Ask question

Ask question

All categories

2 years ago

5

What is the rate of change for y = -3x + 2 over the interval [-3, 4]?

1 answer:

Arte-miy333 [17]2 years ago

4 0

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
\stackrel{y}{f(x)}= -3x+2 \qquad 
\begin{cases}
x_1=-3\\
x_2=4
\end{cases}\implies \cfrac{f(4)-f(-3)}{4-(-3)}
\\\\\\
\cfrac{[-3(4)+2]~~-~~[-3(-3)+2]}{4+3}\implies \cfrac{-10~~-~~[11]}{7}
\\\\\\
\cfrac{-21}{7}\implies \cfrac{-3}{1}\implies -3$

You might be interested in

20 POINTS Which situation shows the constant rate of change

IceJOKER [234]

The answer is A(jsjsjjsusudidjdidj)

5 0

3 years ago

Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long.

givi [52]

<h2>Hello!</h2>

The answer is: There are a total of 16 skits in the video.

<h2>Why?</h2>

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

$TotalDuration=Introduction+n*Skit$

Second equation:

$Skit=6Minutes$

Where,

$TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes$

So, replacing and substituting the second equation into the first equation we have:

$101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16$

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

$101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes$

Have a nice day!

8 0

2 years ago

Last month, Rhonda earned $3200. Of that amount, she spent $1350 on rent. What percent of her income went to rent, to the neares

Reika [66]

Divide 1350 by 3200.

1350 ÷ 3200 = 0.422

42.2% of her income went to rent.

6 0

2 years ago

Can y'all please help.

sattari [20]

Answer:

See explanation

Step-by-step explanation:

<u>Step 1.</u> Substitute for d to solve for n:

From the first equation:

$d=70-n$

Then substitute it into the second equation:

$0.1(70-n)+0.05n=5.5\\ \\7-0.1n+0.05n=5.5\\ \\7+(-0.05n)=5.5\\ \\-0.05n=5.5-7=-1.5\\ \\n=\dfrac{-1.5}{-0.05}=30$

<u>Step 2:</u> Substitute for n to solve for d:

$d+n=70\\ \\d+30=70\\ \\d=70-30=40$

There are 40 dimes and 30 nikels in the piggy bank

6 0

3 years ago

A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F. Af

fgiga [73]

Answer:

53.3324

Step-by-step explanation:

given that a thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F.

By Newton law of cooling we have

T(t) = $T+(T_0-T)e^{-kt}$

where T (t) is temperature at time t,T =surrounding temperature = 40, T0 =70 = initial temperature

After half minute thermometer reads 60° F. Using this we can find k

$T(0,5) = 40+(70-40)e^{-k/2} = 60\\e^{-k/2} =2/3\\-k/2 = -0.4055\\k = 0.8110$

So equation is

$T(t) = 40+(30)e^{-0.8110t}\\$

When t=1,

we get

$T(1) = 40+(30)e^{-0.8110}\\\\=53.3324$

5 0

2 years ago