonal walkway is 21.21 meters

5 0

3 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

What interest is needed to earn $137.50 on a deposit of $500 for five years if it earns simple interest?

sineoko [7]

Answer:

5.5%

Step-by-step explanation:

Given data

Simple interest = $137.50

Principal= $500

time = 5 years

We want to find the rate R

Simple interest= PRT/100

137.50 = 500*R*5/100

137.50=2500R/100

cross multiply

137.5*100= 2500R

13750= 2500R

divide both sides by 2500

R= 13750/2500

R=5.5%

Hence the rate is 5.5%

4 0

3 years ago

SUSTITUTION 3X-6Y=2<br> 5X+4Y=1

Montano1993 [528]

3x - 6y = 2
5x + 4y = 1

(-1/3, -1/6)

~Hope I helped!~

6 0

3 years ago