Plz dont be mean to me i just wanna understand and also its the blue line for answer 1
(5,-3) (-1,6)
y=mx+b
calculate m:
(-3-6)/(5-(-1)
=-9/6=-1.5
y=-1.5x+b
insert the (5, -3) point to calculate b:
-3=-1.5*5+b
-3=-7.5+b
4.5=b
b=the y intercept, so the line intercepts x=0 at y=4.5
Answer:
$542
Step-by-step explanation:
we know that
The equation of a exponential decay function is given by
where
y is the value of the lawnmower
x is the time in years
a is the initial value
r is the rate of change
we have
substitute
For x=5 years
Answer:
- y = 81-x
- the domain of P(x) is [0, 81]
- P is maximized at (x, y) = (54, 27)
Step-by-step explanation:
<u>Given</u>
- x plus y equals 81
- x and y are non-negative
<u>Find</u>
- P equals x squared y is maximized
<u>Solution</u>
a. Solve x plus y equals 81 for y.
y equals 81 minus x
__
b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.
P equals x squared left parenthesis 81 minus x right parenthesis
__
c. Find the domain of the function P found in part b.
left bracket 0 comma 81 right bracket
__
d. Find dP/dx. Solve the equation dP/dx = 0.
P = 81x² -x³
dP/dx = 162x -3x² = 3x(54 -x) = 0
The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...
P is maximized at (x, y) = (54, 27).
