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3 years ago

An item is regularly priced at

Mathematics

1 answer:

jekas [21]3 years ago

7 0

85% = 0.85

1-0.85 = 0.15

80 x 0.15 = 12

the price now is $12

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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

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

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

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

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

What is the quotient. Of 25)9250

saul85 [17]

Answer:

370

Step-by-step explanation:

Isolate the numbers so that you are only dividing sections at a time.

So 25 goes in to 92 three times. so we multiply 25 by three and subtract that from 92. Put the three at the top and repeat throughout.

92-75=17

Bring the next number down and repeat.

6 0

3 years ago

Read 2 more answers

What is the product?<br> 3x [-6 -11<br> 1-14 -9]

Alla [95]

Answer:

9.99

Step-by-step explanation:

8 0

3 years ago

C=2(3.14)r; c=14(3.14) solve for r

tekilochka [14]

Answer:

c=2(3.14)r

given c=14(3.14), then r

make r the subject formula and substitute given c=14(3.14)

r=c/2(3.14)

r=14(3.14)/2(3.14)

r=7

Step-by-step explanation:

7 0

3 years ago

Stephanie is a very good soccer player. She can kick a soccer ball with an initial velocity of 21.3 m/sec. The function that rep

algol [13]

If the ball hit the ground it means that its height is equal to 0. In order to find the time after the ball <span>will hit the ground, we need to find the solution of the equation h(x)=0 which is different to 0.

-4.9x^2+21.3x=0
x(-4.9x+21.3)=0
-4.9x+21.3=0
x=21.3/4.9 = 4.3469 seconds</span>

4 0

3 years ago