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Dahasolnce [82]
3 years ago
5

Duval County Landscaping uses two different sized trucks to deliver mulch. The first truck can transport x cubic yards of mulch,

and the second can transport y cubic yards of mulch. The first truck makes 12 trips to a job site, while the second makes 14 trips. Create an expression that represents the difference in the total number of cubic yards that the first truck delivers compared to the second.

Mathematics
2 answers:
Gre4nikov [31]3 years ago
8 0
For this case, the first thing we must do is define variables.
 We have then:
 x: number of cubic yards of mulch that first truck can transport
 y: number of cubic yards of mulch that second truck can transport
 Now we write the expression.
 The first truck makes 12 trips to a job site:
 12x

 The second makes 14 trips:
 14y

 The difference between the first truck and the second truck is:
 12x - 14y
 Answer:
 
An expression that represents the difference in the total number of cubic yards that the first truck delivers compared to the second is:
 
12x - 14y
gogolik [260]3 years ago
5 0
Uber simple. You're trying to find the difference in amount that truck one can carry compared to truck two. Truck two can make 14 trips and truck one can make twelve. To show the DIFFERENCE (Huge hint), you use the equation 12x-14y.
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Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter
Vaselesa [24]

We have been given a function f(x)=2x^3+3x^2-336x. We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

f'(x)=2(3)x^{2}+3(2)x^1-336

f'(x)=6x^{2}+6x-336

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f'(1)=(1+8)(1-7)=(9)(-6)=-54

Since f'(1), therefore, function is decreasing on interval (-8,7).

Let us check for the derivative at x=8.

f'(x)=(x+8)(x-7)

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(b) Since x=-8,7 are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

f(-8)=2(-8)^3+3(-8)^2-336(-8)

f(-8)=1856

f(7)=2(7)^3+3(7)^2-336(7)

f(7)=-1519

Therefore, (-8,1856) is a local maximum and (7,-1519) is a local minimum.

(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

f''(x)=6(2)x^{1}+6

f''(x)=12x+6

12x+6=0

12x=-6

\frac{12x}{12}=-\frac{6}{12}

x=-\frac{1}{2}

Therefore, x=-\frac{1}{2} is an inflection point of given function.

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3 years ago
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