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2 years ago

Use the distributive property to remove the parentheses. -5(-6w+3v-5)

Mathematics

1 answer:

adelina 88 [10]2 years ago

6 0

Answer:

$30w - 15v + 25$

Step-by-step explanation:

Multiply -5 by each term inside the parentheses.

$-5(-6w+3v-5) =$

$= -5 \times (-6w) + (-5) \times 3v + (-5) \times (-5)$

$= 30w - 15v + 25$

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A credit card company offers a cash back program on transactions. For every transaction over $100 the customer gets $3 back. F

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2 years ago

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3 years ago

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15. If x=a Sin2t (I+Cos2t) and y=b Cos 2t (1-Cos2t) then find dy/dx at =22/7*4

Sav [38]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}$

It looks like we're given

$\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}$

where a and b are presumably constant.

Recall that

$\cos^2t=\dfrac{1+\cos(2t)}2$

$\sin^2t=\dfrac{1-\cos(2t)}2$

so that

$\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}$

Then we have

$\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t$

$\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}$

$\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}$

where the last reduction follows from dividing through everything by $\cos(2t)\cos^2t$ and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

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3 years ago

Solve the equation using square roots. (X+3)^2=0

Vilka [71]

Answer:

x=3

Step-by-step explanation:

(x−3)^2=0

Set the x−3 equal to 0.

x−3=0

Add 3 to both sides of the equation.

x=3

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2 years ago

A new car is purchased for 17000 dollars. The value of the car depreciates at 12.25% per year. What will the value of the car be

Scilla [17]

Answer:

$P(t=14) = 17000 (1-0.1225)^{14}= 2728.404$

Step-by-step explanation:

for this case we have the following model for the cost of the car:

$P(t) = P_o (1-r)^t$

Where $P_o$ is the initial amount on this case 17000, t the amount of years after the initial year and r the depreciation rate on this case:

$r= \frac{12.25}{100}=0.1225$

And for t =14 we can replace into the equation and we got:

$P(t=14) = 17000 (1-0.1225)^{14}= 2728.404$

5 0

2 years ago