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steposvetlana [31]
2 years ago
12

The base of a rectangle lies on the x-axis, while the upper two vertices lie on the parabola y = 13 − x2. Suppose that the coord

inates of the upper right vertex of the rectangle are (x, y). Express the area of the rectangle as a function of x.
Mathematics
1 answer:
Misha Larkins [42]2 years ago
5 0

Answer:

Area of Rectangle = 26x - 2x^3

Step-by-step explanation:

Rectangle two vertices lie on x axis ; two vertices lie on parabola y = 13 - x^2.

Supposing coordinates of upper right vertex of rectangle are P = x , y

Due to parabola symmetry, width of rectangle is twice the distance  horizontal (X) axis distance between Y axis & point P.

Width of rectangle = 2x

Length of rectangle = y  ; y = 13 - x^2

Area of Rectangle = Length x Width

= 2x (y)

= 2x (13 - x^2)

= 26x - 2x^3

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Answer:

3 movies

Step-by-step explanation:

55$-40.99$= 14.01$ left to spend on movies

$14.01/$3.95=3.54

Which means you can buy 3 movies.

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3 years ago
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Westkost [7]

Answer:

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7 0
2 years ago
Malika bought 7 new pairs of shoes. Each pair of shoes cost the same amount and was discounted by $21.75.
ikadub [295]

Multiply the amount of the discount by pairs of shoes:

21.75 x 7 = 152.25

Add that to the total she spent:

152.25 + 654.50 = 806.75

Divide the total by pairs of shoes:

806.75/7 = $115.25

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3 0
2 years ago
Area=<br> Help me please!! Thanks :)
Savatey [412]

Answer:

80π

Step-by-step explanation:

Circle O with radius IO:

large radius = IO = 12 = R

Circle O with diameter JK

IJ = JK = KL = 2 × IO = 24

IJ = JK = KL = 24/3 = 8

small radius = 8/2 = 4 = r

The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.

That is the same as

1 semicircle of radius 12 plus 1 semicircle of radius 4

A = πR²/2 + πr²/2

A = π(12² + 4²)/2

A = 160π/2

A = 80π

8 0
2 years ago
A teacher has two students, one two times as old as the other. The teacher is five times as old as the older student, and in 5 y
kramer
Let's call the younger student's age A and the older student's age B. The teacher's age will be T.

B = 2A
T = 5B
T+5 = 5(A+5)

Simplify the last equation.

T+5 = 5A+25
T = 5A+20

Now we have two equations solved for T, so we can set them equal to each other.

5B = 5A + 20

We can plug 2A in for B

5(2A) = 5A + 20

10A = 5A + 20

5A = 20

A = 4

To find T, we plug 4 in for A in T = 5A + 20

T = 5(4) + 20

T = 40

The answer is 40 years old.


6 0
3 years ago
Read 2 more answers
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