(x - 2(x + 7) = 0 pls help

The cost, in dollars, of producing x belts is given by Upper C (x )equals 970 plus 12 x minus 0.076 x squared. The revenue, i

umka21 [38]

Answer:

$68.44 for each additional belt

Step-by-step explanation:

The cost and revenue functions are:

$C(x) = 970+12x - 0.076x^2\\R(x) =43x^{\frac{3}{4}}$

The profit function, P(x), is given by subtracting the cost function from the revenue function.

$P(x) = R(x) - C(x)\\P(x)=43x^{\frac{3}{4}}+0.076x^2-12x-970\\$

The derivate of the profit function gives us the rate at which profit changes:

$\frac{dP(x)}{dx} =P'(x)=32.25x^{\frac{-1}{4}}+0.152x-12\\$

For x = 484, the rate of change is:

$P'(484)=32.25*484^{\frac{-1}{4}}+0.152*484-12\\P'(484) = \$68.44/belt$

Profit is increasing by $68.44 for each additional belt

3 0

3 years ago

A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28,000 cubic feet. Three differ

pickupchik [31]

Answer:

We have 4 solutions:

No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks
2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks
6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks

Step-by-step explanation:

Let the number of 10-foot truck with a capacity of 350 cubic feet purchased=a

Let the number of 14-foot truck with a capacity of 700 cubic feet purchased=b

Let the number of 24-foot truck with a capacity of 1,400 cubic feet purchased=c

The company wants to purchase 25 trucks, therefore.

a+b+c=25

Furthermore, the combined capacity of the trucks is 28,000 cubic feet.

350a+700b+1400c=28000

Since the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem. The solution is most easily found using an augmented matrix.

The augmented matrix is presented below:

$\left[\begin{array}{ccc|c}1&1&1&25\\350&700&1400&28000\end{array}\right]$

Using the calculator, the reduced row echelon form is:

$\left[\begin{array}{ccc|c}1&0&-2&-30\\0&1&3&55\end{array}\right]$

where

a- 2c=-30 means a =2c-30

b+3c=55 means b= 55-3c

We alter the value of c as long as neither a nor b becomes negative. Suitable values for c are 15, 16, 17, and 18:

$\left|\begin{array}{|c||c||c|}a=2c-30&b=55-3c&c\\0&10&15\\2&7&16\\4&4&17\\6&1&18\end{array}\right|$

We can easily verify that, for each solution, the number of trucks adds up to 25 and the fleet capacity is 28,000 cubic feet.

We therefore have 4 solutions:

No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks
2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks
6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks

4 0

3 years ago

What's the formula length and area with work plz!

dem82 [27]

You would have to put them into different shapes and the formula for the squares is sides^2 and the formula for the triangles is 1/2(b*h), eventually you will add the numbers together

5 0

3 years ago

Read 2 more answers

A deep-sea exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is 200 feet below sea level. How de

VMariaS [17]

It is 20 each because it says

5 0

2 years ago

1+2-3+4+5-6+7+8-9...+97+98-99

zaharov [31]

Answer:

1584

Step-by-step explanation:

The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.

__

<h3>series of partial sums</h3>

The partial sums, taken 3 terms at a time, are

1+2-3 = 0

4+5-6 = 3

7+8-9 = 6

...

97+98-99 = 96

So the original series is equivalent to ...

0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)

That is, the sum is 3 times the sum of the consecutive integers 1..32.

__

<h3>consecutive integers</h3>

The sum of integers 1..n is given by the equation ...

s(n) = n(n+1)/2

__

<h3>series sum</h3>

Using this to find the sum of our series, we find it to be ...

series sum = 3 × (32)(33)/2 = 1584

_____

<em>Alternate solution</em>

The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...

1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)

Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).

Computed that way, we find the sum to be ...

(99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584

3 0

2 years ago

(x - 2(x + 7) = 0 pls help​

(x - 2(x + 7) = 0 pls help