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3 years ago

9

John has 8/9 of a gallon of apple cider vinegar. If it takes 1/7 of a gallon of vinegar to make a batch of collard greens, how m

any batches can john make?

1 answer:

kumpel [21]3 years ago

5 0

1/7 gallon = 1 batch

<em>[multiply by 7 through]</em>
1 gallon = 7 batches

<em>[multiply by 8/9 through]</em>
8/9 gallon = 7 x 8/9
8/9 gallon = 6 2/9

<em>[Good enough to make 6 batches, not enough to make 7 batches]</em>

So he can make 6 batches of collard green

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Use the grouping method to factor the polynomial below completely 3x^3+9x^2+5x+15

Tomtit [17]

Answer:

(x+3)( 3x^2 +5)

Step-by-step explanation:

3x^3+9x^2+5x+15

Split into two groups

3x^3+9x^2 +5x+15

Factor 3x^2 out of the first group and 5 out of the second group

3x^2 ( x+3) + 5(x+3)

Factor out x+3

(x+3)( 3x^2 +5)

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3 years ago

FInd mPQ <br> Geometry question, circles, arc length, chord length,

Fed [463]

Answer:

$\text{B. }26}$

Step-by-step explanation:

Since $\overline{PN}$ and $\overline{PQ}$ are equal, we can set them equal to each other:

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Substitute $x=3$ to solve for $\overline{PQ}$ :

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3 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

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Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

So

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

So

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

So

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

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

So

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

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3 years ago

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3 years ago

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Alexxandr [17]

Answer:

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Step-by-step explanation:

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We will use intersecting secants theorem, which states that measure of an angle formed by two intersecting secants outside a circle is half the difference of intercepted arcs.

Using above theorem, we can set an equation to find the measure of arc WX as:

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$WX=32^{\circ}$

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4 years ago