Instructions: Find the measure of the indicated angle

What is the surface area of this composite figure?

faust18 [17]

Answer:

Step-by-step explanation:

$6\cdot6+5\cdot(6\cdot7)+6\cdot4+2\cdot(\frac12\cdot6\cdot4)=36+210+24+24=294\,cm^2$

4 0

3 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

3 years ago

Every seventh-grade student at Martin Middle School takes one world language class.

koban [17]

Answer:

s = 180

Step-by-step explanation:

s is the total number of seventh-grade students

1/10s take French which is 18

1/10s = 18

s = 18(10)

s = 180

6 0

2 years ago

How many 1-in. cubes can fit into a 2 by 4 by 2 in.<br>prism?

wel

Answer:

16

Step-by-step explanation:

The dimensions of the base of the prism are 4" by 2"; the height is 2".

Looking at the base, we see that (4)(2), or (8) 1" cubes would cover it exactly and wholly. We'd have a 3-dimensional prism with one layer of 1" cubes.

Now if we add a second layer right on top of the first layer, we'd have used (16) 1" cubes.

3 0

3 years ago

Read 2 more answers

Set up the formula to find the balance after 8 years for a total of $12,000 invested at an annual

Natasha2012 [34]

Answer:

A = 12000(1.0002466)²⁹²⁰

Step-by-step explanation:

The formula for the amount after compound interest is: $A = P(1 + i)^{n}$

"A" is the amount, or balance.

"P" is the principal, or starting amount/investment.

"i" is the interest rate for each compounding period.

"n" is the number of compounding periods.

The interest rate each compounding period, "i", is calculated with i=r/c

"r" is the annual interest rate in decimal form.

"c" is the compounding frequency. (If compounded annually, c=1. If monthly, c=12.)

The number of compounding periods, "n", is calculated with n=tc.

"t" is the time in years.

"c" is the compounding frequency.

In this problem:

t = 8

P = 12,000

r = 9%, or r = 0.09 for decimal form.

c = 365

Calculate "i" and "n".

i = r/c

i = 0.09/365

i = 0.00024657534

i ≈ 0.0002466

n = tc

n = 8(365)

n = 2920

Substitute these back into the formula:

A = P(1 + i)ⁿ

A = 12000(1+0.0002466)²⁹²⁰

A = 12000(1.0002466)²⁹²⁰

7 0

3 years ago