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3 years ago

The table shows a proportional relationship.

1 answer:

8 0

(2,2.8)(4,5.6)
slope = (5.6 - 2.8) / (4 - 2) = 2.8/2 = 1.4

y = mx + b
slope(m) = 1.4
use either point (2,2.8)...x = 2 and y = 2.8
now we sub and find b, the y int
2.8 = 1.4(2) + b
2.8 = 2.8 + b
2.8 - 2.8 = b
0 = b

so ur equation is : y = 1.4x + 0..or just y = 1.4x

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a plant is 20 inch tall. if the plant grows 2h inches each week for the next 4 weeks, and h inches for each of the 2 weeks after

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Is it 116? if i didnt add that up wrong thats the answer

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3 years ago

A lake was stocked with 360 trout. Each year, the population decreases by 10. The population of trout in

almond37 [142]

Answer:

Part A) The y-intercept is the point (0,360) and the x-intercept is the point (36,0)

Part B) The graph in the attached figure

Part C) see the explanation

Step-by-step explanation:

Part A) Find the intercepts

Let

x ----> the number of years

f(x) ----> the population of trout in the lake

we have

$f(x)=360-10x$

This is a linear function in slope intercept form

$f(x)=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

$m=-10\ \frac{trout}{year}$ ---> is negative because is a decreasing function

$b=360\ trouts$ ---> initial value

The y-intercept is the point (0,360)

Find the x-intercept

The x-intercept is the value of x when the value of f(x) is equal to zero

For f(x)=0

$0=360-10x$

Solve for x

$10x=360\\x=36$

The x-intercept is the point (36,0)

Part B) Graph the function

Plot the intercepts and join the points to graph the line

see the attached figure

Part C) Complete the interpretation of the intercepts

The x-intercept is the value of x when the value of f(x) is equal to zero

In this context, the x-intercept is the number of years, when the population of trouts is equal to zero

In 36 years, the population of trouts will be equal to zero

The y-intercept is the value of f(x) when the value of x is equal to zero

In this context, the y-intercept is the population of trouts when the number of years is equal to zero

Initially the population of trouts in the lake was 360 trouts

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4 years ago

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Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of t

nirvana33 [79]

Answer:

$\frac{dr}{dt} = -1.325 \ cm/s$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Calculus

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

Step 1: Define

Given:

$V = \frac{4}{3} \pi r^3$

$\frac{dV}{dt} = -116 \ cm^3/s$

$V = 77 \ cm^3$

Step 2: Solve for r

Substitute: $77 = \frac{4}{3} \pi r^3$
Isolate r term: $\frac{77}{\frac{4}{3} \pi} = r^3$
Isolate r: $\sqrt[3]{\frac{77}{\frac{4}{3} \pi}} = r$
Evaluate: $2.63917 = r$
Rewrite: $r = 2.63917 \ cm$

Step 3: Differentiate

Differentiate the Volume Formula with respect to time t.

Define: $V = \frac{4}{3} \pi r^3$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}$
Simplify: $\frac{dV}{dt} = 4 \pi r^2 \cdot \frac{dr}{dt}$

Step 4: Find radius rate

Substitute in variables: $-116 \ cm^3/sec = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}$
Isolate dr/dt rate: $\frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}$
Evaluate: $-1.3253 \ cm/s = \frac{dr}{dt}$
Rewrite: $\frac{dr}{dt} = -1.3253 \ cm/s$
Round: $\frac{dr}{dt} = -1.325 \ cm/s$