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3 years ago

Midway High School has 1500 students. The school district requires that there be 2 janitors for every 125 students.

Mathematics

2 answers:

Phantasy [73]3 years ago

7 0

Answer:

Step-by-step explanation:

VMariaS [17]3 years ago

6 0

Answer:

Step-by-step explanation:

1500 divided by 125 = 12

12 x 2 = 24

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Solve the given integral equation for LaTeX: y(t)y ( t ). LaTeX: y(t)+9\displaystyle{\int_{0}^{t}e^{9(t-v)}y(v)\, dv}=\sin(3t)y

choli [55]

Looks like the equation is

$y(t)+9\displaystyle\int_0^te^{9(t-v)}y(v)\,\mathrm dv=\sin(3t)$

Differentiating both sides yields the linear ODE,

$y'(t)+9e^{9(t-t)}y(t)=3\cos(3t)$

$y'(t)+9y(t)=3\cos(3t)$

Multiply both sides by the integrating factor $e^{9t}$ :

$e^{9t}y'(t)+9e^{9t}y(t)=3e^{9t}\cos(3t)$

$\left(e^{9t}y(t)\right)'=3e^{9t}\cos(3t)$

Integrate both sides, then solve for $y(t)$ :

$e^{9t}y(t)=\dfrac1{10}e^{9t}(\sin(3t)+3\cos(3t))+C$

$y(t)=\dfrac{\sin(3t)+3\cos(3t)}{10}+Ce^{-9t}$

The given answer choices all seem to be missing <em>C</em>, so I suspect you left out an initial condition. But we can find one; let $t=0$ , then the integral vanishes and we're left with $y(0)=0$ . So

$0=\dfrac{0+3}{10}+C\implies C=-\dfrac3{10}$

So the particular solution is

$y(t)=\dfrac{\sin(3t)+3\cos(3t)-3e^{-9t}}{10}$

6 0

3 years ago

Rewrite <br><img src="https://tex.z-dn.net/?f=%20%7Bcos%7D%5E%7B4%7D%20x" id="TexFormula1" title=" {cos}^{4} x" alt=" {cos}^{4}

erastovalidia [21]

All you need is the double angle identity:

$\cos^2x=\dfrac{1+\cos2x}2$

So we have

$\cos^4x=(\cos^2x)^2=\left(\dfrac{1+\cos2x}2\right)^2=\dfrac{1+2\cos2x+\cos^22x}4$

Apply the identity again to the squared term:

$\cos^4x=\dfrac{1+2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3+4\cos2x+\cos4x}8$

6 0

3 years ago

Help please and thank youuuuuuuuu

PilotLPTM [1.2K]

Answer:

Bc equals 17.

you must solve for BA and CA, because this is a isosceles triangle and isosceles have 2 equal sides.

BA = CA

then plug in what you find in for x

8 0

3 years ago

Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder o

lesantik [10]

180+x=450 idk if this is wrong

4 0

3 years ago

Read 2 more answers

I need help seeing what I did wrong

Makovka662 [10]

Answer: The two roots are x = 3/2 and x = -2

=========================================================

Explanation:

You have the right idea so far. But the two numbers should be 3 and -4 since

3*(-4) = -12
3+(-4) = -1

The -1 being the coefficient of the x term.

This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.

---------

Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.

If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2

Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x

So we have the factor -x-2 along the top

The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.

We have the factor 2x-3 along the left side.

---------

The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)

The last thing to do is set each factor equal to 0 and solve for x

2x-3 = 0 solves to x = 3/2 = 1.5
-x-2 = 0 solves to x = -2

The two roots are x = 3/2 and x = -2

8 0

3 years ago