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1 year ago

If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this

Mathematics

2 answers:

otez555 [7]1 year ago

7 0

Answer:

Step-by-step explanation:

If there is a direct relation between two variables x and y then it can be represented as

y = kx ,

where y is dependent variable

x is independent variable

k is constant of variation

_____________________________

First condition

y = 400

x = r

using y = kx then relationship will be

400 = kr

finding k here

k = 400/r

Second condition

y = r

x = 4

using y = kx then relationship will be

r = 4k

finding k

k = r/4

since in both condition equation is same

thus, value of k will also be same

thus,

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

$\sqrt{r^{2} } = \sqrt{1600} \\r = 40$

Thus, 40 is the value of r

k = r/4 = 40/4 = 10

Thus, constant of variation is 10 which is correct choice.

To cross validate

k = 400/r = 400/40 = 10

LiRa [457]1 year ago

6 0

Answer:

A. 10 on Edg2020

Step-by-step explanation:

Hope this helps!!! Have a great day!!! : )

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A fast-food restaurant has a cost of production C(x)=12x+114 and a revenue function R(x)=6x. When does the company start to turn

LekaFEV [45]

Step-by-step explanation:

Given data

C(x)=12x+114

R(x)=6x.

The company will start to run on profit just when revenue equals the production cost, that is

C(x)=R(x)

equating the two expressions we have

12x+114=6x

solving for x we have

12x-6x+114=0

6x+114=0

6x=-114

x=-114/6

x=-19

Hence the company will start to run on proft when they start to produce above 19 items

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2 years ago

a bonus of 4200 is shared by 10 people who works for a company.40% of the bonus is shared equally between 3 managers the rest of

oee [108]

Step-by-step explanation:

if each the bonus is shared equally each will get 420

if 40% is shared by managers each manager will get 560

if 7 sales persons share 60% each will get 360

therefore Peter salesperson will get 360

but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct

7 0

2 years ago

PLEASE HELP! I SUCK AT MATHHH, THANK YOUUU!!!

vfiekz [6]

Answer: 21/400

Step-by-step explanation:

Multivitamin:

8 cherry, 5 grape, and 7 orange

Total fruits in Multivitamin container :

(8 + 5 + 7) = 20

P(orange) = Total required outcome / Total possible outcomes)

P(orange) = 7/20

Calcium vitamin :

11 berry, 3 lemon, and 6 pineapple

Total fruits in calcium vitamin container:

(11 + 3 + 6) = 20

Probability of picking a lemon:

P(lemon) = Total required outcome / Total possible outcomes)

P(lemon) = 3/20

Therefore, probability of picking an orange and a lemon equals:

P(orange) × p(lemon) = (7/20) × (3/20) = 21/400

3 0

2 years ago

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the

Harman [31]

THE QUESTION IS NOT PROPERLY WRITTEN

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If t1 is the time (in seconds) it takes for the object to strike the water, then t1 obeys the equation s = 16t1², where s is the distance (in feet) Solving for t1, we have t1 = √s/4. Let t2 be the time it takes for the sound of the impact to reach your ears. Since sound waves travel at a speed of approximately 1100 feet per second, the time to travel the distance s is t2 = s/1100. Now t1 +t2 is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation; Total elapsed time √s/4 + s/1100.

Find the distance to the water’s surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.

Answer:

229.94 feet

Step-by-step explanation:

Given

t1 = √s/4

t2 = s/1100

From the question, we understand that

t1 + t2 = 4 seconds

Let y = √s

So,

t1 + t2 = 4 becomes

√s/4 + s/1100 = 4

y/4 + y²/1100 = 4 ------ Solve the fractions

(275y + y²)/1100 = 4

275y + y² = 4 * 1100

275y + y² = 4400 ------- Rearrange

y² + 275y - 4400 = 0 (Quadratic Equation)

The standard form of a quadratic equation is ax² + bx + c = 0

Where x =

frac{-b+-\sqrt{bx^{2} - 4ac } }{2a}

Here a = 1, b = 275 and c = -4400

So,

y = (-275+- √(275² - 4*1*-4400))/2

y = (-275+- √75625 + 17600))/2

y = (-275+- √(93225))/2

y = (-275 +- 305.328)/2

y = (-275 + 305.328)/2 or (-275-305.328)/2

y = 30.328/2 or -580.328/2

y = 15.164 or -290.164 -------Negative is not applicable

So, y = 15.164

But y = √s

So, s = y²

S = 15.164²

s = 229.94 ft

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2 years ago

A middle school band has 45 sixth and seventh graders The ratio of sixth to seventh graders is 2 to 3 how many sixth graders are

AnnyKZ [126]

Answer:

Step-by-step explanation:

There are 2+3 = 5 ratio units representing 45 band members, so each ratio unit represents 45/5 = 9 band members.

The 2 ratio units of sixth graders represent 2×9 = 18 sixth grade band members.

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2 years ago