Mathematics, 02.11.2021 23:40, tilsendt

Can someone help me with part b? I've been stuck on it for an hour :(

Answers: 1

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answered: jtal

Check explanation

Step-by-step explanation:

You're given the equation

A=-0.6t^2 + 37.2t + 243

where t is the number of year after 1980.

I guess you'd have learned the average rate of change equation.

$r=\frac{y_2-y_1}{x_2-x_1}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

You're asked to find average rate of change from

t_1=2000-1980=20

t_2=2015-1980=35

So lets plug that in

$r=\frac{A(t_2)-A(t_1)}{t_2-t_1}$

$r=\frac{A(35)-A(20)}{35-20}$

$r=\frac{[-0.6(35)^2 + 37.2(35) + 243]-[-0.6(20)^2 + 37.2(20) + 243]}{35-20}$

$r=\frac{[-0.6(35)^2 + 37.2(35) + 243]-[-0.6(20)^2 + 37.2(20) + 243]}{15}$

plug that in your calculator to get the answer. I dont have a calculator with me so I can't find the answer.

answered: itsmemichellel

The average rate of change is 4.2 billion kilowatt hours per year.

In other words, the amount of nuclear energy increased, on average, by 4.2 billion kilowatt hours per year from 2000 to 2015.

Step-by-step explanation:

Recall that to find the average rate of change between two points, we simply need to find the slope between the two points.

Hence, to find the average rate of change from 2000 to 2015, find the slope between the points A(20) and A(35):

$\displaystyle \begin{aligned} m_\text{avg} & = \frac{A(35)-A(20)}{(35)-(20)} \\ \\ & = \frac{(810)-(747)}{15} \\ \\ & = \frac{63}{15} = 4.2\end{aligned}$

In conclusion, the amount of nuclear energy increased, on average, by 4.2 billion kilowatt hours per year from 2000 to 2015.

answered: Guest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

answered: Guest

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times