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2 years ago

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

7 0

Answer:

$y=\dfrac {60} {x}$ or $xy=60$ (depending on your teacher's format preference)

Step-by-step explanation:

<h3>Proportionality background</h3>

Proportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Direct
Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

$y=kx$ y is directly proportional to x
$y=kx^2$ y is directly proportional to x squared
$y=kx^3$ y is directly proportional to x cubed
$y=k\sqrt{x}}$ y is directly proportional to the square root of x
$y=\dfrac {k} {x}$ y is inversely proportional to x
$y=\dfrac {k} {x^2}$ y is inversely proportional to x squared

From these examples, we see that two things:

things that are directly proportional -- the thing is multiplied to the constant of proportionality "k"
things that are inversely proportional -- the thing is divided from the constant of proportionality "k".

<h3>Looking at our question</h3>

In our question, y is inversely proportional to x, so the equation we're looking at is the following $y=\dfrac {k} {x}$ .

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it: "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

<h3>Solving for k, and finding the general equation</h3>

General Inverse variation equation...

$y=\dfrac {k} {x}$

Substituting known values...

$(12)=\dfrac {k} {(5)}$

Multiplying both sides by 5...

$(12)*5= \left ( \dfrac {k} {5} \right ) *5$

Simplifying/arithmetic...

$60=k$

So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is $y=\dfrac {60} {x}$ .

The way your question is phrased, they may prefer the form: $xy=60$

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Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the popu

tia_tia [17]

Answer:

The minimum head breadth that will fit the clientele is 4.4 inches.

The maximum head breadth that will fit the clientele is 7.8 inches.

Step-by-step explanation:

Let X = head breadths of men that is considered for the helmets.

The random variable X is normally distributed with mean, μ = 6.1 and standard deviation, σ = 1.

To compute the probability of a normal distribution we first need to convert the raw scores to z-scores using the formula:

$z=\frac{x-\mu}{\sigma}$

It is provided that the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.

Compute the minimum head breadth that will fit the clientele as follows:

P (X < x) = 0.043

⇒ P (Z < z) = 0.043

The value of z for this probability is:

z = -1.717

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\-1.717=\frac{x-6.1}{1}\\x=6.1-(1.717\times 1)\\x=4.383\\x\approx4.4$

Thus, the minimum head breadth that will fit the clientele is 4.4 inches.

Compute the maximum head breadth that will fit the clientele as follows:

P (X > x) = 0.043

⇒ P (Z > z) = 0.043

⇒ P (Z < z) = 1 - 0.043

⇒ P (Z < z) = 0.957

The value of z for this probability is:

z = 1.717

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\1.717=\frac{x-6.1}{1}\\x=6.1+(1.717\times 1)\\x=7.817\\x\approx7.8$

Thus, the maximum head breadth that will fit the clientele is 7.8 inches.

5 0

3 years ago

Cuales son los terminos que siguen en cada sucesion:a)2,4,8,16,32,64,....B)1,3,5,7,9,....C)1,3,6,10,15,21,28,36,45

Elanso [62]

Answer:

a) Número siguiente = Número anterior * 2

b) Número siguiente = Número anterior + 2

c) Número siguiente = Número anterior + (n + 1)

Step-by-step explanation:

a) Para la secuencia 2,4,8,16,32,64, ....

El siguiente número es dos veces el número anterior.

Por ejemplo, 4 = 2 * 2, 8 = 4 * 2, 16 = 8 * 2 etc.

b) Para la secuencia 1,3,5,7,9, ....

El siguiente número es igual al número anterior + 2

Por ejemplo, 3 = 1 + 2, 5 = 3 + 2, 7 = 5 + 2 etc.

c) Para la secuencia1,3, 6,10,15,21,28,36,45

La diferencia entre los números aumenta en +1.

3-1 = 2

6-3 = 3

10-6 = 4

15-10 = 5

21-15 = 6

28-21 = 7

3 0

3 years ago

I need the written form for 293,805

yan [13]

Two hundred ninety three thousand eight hundred and five

5 0

4 years ago

Consider the differential equationy′′+3y′−10y=0.(a) Find the general solution to this differential equation.(b) Now solve the in

RSB [31]

Answer:

Y= 2e^(5t)

Step-by-step explanation:

Taking Laplace of the given differential equation:

s^2+3s-10=0

s^2+5s-2s-10=0

s(s+5)-2(s+5) =0

(s-2) (s+5) =0

s=2, s=-5

Hence, the general solution will be:

Y=Ae^(-2t)+ Be^(5t)………………………………(D)

Put t = 0 in equation (D)

Y (0) =A+B

2 =A+B……………………………………… (i)

Now take derivative of (D) with respect to "t", we get:

Y=-2Ae^(-2t)+5Be^(5t) ....................... (E)

Put t = 0 in equation (E) we get:

Y’ (0) = -2A+5B

10 = -2A+5B ……………………………………(ii)

2(i) + (ii) =>

2A+2B=4 .....................(iii)

-2A+5B=10 .................(iv)

Solving (iii) and (iv)

7B=14

B=2

Now put B=2 in (i)

A=2-2

A=0

By putting the values of A and B in equation (D)

Y= 2e^(5t)

6 0

4 years ago

2s plus 5 _> 49 please solve

Phoenix [80]

Fist subtract 5 from both sides
Equation is now 2s is greater than or equal to 44
Now divide by 2
Equation is now s is less than or equal to 22
Be sure to flip equality sign when dividing

8 0

3 years ago

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.​

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.