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Vinvika [58]
3 years ago
6

Matinee movie tickets cost 5$ each for adults and 2$ each for kids. For one showing, 460 tickets where sold, and 1880$ was colle

cted. How many of each type were sold.
Mathematics
1 answer:
bekas [8.4K]3 years ago
3 0
320 adult tickets and 140 kids tickets 
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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si
Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

Area = 128

Let the dimension of the paper be x and y;

Such that:

Length = x

Width = y

So:

Area = x * y

Substitute 128 for Area

128 = x * y

Make x the subject

x = \frac{128}{y}

When 1 inch margin is at top and bottom

The length becomes:

Length = x + 1 + 1

Length = x + 2

When 2 inch margin is at both sides

The width becomes:

Width = y + 2 + 2

Width = y + 4

The New Area (A) is then calculated as:

A = (x + 2) * (y + 4)

Substitute \frac{128}{y} for x

A = (\frac{128}{y} + 2) * (y + 4)

Open Brackets

A = 128 + \frac{512}{y} + 2y + 8

Collect Like Terms

A = \frac{512}{y} + 2y + 8+128

A = \frac{512}{y} + 2y + 136

A= 512y^{-1} + 2y + 136

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

A' = -512y^{-2} + 2

Set

A' = 0

This gives:

0 = -512y^{-2} + 2

Collect Like Terms

512y^{-2} = 2

Multiply through by y^2

y^2 * 512y^{-2} = 2 * y^2

512 = 2y^2

Divide through by 2

256=y^2

Take square roots of both sides

\sqrt{256=y^2

16=y

y = 16

Recall that:

x = \frac{128}{y}

x = \frac{128}{16}

x = 8

Recall that the new dimensions are:

Length = x + 2

Width = y + 4

So:

Length = 8 + 2

Length = 10

Width = 16 + 4

Width = 20

To double-check;

Differentiate A'

A' = -512y^{-2} + 2

A" = -2 * -512y^{-3}

A" = 1024y^{-3}

A" = \frac{1024}{y^3}

The above value is:

A" = \frac{1024}{y^3} > 0

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0
2 years ago
jacob used 1/7 of a liter to fill 1/9 of the fush aquarium. how many liters if water are needed to fill the aquariam? please lea
Sveta_85 [38]

Answer:

1.2 liters

Step-by-step explanation:

7/7 of a liter is one liter. and you still are only at 7. you need to get to 9 you and 2 1/7 liters and that becomes 9/7 liters which = 1.2

7 0
3 years ago
The cost of 3 movie rentals and 7 boxes is 16:50.the cost of 5 movie rentals and 2 boxes of candy is 13 how much does 1 box of c
Zigmanuir [339]
One box of candy costs $1.50. A movie rental costs $2.
7 0
3 years ago
What is 21.2264 rounded to the nearest tenths
Marizza181 [45]

21.2264 is 21.2 rounded to the nearest tenths; the place after the decimal is there tenths place so in the hundreths place, the number 2 is less than 5 therefore rounding it to 2.

7 0
3 years ago
Read 2 more answers
I dont understand this question. Also if anyone is on geometry byu part two let me know and we can work together !
damaskus [11]

Answer:

Area of circle R = 75π un² or ≈235.5 un²

Step-by-step explanation:

The problem says that m∠TRS = 120º. The total number of degrees in a circle is 360º. 120º is a third of 360º. Therefore, we can prove that the shaded sector is a third of the circle.

The problem then says that the area of the shaded sector is 25π and we have to calculate the area of the entire circle. Since we already know that the shaded sector is a third of the circle, we can simply multiply 25π by 3 in order to calculate the area of t he entire circle.

25π × 3 = 75π.

Area of circle R = 75π un² or ≈235.5 un²

4 0
3 years ago
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