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Can you please help me with Questions #18-22 on this Math Worksheet

CaHeK987 [17]

21. 4x+4y
22. 16 girls

3 0

2 years ago

HELP!! joels apartment building is 42 ft tall and casts a shadow of 20ft. If Joel is 6 ft tall, how long is his shadow

zhenek [66]

Step-by-step explanation:

an object and its shadow create a right-angled triangle.

2 objects and their shadows create 2 similar right-angled triangles.

that means the angles are the same, and the side lengths of one triangle all correlate with the corresponding side lengths of the other triangle via the same factor.

so,

42 × f = 6

f = 6/42 = 1/7

the length of Joel's shadow is then

20 × f = 20 × 1/7 = 2.857142857... ft

5 0

1 year ago

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.

3 0

2 years ago

A group of students wanted to investigate the claim that the average number of text messages sent yesterday by

Likurg_2 [28]

First we need to write the null and alternate hypothesis for this case.

Let x be the average number of text message sent. Then

Null hypothesis: x = 100
Alternate hypothesis: x > 100

The p value is 0.0853

If p value > significance level, then the null hypothesis is not rejected. If p value < significance level, then the null hypothesis is rejected.

If significance level is 10%(0.10), the p value will be less than 0.10 and we reject the null hypothesis and CAN conclude that:
The mean number of text messages sent yesterday was greater than 100.

If significance level is 5%(0.05), the p value will be greater than 0.05 and we cannot reject the null hypothesis and CANNOT conclude that:
The mean number of text messages sent yesterday was greater than 100.

7 0

2 years ago

-6/7 × (-3/8) answer?/

Mumz [18]

Answer:

Step-by-step explanation:

0.32142857142

3 0

1 year ago

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