All categories

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!!! : )

You might be interested in

Find the product: (30 gallons 3 quarts 1 pint) × 5

SpyIntel [72]

30 gallons * 5 = 150 gallons

3 quarts * 5 = 15 quarts

1 pint * 5 = 5 pints

Four quarts in a gallon: 15/4 = 3 gallons, 2 quarts

2 pints in a quart: 5/2 = 2 quarts, 1 pint

2 quarts + 2 quarts = 1 gallon

150 + 3 + 1 gallons + 1 pint = 153 gallons, 1 pint.

4 0

2 years ago

Read 2 more answers

At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decima

Firdavs [7]

$\mathbf r(t)=\langle x(t),y(t),z(t)\rangle=\langle\sin t,\cos t,t\rangle$

$x^2+y^2+z^2=\sin^2t+\cos^2t+t^2=65$
$\implies t^2=64$
$\implies t=\pm8$

7 0

1 year ago

An investor has $ 500000 to spend. There investments are being considered, each having an expected annual interest rate. The int

enyata [817]

That's a lot of money and words. I don't appreciate this. I would probably just break down and cry tbh

8 0

2 years ago

Which term describes a time period marked by a change that begins a new period of development? century decade era millennium

defon

Answer:

Era

Step-by-step explanation:

Century, Decade and Millennium have something in common and that which they have in common is that they are all measurement of time.

The keyword measurement implies that they are units of time just like seconds, minutes, hours, etc.

Century -> 100 years

Decade -> 10 years

Millennium -> 1000 years

However, era is used to describe events in history;

Take for instance; the era of the first generation of computer;

So, from the list of given options; Era best answers the question

8 0

2 years ago

Read 2 more answers

Mrs. Kong uses 1 over 3 of a stick of butter in a sauce she then uses 5 over 8 of the butter to make garlic bread what fraction

Allisa [31]

Answer=1/24

1/3+5/8=
to solve for this, we need the denominators of the fractions to match.

The LCM of 3 and 8 is 24

1/3=8/24
5/8=15/24

8/24+15/24=23/24

Now if we're using 23/24, then only 1/24 is left.

24/24-23/24=1/24

8 0

1 year ago