All categories

3 years ago

Identify the constant of proportionality (k) 8Y = 16x k=

Mathematics

1 answer:

RUDIKE [14]3 years ago

6 0

Answer:

JUST WRITE THIS AS YOUR ANSWER

Step-by-step explanation:

Step 1: Put together the general equation.

Step 2: Solve for the constant of proportionality.

Step 3: Plugging the constant into the equation, solve for the unknown variable.

Let's solve a few problems to see how this works, shall we?

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

You might be interested in

It takes two apples to make an apple pie. If a chef bought nine apples, the last pie

defon

Hey!

-------------------------------------------------

If a chef bought 9 apples and each pie takes 2 apples then all we have to do is divide.

9 / 2 = 4.5

4 full pies can be made with 9 apples.

4 x 2 = 8 (apples were used to make 4 pies.)

9 - 8 = 1 (apple remaining)

If one pie needs 2 apples, subtract.

2 - 1 = 1 (pies the chef needs to make the last one)

-------------------------------------------------

Answer: The last pie would need 1 more apple.

-------------------------------------------------

Hope This Helped! Good Luck!

5 0

3 years ago

Does anyone know how to do this?

sineoko [7]

Answer:

$\boxed{\tt x=\sqrt{85} }$

Step-by-step explanation:

When making a right triangle with 2 points, the distance is the hypotenuse which can be represent as "x"

To find the distance we can use the Pythagorean theorem.

$\boxed{{\tt a^2+b^2=c^2}}$

→ $\tt a=9$

→ $\tt b=2$

→ $\tt c=x$

Let's Plug in the side lengths:

$\tt 9^2+2^2=x^2$

Evaluate 9²= 81 and 2²= 4:

$\tt 81+4=x^2$

Now, add 81+4= 85

$\tt 85=x^2$

Take the square root of both sides:

$\tt x=\sqrt{85}$

_____________________________

5 0

3 years ago

A jet moving at constant speed traveled 6,600 km in 3 hours. What was the speed of the jet?

DanielleElmas [232]

Answer:

The speed of the jet is $2,200\frac{km}{h}$

Step-by-step explanation:

The speed traveled by the jet can be found using the relationship between distance and time. Because the problem gives the values for distance and time, they must be replaced in the equation and in this way the requested speed will be found.

1. Write the general equation for the speed:

$Speed=\frac{Distance}{Time}$

2. Replace the values of distance and time on the general equation for the speed and make the mathematical operations:

$Speed=\frac{6,600km}{3hours}$

$Speed=2,200\frac{km}{h}$

Therefore the speed of the jet is $2,200\frac{km}{h}$

3 0

3 years ago

Read 2 more answers

You decided to throw a fair die four times.

Finger [1]

Answer:

If all you care about is whether you roll 2 or not, you get a Binomial distribution with an individual success probability 1/6. The probability of rolling 2 at least two times, is the same as the probability of not rolling 2 at zero or one time.

the answer is, 1 - bin(k=0, n=4, r=1/6) - bin(k=1, n=4, r=1/6). This evaluates to about 13%, just like your result (you just computed all three outcomes satisfying the proposition rather than the two that didn’t).

Step-by-step explanation:

7 0

2 years ago

A bag contains rubber bands with lengths that are normally distributed with a mean of 6cm of length, and a standard deviation of

Phoenix [80]

There are 2cm is the answer is this what your looking for

6 0

4 years ago