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iragen [17]
3 years ago
5

One number is 4 more than another. the difference between their squares is 64. what are the numbers

Mathematics
1 answer:
lora16 [44]3 years ago
5 0
We have to set up 2 different equations if we are to solve for 2 unknowns.  The first equation is x = y + 4.  One number (x) is (=) 4 more than another (y + 4).  Since we have determined that x is larger (cuz it's 4 more than y), when we set up their difference, we are going to subtract y from x cuz x is bigger.  The second equation then is x^{2} - y^{2} =64.  In our first equation we said that x = y + 4, so let's sub that value in for x in the second equation: (y+4) ^{2} - y^{2} =64.  Expand that binomial to get y^{2} +8y+16- y^{2} =64.  Of course the y squared terms cancel each other out leaving us with 8y + 16 = 64.  Solving for y we get that y = 6.  Subbing 6 in for y in our first equation, x = 6 + 4 tells us that x = 10. Yay!

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The required value of y is 2645 / 77 when x = 77.

Step-by-step explanation:

1. Let's check the information given to answer:

if y varies inversely as x, and y = 23 when x = 115. Find y when x=77

2. What is y when x = 77?

As the statement "y varies inversely as x" translates into y = k/x

If we let y = 23 and x = 115, the constant of variation becomes

        23 = k ÷ 115

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          y = 2645 ÷ 77

<u>So, The required value of y = 2645 / 77 when x = 77</u>

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Alguém aí ajuda fazendo o favor?
Anastasy [175]
3y
---- -2 =9
 4

3y 
---- = 11
 4

3y = 44

y = 44/3

hope helped 
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2 years ago
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