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Lana71 [14]
3 years ago
15

Which expression is equivalent to

Mathematics
2 answers:
Aneli [31]3 years ago
6 0
<h3> ♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ 5 is multiplied by itself giving this value:

5^{6}

However, the 3 isn't involved with the exponents so the answer would be:

3(5)^{6}

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Mice21 [21]3 years ago
6 0

Answer:

C) 3(5)^6

Step-by-step explanation:

Note the amount of 5's inside the expression and 3's inside the expression.

In the given expression (3 x 5 x 5 x 5 x 5 x 5 x 5), there are 6 5's and 1 3's.

Note that, when changing multiplication into powers, the amount of the same number multiplied together will equal the number you put as a power. For example:

5 x 5 = 5²

5 x 5 x 5 = 5³

In this case:

5 x 5 x 5 x 5 x 5 x 5 = 5^6

Note that there is still a 3 multiplied inside the expression, and so remember to keep it in the answer.

3(5)^6, or C) is your answer.

~

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Answer:

your answer is 5 dollars per hour

Step-by-step explanation:

35/7 = 5

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What is the area of this figure?
coldgirl [10]
Answer: 102

-----------------------------------------------

We'll use the formula 
A = h*(b1+b2)/2
where
A = area of trapezoid
h = height
b1 & b2 are the parallel bases

In this case,
b1 = 6+7 = 13
b2 = 21
h = 6

Making the area to be
A = h*(b1+b2)/2
A = 6*(13+21)/2
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3 0
3 years ago
CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is
Rufina [12.5K]

Answer:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

y=\sin(x)\cos(x)

Take the derivative of both sides with respect to x:

\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]

We need to use the product rule:

(uv)'=u'v+uv'

So, differentiate:

y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]

Evaluate:

y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))

Simplify:

y'=\cos^2(x)-\sin^2(x)

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

0=\cos^2(x)-\sin^2(x)

Now, let's solve for x. First, we can use the difference of two squares to obtain:

0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))

Zero Product Property:

0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)

Solve for each case.

Case 1:

0=\cos(x)-\sin(x)

Add sin(x) to both sides:

\cos(x)=\sin(x)

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

0=\cos(x)+\sin(x)

Subtract sine from both sides:

\cos(x)=-\sin(x)

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

And we're done!

Edit: Small Mistake :)

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Try this solution:
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answer: 7
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