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Arturiano [62]
3 years ago
15

At a grocery store, the price of a watermelon is determined by how many pounds the watermelon weighs. The price of a watermelon

that weighs 7.3 pounds is $4.38. ​ Write an equation that can be used to determine the price, p, in dollars, of any watermelon based on the number of pounds, w, the watermelon weighs. Explain the process you used to determine the equation. ​
Mathematics
1 answer:
Alexxx [7]3 years ago
7 0

Answer:

p=0.60w

Step-by-step explanation:

Let

p ----> the price of a watermelon in dollars

w ---> the weight of a watermelon in pounds

In this problem we have a proportional relationship

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

p=kw

The value of the constant of proportionality k is the same that the unit rate

Find out the unit rate

Divide the total cost by the total weight

k=\frac{4.38}{7.3}=\$0.60\ per\ pound

substitute in the equation

p=0.60w

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Find the largest prime divisor of $15^6 - 7^6$<img src="https://tex.z-dn.net/?f=Find%20the%20largest%20prime%20divisor%20of%20%2
Novosadov [1.4K]

Answer:

Largest prime factor of the given expression is <em>379.</em>

Step-by-step explanation:

Given the expression:

15^6 - 7^6

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

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Let us learn two formula:

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x^3-y^3 = (x-y)(x^2+y^2+xy)

Applying the above formula in the expression written above:

(15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2 ...... (1)

Similarly:

(15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379........ (2)

Multiplying the expressions from (1) and (2) to get the result:

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