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1 year ago

NEED HELP FAST! 50 POINTS see the image below

Mathematics

1 answer:

ale4655 [162]1 year ago

4 0

Answer:

90 in²

Step-by-step explanation:

First,check the figure I provided .

Area of the figure = area1 + area2 + area3 + area4

= (3×2) + (7×7) + (7×2) + (7×6)÷2

= 6 + 49 + 14 + 21

= 90

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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

2 years ago

What is the value of x in 34 + 2x = 40

alekssr [168]

Hello from MrBillDoesMath!

Answer:

Discussion:

34 + 2x = 40 => subtract 34 from both sides

(34-34) + 2x = 40 - 34 => as (34-34) = 0 and 40-34 = 6

2x = 6 => divide both sides by 2

x = 6/2 = 3

Check the answer:

Does 34 + 2x = 40 if x = 3 ?

Does 34 + 2(3) = 40 ?

Does 34 + 6 = 40 ? YES! so the answer checks.

Thank you,

MrB

4 0

2 years ago

Read 2 more answers

If s(x) = 2 - x and t(x) = 3x, which value is equivalent to (s•f)(-7)?

erica [24]

Answer:

Step-by-step explanation:

t(-7)= 3(-7)= -21

s(-21)= 2-(-21)= 2 + 21= 23

4 0

5 months ago

2. A book with a green sticker costs $2 less than half the price of a

Damm [24]

For this case we can propose an equation that will allow us to find the price of one of the books knowing the price of the other.

x: Let the variable that represents the price of the book with a green sticker

y: Let the variable that represents the price of the book with a yellow sticker

According to the statement we have:

$x = \frac {y} {2} -2\\$

$y=2(x+2)$

Finally, we can substitute the price of one of the books and clear the value of the other as the case may be.

Answer:

$x = \frac {y} {2} -2$

8 0

2 years ago

231 ( 40 + 15 ) = 231 x 40 + ------------ x -----------<br><br> which property is this

a_sh-v [17]

Answer:

12705

Step-by-step explanation:

The problem could be solved in two different methods:

231×(55)=12705

231×40+231×15=9240+3465=12705

6 0

1 year ago