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2 years ago

15

Melissa is making clothes for her dolls. She has 7/8 yard of fabric. Each doll shirt requires 2/7 of a yard of fabric. How many

whole shirts can she make for her dolls?

1 answer:

igor_vitrenko [27]2 years ago

8 0

Answer:

She can make three shirts and will have 7/56 left.

Step-by-step explanation:

49/56-14/56=35/56 (one shirt) 35/56-14/56=21/56 (two shirts) 21/56-14/56=7/56 (three shirts)

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Put it in decimal form plssss………

raketka [301]

The answer is 58, because 2/5 is equal to 0.4, and 0.4 multiplied by 145 is 58.

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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

What’s the correct answer for this?

VMariaS [17]

Answer:

Second option is the correct answer

$(x+11)^2+(y+6)^2 = 324$

Step-by-step explanation:

$x^{2} +12y+22x+y^2-167=0\\x^{2}+22x +y^2 +12y-167=0\\(x^{2}+22x +121)-121 +(y^2 +12y+36)-36-167=0\\(x+11)^2+(y+6)^2-324 = 0\\\huge\red{\boxed{(x+11)^2+(y+6)^2 = 324}}\\$

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3 years ago

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The sum of 5x2y and (2xy2 + x2y) is

allochka39001 [22]

<span>5x²y + 2xy² + x²y

Combining like terms would be
6x²y + 2xy²

The two terms are now unique and cannot be combined any further. </span><span>
</span>

6 0

2 years ago

HELP ME EVERYONE PLZ

yawa3891 [41]

Answer:

Option D. 23.4 pounds

Step-by-step explanation:

step 1

Find the pieces of glass for 22.5 pounds of copper in the sculpture.

using proportion

$\frac{12}{1}=\frac{x}{22.5} \\ \\x=22.5*12\\ \\x=270\ piece\ of\ glass$

step 2

Find the pounds of bronze used in the sculpture

using proportion

$\frac{6.5}{75}=\frac{x}{270} \\ \\x=270*6.5/75\\ \\x=23.4\ pounds$

7 0

3 years ago