Ask question

Ask question

All categories

3 years ago

8

a flower garden is 4 feet longer than its width. write a polynominal that represents the area of the garden

1 answer:

LenaWriter [7]3 years ago

3 0

L = W+4
A = L x W
A = w + 4 x w
A = w² +4w

You might be interested in

Round 12.034 to the nearest tenth

vovangra [49]

The answer is 12. Thanks (;

5 0

3 years ago

Read 2 more answers

The profit per acre from a grove of orange trees is given by x(190 − x) dollars, where x is the number of orange trees per acre.

nasty-shy [4]

Answer:

$P(x) = 190 x -x^2$

In order to maximize the last equation we can derivate the function in term of x and we got:

$\frac{dP}{dx} = 190 -2x$

And setting this derivate equal to 0 we got:

$\frac{dP}{dx} = 190 -2x=0$

And solving for x we got:

$x = 95$

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

$P(x=95)= 95(190-95)= 95*95 = 9025$

Step-by-step explanation:

For this case we have the following function for the profit:

$P(x) = x(190-x)$

And we can rewrite this expression like this:

$P(x) = 190 x -x^2$

In order to maximize the last equation we can derivate the function in term of x and we got:

$\frac{dP}{dx} = 190 -2x$

And setting this derivate equal to 0 we got:

$\frac{dP}{dx} = 190 -2x=0$

And solving for x we got:

$x = 95$

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

$P(x=95)= 95(190-95)= 95*95 = 9025$

7 0

3 years ago

Read 2 more answers

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

Write 45/30 in simplest form

RideAnS [48]

Answer:

1 1/2

Step-by-step explanation:

SO first convert into mixed

1 15/30

Now simplify

1 1/2

IF YOU DONT WANT MIX AND LEAVE AS IMPROPER

3/2

7 0

3 years ago

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage r

Whitepunk [10]

Answer:

0.32 decay

Step-by-step explanation:

3 0

3 years ago