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3 years ago

7

Choose an inverse function and use SohCahToa to find angle A.

1 answer:

Sergeu [11.5K]3 years ago

6 0

Answer:

$m\angle A=53.13^o$

Step-by-step explanation:

we know that

In the right triangle of the figure

The cosine of angle A is equal to divide the adjacent side to angle A by the hypotenuse

so

$cos(A)=\frac{6}{10}$ ----> by CAH

Find the measure of the angle A

$m\angle A=cos^{-1}(\frac{6}{10})$

$m\angle A=53.13^o$

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Step-by-step explanation:

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3 years ago

Ann works at a store in the mall and earns a wage of 8 dollars an hour. She earns 10 dollars an hour is she works on the weekend

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Answer:

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3 years ago

Consider the initial value problem y′+5y=⎧⎩⎨⎪⎪0110 if 0≤t<3 if 3≤t<5 if 5≤t<[infinity],y(0)=4. y′+5y={0 if 0≤t<311 i

rosijanka [135]

It looks like the ODE is

$y'+5y=\begin{cases}0&\text{for }0\le t$

with the initial condition of $y(0)=4$ .

Rewrite the right side in terms of the unit step function,

$u(t-c)=\begin{cases}1&\text{for }t\ge c\\0&\text{for }t$

In this case, we have

$\begin{cases}0&\text{for }0\le t$

The Laplace transform of the step function is easy to compute:

$\displaystyle\int_0^\infty u(t-c)e^{-st}\,\mathrm dt=\int_c^\infty e^{-st}\,\mathrm dt=\frac{e^{-cs}}s$

So, taking the Laplace transform of both sides of the ODE, we get

$sY(s)-y(0)+5Y(s)=\dfrac{e^{-3s}-e^{-5s}}s$

Solve for $Y(s)$ :

$(s+5)Y(s)-4=\dfrac{e^{-3s}-e^{-5s}}s\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}{s(s+5)}+\dfrac4{s+5}$

We can split the first term into partial fractions:

$\dfrac1{s(s+5)}=\dfrac as+\dfrac b{s+5}\implies1=a(s+5)+bs$

If $s=0$ , then $1=5a\implies a=\frac15$ .

If $s=-5$ , then $1=-5b\implies b=-\frac15$ .

$\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}5\left(\frac1s-\frac1{s+5}\right)+\dfrac4{s+5}$

$\implies Y(s)=\dfrac15\left(\dfrac{e^{-3s}}s-\dfrac{e^{-3s}}{s+5}-\dfrac{e^{-5s}}s+\dfrac{e^{-5s}}{s+5}\right)+\dfrac4{s+5}$

Take the inverse transform of both sides, recalling that

$Y(s)=e^{-cs}F(s)\implies y(t)=u(t-c)f(t-c)$

where $F(s)$ is the Laplace transform of the function $f(t)$ . We have

$F(s)=\dfrac1s\implies f(t)=1$

$F(s)=\dfrac1{s+5}\implies f(t)=e^{-5t}$

We then end up with

$y(t)=\dfrac{u(t-3)(1-e^{-5t})-u(t-5)(1-e^{-5t})}5+5e^{-5t}$

3 0

3 years ago

Mrs. Maldonado has $3,000 she wants to invest for the next 4 years. Her credit union offers a 5.96% interest rate compounded yea

pishuonlain [190]

The answer is
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3 years ago

Nicolette needs 1/3 yard of fabric. Which fraction is equivalent to 1/3

Inessa05 [86]

<u>Answer:</u>

The correct answer is 5/15

<u>Step-by-step explanation:</u>

The only number out of 1/9, 5/15, 2/3, and 15/5, 5/15 is the only equivalent number to 1/3.

Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

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3 years ago