Find the area of a circle with radius, r = 41cm. Give your answer rounded to 3 SF.

Which expression is the simplest form of...

Lemur [1.5K]

Answer:

The answer is option A

Step-by-step explanation:

Using the rules of indices

That's

<h3> $( { {a}^{x} })^{y} = {a}^{x \times y}$ </h3>

Simplify the expression

We have

<h3> $( { {x}^{ - \frac{4}{7} } })^{7} = {x}^{ - \frac{4}{7} \times 7 } \\ = {x}^{ - 4}$ </h3>

Again using the rules of indices

That's

The final answer is

Hope this helps you

5 0

3 years ago

Read 2 more answers

Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units left and 2 units d

Vsevolod [243]

Let

g(x)--------> the translation of the function f(x)

we know that

the rule of the translation is

$3$ units left and $2$ units down

that means

$(x,y)-------> (x-3,y-2)$

so

In the function f(x) the point $(0,0)$ is equal at the point $(-3,-2)$ in the function g(x)

therefore

the function g(x) is equal to

$g(x)=f(x+3)-2$

$g(x)=(x+3)^{3} -2$

<u>The answer is</u>

a) the rule of the translation is $(x,y)-------> (x-3,y-2)$

b) The graph in the attached figure

5 0

2 years ago

Identify the coefficients and constants in the expression. 2x – y + 5x

garri49 [273]

I believe the answer is 7x-y

7 0

2 years ago

The product of 4 and the sum of a number x and 8

Mademuasel [1]

Answer:

4(x+8)

Step-by-step explanation:

hope this helps

Then if you want to know the value of x.

This is the solution 4(x+8)

4x+32 to find the x divide both by side by 4.

4x/4+32/4

x=8

7 0

3 years ago

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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 :)

5 0

2 years ago