Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The processing speeds of Peach brand computers is increasing at a rate of $r(t)$ megahertz per year (where $t$ is the time in years). When $t=4$ , the computers had a processing speed of $2500$ megahertz. $\newline$ What does $2500+\int_{4}^{7} r(t) d t$ represent? $\newline$ Choose $1$ answer: $\newline$ (A) The average rate of change in the processing speed of the computers between $t=4$ and $t=7$ $\newline$ (B) The processing speed of the computers when $t=7$ $\newline$ (C) The net change in processing speeds of the computers between $t=4$ and $t=7$ $\newline$ (D) The average processing speed of the computers between $t=4$ and $t=7$

View step-by-step help

View step-by-step help

Understanding integers

Full solution

Q. The processing speeds of Peach brand computers is increasing at a rate of

r(t)

megahertz per year (where

t

is the time in years). When

t=4

, the computers had a processing speed of

2500

megahertz.

\newline

What does

2500+\int_{4}^{7} r(t) d t

represent?

\newline

Choose

1

answer:

\newline

(A) The average rate of change in the processing speed of the computers between

t=4

and

t=7

\newline

(B) The processing speed of the computers when

t=7

\newline

(C) The net change in processing speeds of the computers between

t=4

and

t=7

\newline

(D) The average processing speed of the computers between

t=4

and

t=7

Understand integral expression: Understand the integral expression. $\newline$ The integral $\int_{4}^{7}r(t)\,dt$ represents the total change in processing speed from time $t=4$ to $t=7$ . This is because the integral of a rate of change gives the net change over the interval.
Interpret initial value: Interpret the initial value. $\newline$ The value $2500$ megahertz is the processing speed at time $t=4$ . This is given in the problem statement.
Combine initial value and integral: Combine the initial value and the integral. Adding the initial processing speed ( $2500$ megahertz) to the integral of the rate of change ( $\int_{4}^{7}r(t)dt$ ) gives us the total processing speed at time $t=7$ . This is because we start with the initial speed and add the change in speed over the time interval.
Match expression to correct answer: Match the expression to the correct answer. $\newline$ The expression $2500 + \int_{4}^{7}r(t)dt$ does not represent an average rate of change (A), nor does it represent an average processing speed (D). It represents the processing speed at a specific time ( $t=7$ ) after accounting for the change from $t=4$ to $t=7$ , which is the net change in processing speed (C).

More problems from Understanding integers

Question

g

can be thought of as a scaled version of

f(x)=|x|

\newline

What is the equation for

g(x)

\newline

1

\newline

g(x)=-\frac{4}{3}|x|

\newline

g(x)=\frac{4}{3}|x|

\newline

g(x)=-\frac{3}{4}|x|

\newline

g(x)=\frac{3}{4}|x|

Posted 2 months ago

Question

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{5}{3}

\newline

What is the equation of the new graph?

\newline

1

\newline

y=-\frac{5}{3}|x|

\newline

y=\frac{3}{5}|x|

\newline

y=-|x-5|+3

\newline

y=|x-3|+5

Posted 4 months ago

Question

\$ 200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

hats. If Aiden purchases only

t

-shirts, he will get

80

\mathrm{t}

-shirts. Which of the following best models the relationship between the number of hats,

h

, and the number of

\mathrm{t}

t

, that Aiden could purchase with this money?

\newline

1

\newline

40 h+80 t=400

\newline

80 h+40 t=200

\newline

5 h+2.5 t=200

\newline

2.5 h+5 t=200

Posted 4 months ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right.

\newline

One of the intersection points is

(-2,2)

\newline

Find the other intersection point. Your answer must be exact.

Posted 4 months ago

Question

\mathbf{2 2}

dollars. Colleen has

x

dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?

\newline

1

\newline

x-22

\newline

x+22

\newline

22 x

\newline

22 x+22

Posted 4 months ago

Question

Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of

30

meters and a depth of

15

meters. He wants to increase the radius to

40

meters and the depth to

20

meters. How much more water will the pond hold, in thousands of cubic meters?

\newline

(Round to the nearest thousand cubic meters.)

Posted 25 days ago

Question

Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are

36

inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?

\newline

1

\newline

32

\newline

42

\newline

55

\newline

60

Posted 18 days ago

Question

Ari thinks the perfect milkshake has

5

scoops of ice cream for every

3

spoonfuls of caramel. Freeze Zone makes batches of milkshakes with

10

scoops of ice cream and

7

spoonfuls of caramel.

\newline

What will Ari think about the amount of caramel in Freeze Zone's milkshakes?

\newline

1

\newline

(A) Freeze Zone's milkshakes have too much caramel.

\newline

(B) Freeze Zone's milkshakes have too little caramel.

\newline

(C) Freeze Zone's milkshakes are just right.

Posted 2 months ago

Question

Nayeli lights a

4 \mathrm{~m}^{2}

12

candles. Citlali lights a

10 \mathrm{~m}^{2}

30

of the same type of candles.

\newline

Whose space is lit brighter?

\newline

1

\newline

(A) Nayeli's area

\newline

(B) Citlali's area

\newline

(C) The spaces are equally bright.

Posted 4 months ago

Question

Lashawn makes scrambled eggs with

3

spoonfuls of salsa for every

2

eggs. Gilberta adds

7

spoonfuls of salsa for every

5

\newline

Whose scrambled eggs have a stronger salsa taste?

\newline

1

\newline

(A) Lashawn's eggs

\newline

(B) Gilberta's eggs

\newline

(C) The dishes of scrambled eggs have equal salsa tastes.

Posted 2 months ago