Josh practices free throws during basketball practice on Monday and Tuesday. On Monday, he attempts 15 free throws and 6 basketb

Answer:

Step-by-step explanation:

a. Create a direction field for the specified differential equation

b. By observing the direction field, comment on the behavior of the solutions as t becomes large.

The solutions seem to oscillate

All solutions appear to approach the function y0(t)=4

All solutions seem to converge to the function y0(t)=0

All solutions appear to have negative slopes eventually and thus decrease indefinitely

All solutions seem to have positive slopes eventually and therefore increase without limit

C

As t approaches infinity

All solutions seem to exhibit positive slopes eventually and thus decrease indefinitely

The solutions seem to gradually approach the function y0(t)=0

All solutions appear to eventually have negative slopes leading to decrease without bounds

All solutions seem to converge to the function y0(t)=4

The results are oscillatory

Answer:

40 * x - 600 = 0

Step-by-step explanation:

Initially, identify the variable (x) in the equation, representing the number of days it takes Leilah to review her flashcards. To study 600 out of her 2400 cards, having gone through 1800 already, we arrive at:

2400 - 1800 = 40 * x

rearranging leads to

40 * x - 600 = 0

This equation describes the situation above

Answer:

Step-by-step explanation:

Refer to the attached digram.

The track's perimeter consists of the rectangle's perimeter plus the perimeters of the two semicircles.

The perimeter of a rectangle can be expressed as 2(x+r) where:

x is the length

2r represents the rectangle's width, equivalent to the semicircle's diameter.

The perimeter of one semicircle is calculated as 2πr/2, simplifying to πr.

Thus, the total perimeter contributed by the two semicircles is 2πr.

Therefore, the full track perimeter is expressed as 2(x+2r) + 2πr

where r indicates the semicircle's radius.

Expanding this gives us

Perimeter of the track = 2x + 4r + 2πr

which can also be represented as Perimeter of the track = 2(x + 2r + πr)

b) Given P = 2(x + 2r + πr), we need to rearrange the equation to isolate x.

P = 2x + 4r + 2πr

By subtracting 4r and 2πr from both sides, we get P - 4r - 2πr = 2x

Next, we divide each side by 2.

(P - 4r - 2πr) / 2 = 2x

Thus, x = (P - 4r - 2πr) / 2

c) Given

P = 600ft

r = 50ft

x = (600 - 4(50) - 2π(50)) / 2

x = (600 - 200 - 100(3.14)) / 2

x = 400 - 314 / 2

x = 86 / 2

x = 43ft

Therefore, rounding to the nearest foot, the value of x is 43ft

D(2, –4) transforms to D' = (-4, 2)

E(1, –1) changes to E' = (-1, 1)

F(5, 1) shifts to F' = (1, 5)

What is the mathematical representation for a reflection over the line y = x?

rx = y(x, y) = (y, x)