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klemol [59]
2 years ago
7

The amount a tree grows in one month is directly proportional to the amount of water it is given. When a tree is giving 21 gallo

ns of water it grows 8 cm that month. What is the constant of proportionality for this variation? record your answer to the nearest thousand.
Mathematics
1 answer:
mr_godi [17]2 years ago
8 0

Answer:

k = 0.381cm/gallon

Step-by-step explanation:

Let the amount a tree grows in one month be x

Let amount of water it is given be y

If the amount a tree grows in one month is directly proportional to the amount of water it is given, then;

x ∝ y

x = ky

k is the constant of proportionality

k = x/y

Given

x = 8cm

y = 21 gallons

k = 8/21

k = 0.381cm/gallon

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katrin [286]
Multiply 7 x 12 which is 84, 8x2 is 16, 16 divded by 3 is 5, so 5 minutes
3 0
2 years ago
Pls help I don't understand:
sineoko [7]

Answer:

Part a) T(d)=2d+30

Part b) T(6)=42\ minutes

Step-by-step explanation:

Part a) Write an equation for T (d)

Let

d ----> the number of days

T ---> the time in minutes of the treadmill

we know that

The linear equation in slope intercept form is equal to

T=md+b

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope or unit  rate is

m=2\ \frac{minutes}{day}

The y-intercept or initial value is

b=30\ minutes

substitute

T(d)=2d+30

Part b) Find T (6), the minutes he will spend on the treadmill on day 6

For d=6

substitute in the equation and solve for T

T(6)=2(6)+30

T(6)=42\ minutes

8 0
2 years ago
Rewrite 27+36 using GCF and distributive property
valkas [14]

Answer:

27+36=9 (3+7)

Step-by-step explanation:

27+36= 2(70+36)

8 0
3 years ago
Jefferson's Popcorn & Roasted Nuts Shop sells cone-shaped bags of roasted cashews, shown below. What is the volume of the ba
DanielleElmas [232]

The volume of the bag of nuts is the amount of nuts it can contain

The volume of the bag of nuts is 84.78 cubic inches

<h3>How to determine the volume of the bag?</h3>

From the figure, we have the following parameters:

  • Radius, r = 3 in
  • Height, h = 9 in

The volume of a cone is calculated using:

V = 1/3 πr^2h

Substitute the known values

V = 1/3  * 3.14 * 3^2 * 9

Evaluate the product

V = 84.78

Hence, the volume of the bag of nuts is 84.78 cubic inches

Read more about volumes at:

brainly.com/question/1972490

3 0
2 years ago
How do you find direct variation. I’m having trouble understanding some of these examples.
Rufina [12.5K]
Direct variation is a relation that has the form

y = kx

where k is the constant of proportionality.

If you are told that a relation is a direct proportion, and you are given one data point, you can find k. The you can write the equation of the direct relation.

Here is an example.
The price of gasoline follows a direct variation.
John bought 5 gallons of gas and paid $15.
a) Write an equation for the relation.
b) Using the relation you found, how much do 13.8 gallons cost?

Solution:
Since the relation is a direct variation, it follows the general equation of a direct variation:

y = kx

We are given one data point, 5 gallons cost $15.
We plug in  5 for x and 15 for y and we find k.

y = kx
15 = k * 5
k = 3

Now that we know that k = 3, we rewrite the relation using our value of k.

y = 3x

This is the answer to part a).

Part b)

We use our relation, y = 3x, and we plug in 13.8 into x and find y.

y = 3x

y = 3 * 13.8

y = 41.4

The price of 15 gallons of gas is $41.40.
5 0
2 years ago
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