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Alina [70]
2 years ago
10

Which price is equivalent to $1.50 for 1 pound of apples?

Mathematics
1 answer:
olga_2 [115]2 years ago
6 0
A. 6 pounds of apples for $9
9/6=1.5=$1.50 per pound
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Simplify x + (7+14x)​
Brilliant_brown [7]

Answer:

15x + 7

Step-by-step explanation:

x + (7 + 14x)

x + 7 + 14x

15x + 7

8 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 :)

5 0
2 years ago
How many times can 5 go into 1620
kaheart [24]
1620/ 5 is =324
To check just multiply
5 * 324
5 0
3 years ago
What is the equation of circle C???
BigorU [14]

Answer:

(x-5)²+(y-7)²=80

Step-by-step explanation:

3 0
2 years ago
How many solutions are there to the equation below?
Vikentia [17]

Answer:

5x + 48 + 7x = 12(x + 4) \\ 5x + 48 + 7x = 12x + 48 \\ (5x + 7x) + 48 = 12x + 48 \\ 12x + 48 = 12x + 48 \\ 12x - 12x = 48 - 48 \\ 0 = 0

<u>There</u><u> </u><u>is</u><u> </u><u>no</u><u> </u><u>solution</u>

4 0
2 years ago
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