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3 years ago

You read 165 pages in 3 hours find the unit rate

Mathematics

1 answer:

Aliun [14]3 years ago

8 0

Answer:

55 pages per hour

Step-by-step explanation:

You divide 165 by 3 = 55

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The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6

Arlecino [84]

Answer:

$\approx \bold{6544\ in^3/sec}$

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

$\dfrac{dr}{dt} = +7\ in/sec$

(This is increasing rate so positive)

Rate of change of height of cylinder:

$\dfrac{dh}{dt} = -6\ in/sec$

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

$V = \pi r^2h$

Differentiating it w.r.to 't':

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)$

Let us have a look at the formula:

$1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))$

$3.\ \dfrac{dx^n}{dx} = nx^{n-1}$

Applying the two formula for the above differentiation:

$\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}$

Now, putting the values:

$\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}$

So, the answer is: $\approx \bold{6544\ in^3/sec}$

3 0

3 years ago

Unit rate for 3 ounces for every 3/4 cup

Vanyuwa [196]

Answer:

4 ounces per cup

Step-by-step explanation:

To find the unit rate, we take the ounces and divide by cups. We want a 1 in the denominator

3 ounces÷3/4 cup

Copy dot flip

3 ounces * 4/3 per cup

4 ounces per cup

7 0

3 years ago

Lauren coordinates a construction projects for a cement company. A government project requires constructing two rectangular conc

I am Lyosha [343]

Answer:

Step-by-step explanation:

Total concrete for slabs

24 * 24 * 1 = 576 ft³

Additional 20 %

By rule of three

if 576 ⇒ 100

x?? ⇒ 20 x = 115,2

And there are 2 slabs, the total volume of concrete is:

Q(t) = 2* (576 + 115,2 ) Q(t) = 1382,4 ft³ (1)

If the truck can carry a maximum of 8 yd³, as 1 ft³ = 0,037 yd³

then a truck can carry a maximum of

8/ 0,037 = 216,21 ft³

Now the total quantity is 1382,4

Then

1382,4/216,21 = 6,39

And as nobody can send a fraction of a truck , the fewest number of truck is 7

5 0

4 years ago

Find measure of angle labeled X

trasher [3.6K]

Is it number15?
then it is
3x = 180
x = 60
x will be 60

7 0

3 years ago

Read 2 more answers

The hover dam contains 3 1/2 millon cubic yards of concrete.The grand coulee dam contains 2 1/2 times as much. How much concrete

Margarita [4]

grand coulee dam (g) contains 2.5 times as much concrete as the hover dam (h)

Therefore,

g = 2.5 * h

h = 3.5 million

g = 2.5 * 3.5

g = 8.75 million yards of concrete

8 0

4 years ago