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2 years ago

5

Mason randomly chooses a card from a standard deck or cards What is the probability that it is a face card given that it is a he

arts

1 answer:

joja [24]2 years ago

5 0

25 percent i think or

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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,

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

or

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

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

2 years ago

Mr. Layte needs a mortgage to buy his first house. Which describes how this will affect Mr. Layte's financial situation?

Norma-Jean [14]

9514 1404 393

Answer:

A, D

Step-by-step explanation:

Assuming that Mr. Layte must pay for his mortgage from his (otherwise) disposable income, that disposable income will decrease. As in choice A, there will likely be additional ownership expenses besides the mortgage. Under our assumption, Mr. Layte's disposable income does not remain the same or increase.

The appropriate choices are A and D: the amount of money he has to spend on things will decrease ...

8 0

3 years ago

Place the quadratic y=2x^2+24x+79 into vertex form by using the method of completing the square and then state the coordinates o

katrin2010 [14]

Answer:

$y=2(x+6)^2+7$

$(-6,7)$

Step-by-step explanation:

$y=2x^2+24x+79$

Completing the square is a process of converting a quadratic equation in standard form into vertex form.

The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.

$y=(2x^2+24x)+79$

Factor out the coefficient of the quadratic term,

$y=2(x^2+12x)+79$

Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.

$y=2(x^2+12x+36-36)+79$

Simplify,

$y=2(x^2+12x+36)+79+(2)(-36)$

$y=2(x+6)^2+79-72$

$y=2(x+6)^2+7$

The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.

$(-6,7)$

7 0

2 years ago

Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the $48 among the j of them. A

saw5 [17]

What were your given answer choices

8 0

3 years ago

This is due tomorrow and I k ow for a fact these are both wrong, someone help

Naya [18.7K]

#1 answer is D and #2 answer is D also

6 0

2 years ago

Read 2 more answers