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Tju [1.3M]
3 years ago
13

The cost for a certain music plan is $9.99 per year plus $0.25 per song you download. If you paid $113.74 one year, determine th

e number of songs you downloaded
Mathematics
1 answer:
Oliga [24]3 years ago
7 0
 if you add 9.99 plus 0.25 you get 10.24     you dived 113,74 by 10.24
11.107421875 songs
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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
Write an equation of the circle with center (-3, 7) and radius 2.
jok3333 [9.3K]

Answer:

(x+3)^2 + (y-7)^2 = 2^2

Step-by-step explanation:

Follow the standard form of a circle, (x-h)^2 + (y-k)^2 = r^2, given that (-3,7) is (h,k) and 2 is r.

4 0
2 years ago
Find x. Give your answer in the
garri49 [273]

Answer:

x = 4

Step-by-step explanation:

sin 30 = x/8

0.5 = x/8

x = 4

7 0
3 years ago
jamal works in a city and sometimes takes a taxi to work. the taxicab charge $1.50 for the first 1/5 miles and $0.25 for each ad
Llana [10]
One and one-fifth mile
6 0
3 years ago
Two straight lines VZ and YW intersect at X
Alexeev081 [22]

Answer:

∠WVX = 35°

Step-by-step explanation:

Look at the rough draw.

As you can see,

VW ║ YZ

So ∠XWV is congruent to ∠XYZ through alternate interior angle.

We can solve ∠WVX by considering the two other angles, 88° and 57°.

Total angle of a triangle is 180°.

So,

? + 88 + 57 = 180

? + 145 = 180

? = 180 - 145

? = 35°

5 0
3 years ago
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