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iragen [17]
3 years ago
10

Which table represents a direct variation function?

Mathematics
2 answers:
sineoko [7]3 years ago
8 0

Answer:

Option C is correct.

Step-by-step explanation:

A direct variation function is

y/x = k

i.e. we can say that the ratio of y and x is equal to a constant value k.

We will check for each Option given.

Option A

7/2 = 7/2

8/3 = 8/3

9/4 = 9/4

10/5 = 2

11/6 = 11/6

Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant

Option B

-3/2 = -3/2

-5/4 = -5/4

-6/6 = -1

-7/8 = -7/8

-8/10 = -4/5

Option B is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant

Option C

10/-5 = -2

8/-4 = -2

6/-3 = -2

4/-2 = -2

2/-1 = -2

Option C is correct as y/x = k as ratio of y/x for each value in table c is equal to constant value -2

Option D

-3/-2 = 3/2

-3/1 = -3

-3/0 = 0

-3/1 = -3

-3/2 = -3/2

Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant .

SO, Option C is correct.

Marrrta [24]3 years ago
5 0

Answer: OPTION C

Step-by-step explanation:

The function of direct variation has this form:

y=kx

Where k is the constant of variation.

Let's  check if there is a constant of variation on the Options "a" and "b":

On Option A:

 \frac{7}{2}=3.5\\\\\frac{8}{2}=4

On Option B:

\frac{-3}{2}=-1.5\\\\\frac{-5}{4}=-1.25

There is no constant of variation, then these tables do no represent a direct variation.

On the table shown in Option "d" you can observe that "y" does not change when "x" changes. Then it does not represent a direct variation.

Since on the table shown in Option "c":

k=-2

 This table represents a direct variation.

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g If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in cm/min) at which the diameter
maks197457 [2]

Answer:

Rate of change of the diameter is equal to 0.053cm/min

Step-by-step explanation:

A snowball is of the shape of a sphere

Surface area of Sphere (S)= 4*pi*R^2

Rate of change of surface area

dS/dt = -4cm^2/min

the negative sign indicates the surface area is decreasing.

Radius = d/2 where d represents diameter

using this is the surface area equation

S = 4*pi*(d/2)^2

   = pi*d^2

dS/dt = 2*pi*d*d(d)/dt

4 = 2*pi*d*(d)/dt

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so the rate of change of the diameter is equal to 0.053cm/min

5 0
2 years ago
Approximate the change in the volume of a sphere when its radius changes from r= 5ft to r= 5.1ft (v(r)= 3/4 pi r^3)?
leva [86]

Answer:

18.03 cubic feet

Step-by-step explanation:

Hello,

Step 1

find the volume of the sphere when radius= 5 ft

v(r)= \frac{3}{4} \pi r^3\\v(5)= \frac{3}{4}\pi (5\ ft)^3\\v(5)= \frac{3}{4}\pi *125\ ft^{3} \\v(5)=294.52\ cubic\ feet\\

Step 2

find the volume of the sphere when radius= 5.1 ft

v(r)= \frac{3}{4}\pi r^3\\v(5.1)= \frac{3}{4} \pi (5.1\ ft)^3\\v(5.1)= \frac{3}{4}\pi *132.651\ ft^{3} \\v(5.1)=312.551\ cubic\ feet\\\\

Step 3

Compare the Volumes to find the change

\frac{v(r_{2})}{v(r_{1})} =\frac{312.551}{294.52} =1.06

the volumen of the sphere with radius = 5.1 is 1.06 times bigger than the first one(r=5)

Now, find the change

change= {v(r_{2})-{v(r_{1})}} \\change=312.551\ cubic\ feet\ -294.52 cubic feet \\ change=18.031\ cubic\ feet

change=18.03 cubic feet

Have a great day.

4 0
2 years ago
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