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4 years ago

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A total of 720 people attended the school-basketball game. adult tickets cost $2.50 each and student tickets cost $1.50 each. if

$1220 worth of tickets were sold, how many students and how many adults attended?

1 answer:

Nesterboy [21]4 years ago

5 0

They were sold 123456 sold

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Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

DiKsa [7]

Answer:

C

Step-by-step explanation:

We must compute the derivatives and check if the equation is satisfied.

A. $y'=(3\sin x)'=3\cos x$ . Differentiate again to get $y''=(3\cos x)'=-3\sin x$ , then $y''+y=-3\sin x+3\sin x=0\neq 3\sin x$ so this choice of y doesn't solve the equation.

B. $y'=3\sin x+3x\cos x-5\cosx +5x\sin x=(5x+3)\sin x+(3x-5)\cos x$ and $y''=5\sin x+(5x+3)\cos x+3\cos x-(3x-5)\sin x=(10-3x)\sin x+(5x+6)\cos x$ , then $y''+y=10\sin x+6\cos x\neq 3\sin x$ so y is not a solution

C. $y'=\frac{-3}{2}\cos x+\frac{3}{2}x\sin x$ hence $y''=\frac{3}{2}\sin x+\frac{3}{2}\sin x+\frac{3}{2}x\cos x=3\sin x+\frac{3}{2}x\cos x$ . Then $y''+y=3\sin x+\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\sin x$ so y is a solution.

D. $y'=-3\sin x$ and $y''=-3\cos x$ , then $y''+y=0$ thus y isn't a solution

E. $y'=\frac{3}{2}\sin x+\frac{3}{2}x\cos x$ hence $y''=\frac{3}{2}\cos x+\frac{3}{2}\cos x-\frac{3}{2}x\sin x=3\cos x-\frac{3}{2}x\cos x$ . Then $y''+y=3\cos x-\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\cos x\neq 3\sin x$ then y is not a solution.

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3 years ago

a rectangular park has an area of 6 square miles. the width of the property is 3/8 the length of the property. what is the width

xz_007 [3.2K]

L = the length of the property
W = the width of the property
Area
L * W = 6
but it says," The width of the property is of 3/8 the length he property."
therefore
W = 3%2F8L
or
W = .375L

In the area equation, replace W with .375L
L * .375L = 6
.375L^2 = 6
L^2 = 6%2F.375
L^2 = 16
L = sqrt%2816%29
L = 4 mi is the length
then
.375(4) = 1.5 mi is the width

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the largest rectangular area is actually a square.

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