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Over [174]
2 years ago
7

Y is directly proportional to (x-4) when x=16, y=3 find y in terms of x

Mathematics
2 answers:
Paha777 [63]2 years ago
6 0

Answer:

y = ¼(x-4)

Step-by-step explanation:

Before solving the question, let's look at one example,

  • A is directly proportional to B means A∝B which also means A=kB where k is a constant.

In this case, y is directly proportional to (x-4) means that y∝(x-4) which can also mean that y=k(x-4).

Hence, to find the value of k, substitute x=16, y=3 into y=k(x-4),

3=k(16-4)

k=3/12

k=1/4

After that, substitute the k value into the equation,

<h3>y = ¼(x-4)</h3>

dalvyx [7]2 years ago
4 0
Y = x/4 - 1

Step by step explanation in pic

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(i) Let E the expression that we are analyzing:

E=2x^2-4x+5\\\\ E=2x^2-4x+2-2+5\\\\ E=2(x^2-2x+1)-2+5\\\\ E=2(x-1)^2+3

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(ii) Manipulating the expression:

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8) Let E the expression that we want to calculate:

E=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)+1\\\\ E-1=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)

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(2-1)(E-1)=(2-1)(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ (E-1)=\underbrace{(2-1)(2+1)}_{2^2-1}(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ (E-1)=\underbrace{(2^2-1)(2^2+1)}_{2^4-1}(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ ... Repeating the process, we obtain: ...\\\\ E-1=(2^{32}-1)(2^{32}+1)\\\\ E-1=2^{64}-1\\\\ \boxed{E=2^{64}}
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