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3 years ago

How to rearrange 3x+6y-1=0

1 answer:

6 0

3x+6y-1=0
All the letters and all the numbers should be on seperate sides so...
The -1 is added onto the zero like this:
3x+6y=0+1
3x+6y=1

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

Find the product 4×6×50 tell what strategy you used

Brut [27]

Answer:

1200

Step-by-step explanation:

4x6= 24

24x 5= 120

120x 10= 1200

5 0

3 years ago

Read 2 more answers

Maria's height while jumping on a a trampoline can be modeled by the equation h=-16t^2+18t+5. Where t=time in seconds and h=heig

Vadim26 [7]

Answer:

10.06 ft

Step-by-step explanation:

Maria's maximum height will occur when her velocity reaches zero (0). This means that she has stopped ascending and is about to begin descent.

The equation for the height reached by Maria on the trampoline is given as:

$h=-16t^2+18t+5$

To find her maximum height, we first have to find the time it will take her to get to that height and corresponding velocity (zero).

Her velocity can be found by differentiating her height i.e. dh/dt:

$v = \frac{dh}{dt} = -32t + 18$

Therefore, when v = 0:

$0 = -32t+ 18\\\\=> 32t= 18\\\\t = 18 / 32 = 0.5625 secs$

It takes her 0.5625 seconds to get to her maximum height.

Therefore, her height at that time (0.5625 seconds) is:

$h=-16(0.5625)^2+18(0.5625)+5\\\\h = -16 * (0.3164) + 10.125+5\\\\h = -5.0624 + 15.125\\\\h = 10.06 ft$

Therefore, her maximum height is 10.06 ft.

3 0

3 years ago

If a new car is valued at $26,000 and 10 years later it is valued at $7000, then what is the average rate of change

frez [133]

Answer:

The change in value is 19,000 altogether and 1900/year

Step-by-step explanation:

Change in value:

initial value - final value

= $26,000 - $7000

= $19,000

Change in value/year:

change in value/time

= $19,000/10

= $1900/year

7 0

2 years ago

Evaluate 17s^2 + 32s +180

dezoksy [38]

Answer: 66s + 180

How:

17 s ^ { 1 } 2 + 32 s + 180
Calculate s to the power of 1 and get s.

17s\times 2+32s+180
Multiply 17 and 2 to get 34.

34s+32s+180
Combine 34s and 32s to get 66s.

Final answer should be 66s + 180

7 0

3 years ago