Mathematics, 19.12.2019 21:31 blachaze8729

Arectangle has one of its sides on the x-axis and corners of the opposite side on the piece of the parabola y = 12 − x 2 above the x-axis. (a) (6 points) let (x, 0) be the coordinates of the lower right vertex of the rectangle. find an expression a(x) for the area of the rectangle.

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Answer from: Kitkatuu

A(x) = 24x - 2x^3

Step-by-step explanation:

first we need to visualize what the question is trying to represent

A rectangle with one of its sides on the x-axisThe corners of the opposite two sides of the rectangle intersect with a parabolathe equation of the parabola is y = 12 - x^2

the equation of the parabola can also be written as

y = -x^2 + 12 this shows that the parabola has a $\cap$ shape and the turning point (peak) lies at the y-axis at y = 12. The parabola is symmetric along the y-axis!

right corner of the lower side of the rectangle has the coordinates (x,0)

we can also say that the coordinates of the lower left side are (-x,0). This is because the parabola is symmetric along the y-axis.

Solution:

We have enough information to express the sides lengths of the rectangle:

1) Lower side, (L)

We'll name the lower side 'L' and since this is a rectangle, this side length is the same as the upper side.

The lower side coordinates are (-x,0) and (x,0). Hence the side length is the difference of the two coordinates.

L = x-(-x)

L = 2x

2) The Left and Right side have the same height (H)

since the the lower side is on the x-axis (y=0), the only side moving is the upper one, i.e the coordinates of the upper corners are (0,y) where y = 12- x^2 . The side length of either the left or right sides is

H = y

H = 12 - x^2

The Area of the rectangle is:

$Area\,\,= L \times H$

$Area\,\,= 2x(12 - x^2)$

$Area\,\,= 24x-2x^3$

Answer from: Quest

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!

Answer from: Quest

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

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