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3 years ago

When x=3, y=16 and when x=6, y=8. Which inverse variation equation can be used to model this function

Mathematics

1 answer:

MakcuM [25]3 years ago

8 0

Inverse variation equations take the following form:

y = a/x, where a is some constant

We know x=3, y=16 and x=6, y=8 satisfy the equation.

Let's find the value of a.

16=a/3

Multiply both sides by 3

16*3 = a

48 = a

Thus, the equation is:

y = 48/x

You can use the other values of x and y to test, but I'm sure this is the correct equation. :)

(This answer was sent on mobile, so please pardon any spelling errors I may have)

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Can someone please help me?

kvasek [131]

now, let's recall the rational root test, check your textbook on it.

so p = 18 and q = 1

so all possible roots will come from the factors of ±p/q

now, to make it a bit short, the factors are loosely, ±3, ±2, ±9, ±1, ±6.

recall that, a root will give us a remainder of 0.

let us use +3.

$\bf x^4-7x^3+13x^2+3x-18 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{r|rrrrr} 3&1&-7&13&3&18\\ &&3&-12&3&18\\ \cline{1-6} &1&-4&1&6&0 \end{array}\qquad \implies (x-3)(x^3-4x^2+x+6)$

well, that one worked... now, using the rational root test, our p = 6, q = 1.

so the factors from ±p/q are ±3, ±2, ±1

let's use 3 again

$\bf \begin{array}{r|rrrrr} 3&1&4&1&6\\ &&3&-3&-6\\ \cline{1-5} &1&-1&-2&0 \end{array}\qquad \implies (x-3)(x-3)(x^2-x-2)$

and of course, we can factor x²-x-2 to (x-2)(x+1).

(x-3)(x-3)(x-2)(x+1).

7 0

3 years ago

The perimeter P of a square (measured in inches) is expanding in size at a constant rate of change of 4 inches per inch with res

vivado [14]

Answer:

a. 10 inches

b. 8 inches

c. $\frac{dP}{ds} = 4$

Step-by-step explanation:

a. At side 0, perimeter is 0*4 = 0 in. At side 2.5 inches, perimeter = 2.5*4 = 10 inches, a change of 10 - 0 = 10 inches

b. At side 1, perimeter is 1*4 = 4 inches. At side 3 inches, perimeter = 3*4 = 12 inches, a change of 12 - 4 = 8 inches.

c. We can express the change in the square's perimeter P in terms of the change in the square's side length s as

$\frac{dP}{ds} = 4$

6 0

3 years ago

Two towns that are 31.5 km apart are 3 cm apart on a map. what is the scale of the map?

VLD [36.1K]

<u>Answer:</u>

1 cm : 10.5 km

<u>Step-by-step explanation:</u>

We are given that two towns are 31.5 km in real and are 3 cm apart on a map and we are to find the scale of the map.

For this, we can use the ratio method.

$\frac { 3 cm } { 1 c m } = \frac { 3 1 . 5 k m } { x }$

$x = \frac { 3 1 . 5 \times 1 } { 3 }$

$x = 1 0 . 5$

Therefore, the scale of the map would be 1 cm : 10.5 km.

8 0

3 years ago

Read 2 more answers

Which function corresponds to the table of inputs and outputs?

Anarel [89]

Answer:

f(x) = 3x + 2

Step-by-step explanation:

That's easy to find out. You have your input number, which is your x value, and you have your output number which is your y value (or f(x)).

All you have to do is see if each of the proposed answer works for ALL entries in the data set.

f(x) = 3x + 2

for x = 3 ===> 11 = 3 (3) + 2 = 11 YES

for x = 5 ===> 17 = 3 (5) + 2 = 17 YES

for x = 7 ===> 23 = 3 (7) + 2 = 23 YES

for x = 9 ===> 29 = 3 (9) + 2 = 29 YES

f(x) = 2x + 5

for x = 3 ===> 11 = 2 (3) + 5 = 11 YES

for x = 5 ===> 17 = 2 (5) + 5 = 15 NO - we stop here for this function

f(x) = x + 7

for x = 3 ===> 11 = (3) + 7 = 10 NO - we stop here for this function

f(x) = 3x + 1

for x = 3 ===> 11 = 3 (3) + 1 = 10 NO - we stop here for this function

7 0

3 years ago

A diver at -60 feet stops every 5 feet before reaching the surface. How many stops will the

Art [367]

The diver will make 12 stops before reaching the surface.

5 0

3 years ago

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