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lozanna [386]
3 years ago
7

if the value of x varies directly as the value of y , and x = 16 when y = 3/4 , what is the value of x when y = 3/8 ?

Mathematics
1 answer:
Olin [163]3 years ago
3 0

Answer:

x=8

Step-by-step explanation:

If the value of x varies directly as the value of y we can say they are directly proportional. This implies that when y increases x will increase too, and when y decreases x will also decrease.

If x=16 when y=3/4 we can write their relation as:

x/y = 16/(3/4) = 16*(4/3) = 64/3

So, for every value of y, the ratio x/y must maintain equal to 64/3 because both values are proportional.

Now we can see what happens to x when y varies. If y=3/8:

x/(3/8) = 64/3

Multiply both sides by 3/8 to eliminate the 3/8 in the denominator.

x/(3/8) * (3/8) = (64/3) * (3/8)

See that we have a 3 multiplying and another dividing, we can eliminate them.

x = 64/8

x = 8

So, if y decreases to 3/8 x will decrease to 8. Notice that y is decreasing in a half as 3/8 is the half of 3/4, and x is also decreasing in a half from 16 to 8, what makes sense.

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Rasek [7]

Let's do this by Briot-Ruffini


First: Find the monomial root


x - 2 = 0

x = 2


Second: Allign this root with all the other coeficients from equation

Equation = -3x³ - 2x² - x - 2

Coeficients = -3, -2, -1, -2

2 | -3 -2 -1 -2


Copy the first coeficient


2 | -3 -2 -1 -2

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Multiply him by the root and sum with the next coeficient


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2 | -3 -2 -1 -2

-3 -8


Do the same


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-16 + (-1) = -17


2 | -3 -2 -1 -2

-3 -8 -17


The same,


2.(-17) = -34

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2 | -3 -2 -1 -2

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Now you just need to put the "x" after all these numbers with one exponent less, see


2 | -3x³ - 2x² - 1x - 2

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You may be asking what exponent -36 should be, and I say:


None or the monomial. He's like the rest of this division, so you can say:


(-3x³ - 2x² - x - 2)/(x - 2) = -3x² - 8x - 17 with rest -36 or you can say:

(-3x³ - 2x² - x - 2)/(x - 2) = -3x² - 8x - 17 - 36/(x - 2)


Just divide the rest by the monomial.

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To solve an equation for a variable, you must isolate the variable on either side of the equation. To do this, simply subtract 32 from both sides of the original equation:

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