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3 years ago

8

The engine life for a certain brand of lawn mower is modeled by the function f(h) = 50 - 1 3 h where h represents hours used. Wh

at does the function mean?

1 answer:

Colt1911 [192]3 years ago

4 0

Answer: C. Engine life decreases steady with time.

Step-by-step explanation:

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Josh is hiking Glacier National Park. He has now hiked a total of 17 km and is 2 km short of being 1/2 half of the way done his

katovenus [111]

What is the question? If it is how long is the total hike, then 17+2=19 (that’s half way).

19x2 =38. 38k is the total round trip of the hike.

4 0

4 years ago

Read 2 more answers

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago

6 gallons/minute is equal to how many qt an hour show work

amm1812

6x60=360. 4 quarts is equal to 1 gallon so multiply 360 by 4 and you’d get 1440. So the answer should be 1440.

7 0

3 years ago

A roofing job take 6 workers 8 hours to complete. If the number of workers is inversely proportional to the time a job takes to

Wewaii [24]

its a long time before finishing

7 0

3 years ago

Urgently needed<br> see image

Lorico [155]

y2-y1 =M(x2-x1)

Ok Sir, you gave points : (2,1) and (3,4)

4-1/3-2 = 3

Ok we know our slope is 3, now pick any of the two points, and make an equation for this line, so lets go ahead and pick #1, (2,1)

Formula is same as before

y-1=3x-6

y=3x-5

I think its correct, pick as brainless sir, thanks.

7 0

3 years ago