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Anon25 [30]
2 years ago
5

From which store should Dylan make his purchase if he wants to get the best price per unit?

Mathematics
1 answer:
KATRIN_1 [288]2 years ago
6 0

Answer:

Store 1

Step-by-step explanation:

Given

See attachment

Required

Determine the store with the best price per unit

It should be noted that the store with the best has the least price per unit.

So, we have:

<u>Store 1</u>

Quantity = 10\ ft

Price = \$2.50

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$2.50}{10\ ft}

Rate = $0.250 per feet

<u>Store 2</u>

Quantity = 2\ yd

Price = \$1.85

Convert quantity to feet

Quantity = 2 * 3ft = 6ft

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$1.85}{6\ ft}

Rate = $0.308 per feet

<u>Store 3</u>

Quantity = 12\ ft

Price = \$3.40

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$3.40}{12\ ft}

Rate = $0.283 per feet

<u>Store 4</u>

Quantity = 5\ yd

Price = \$4.00

Convert quantity to feet

Quantity = 5 * 3ft = 15ft

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$4.00}{15\ ft}

Rate = $0.267 per feet

From the calculations above; store 1 has the least unit rate.

Hence, store 1 has the best price per unit

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Add sin(x) to both sides:

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To solve this, we can use the unit circle.

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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:

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Subtract sine from both sides:

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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}\}

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