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andriy [413]
2 years ago
7

Help me please I beg

Mathematics
1 answer:
valentina_108 [34]2 years ago
8 0

Answer:

$8,500

Step-by-step explanation:

Interest = 5000 x 5 x 0.14

            = 1000 x 0.14 x 25

            = 140 x 25

            = 3500

5000 + 3500 = 8500

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A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3
zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

  • l represents the length.
  • w represents the width.
  • h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

h = 3/x²

For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

x³ = 30/24

x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

#SPJ1

5 0
2 years ago
Solve.
Furkat [3]

Answer:

-0.03

Step-by-step explanation:

-59x+3.2=5

-59x=5-3.2

-59x=1.8

x=1.8/-59

x=-0.03

3 0
2 years ago
Solve the following equations for x<br> x(14-x) = 33
Katarina [22]

ANSWER :

14x-x^2 = 33

Step-by-step explanation:

x(14-x) = 33

14x-(x)^2 = 33

7 0
2 years ago
Convert 29 inches to feet. Round answers to the nearest tenth
Bess [88]
29 ÷ 12 = 2.41667
Your answer is 2.4 feet
7 0
3 years ago
Use the following graph of the function f(x) = −3x4 − x3 + 3x2 + x + 3 to answer this question: graph of negative 3 x to the fou
Serggg [28]

Answer:

The average rate of change from x=0 to x=1 for f(x) is 0.

Step-by-step explanation:

We are given the function f(x)=-3x^{4}-x^{3}+3x^{2}+x+3.

Now, the rate average rate of change of a function from y=x_{1} to y=x_{2} is given by \frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}.

As, we need the rate of change from x = 0 to x = 1.

So, we will find the values of f(0) and f(1).

i.e. f(0)=-3\times0^{4}-0^{3}+3\times0^{2}+0+3 i.e. f(0)  = 3

and f(1)=-3\times1^{4}-1^{3}+3\times1^{2}+1+3 i.e. f(1)=-3-1+3+1+3 i.e. f(1) = 3

Thus, the rate of change from x=0 to x=1 is \frac{f(1)-f(0)}{1-0} i.e.  \frac{3-3}{1-0} i.e. 0

Hence, the average rate of change from x=0 to x=1 for f(x) is 0.

7 0
3 years ago
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