The sum of 15 and r.
Sum is the term used in verbal addition problems.
This is an expression therefore, you do not state what it equals. We no this because there is no equals sign.

5 0

3 years ago

If a spring is oscillating (moving) according to the velocity equation v(t) = 2sin(t) (in ft/s), then what is its displacement o

Feliz [49]

ANSWER

4 ft

EXPLANATION

The velocity equation of the oscillating spring is given by the function.

$v(t)=2 \sin(t) \: \: {ms}^{ - 1}$

To find the displacement function, we need to to Integrate the velocity function.

$s(t) = \int \: 2 \sin(t) dt$

$s(t) = - 2 \cos(t) + k$

At time t=0, there was no displacement.

This implies that,

$s(0) = 0$

$0= - 2 \cos(0) + k$

$0= - 2 + k$

$k = 2$

The displacement function then becomes,

$s(t) = - 2 \cos(t) + 2$

To find the displacement over the first π seconds, we put

$t = \pi$

into the equation for the displacement to get,

$s(\pi) = - 2 \cos(\pi) + 2$

$s(\pi) = - 2 ( - 1) + 2$

$s(\pi) = 2 + 2 =4 ft$

7 0

3 years ago

The volume of a cylinder is 12,566.4 cm3. The height of the cylinder is 8 cm.

scoundrel [369]

Using the formulas here: http://www.1728.org/diamform.htm

A) Volume = π • r² • height
radius^2 = Volume / (PI*height)
radius^2 = 12,566.4 / (PI * 8)
radius^2 = 500.0011692175 
radius = 22.3607059195 
radius (rounded) = 22.4 cm

B) Area of base = PI * radius^2
Area of base = 3.14159265 * 500
Area of base = 1,570.7963267949 
Area of base (rounded) = 1,570.8 square cm

C) lateral area = 2 • π • r • height 
lateral area = 2 • π • 22.4 * 8
lateral area = 1,125.9468070466 
lateral area = 1,125.9 square cm

D) Total Surface Area = (2 • π • r²) + (2 • π • r • height)
Total Surface Area = 2 * (top AND bottom area which is the Part B answer times 2) + (the lateral area which is the Part C answer)

Total Surface Area = ( 2 * 1,570.8 ) + (1,125.9)
Total Surface Area = 3,141.6 + 1,125.9
Total Surface Area = 4,267.5 square cm

3 0

3 years ago