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zaharov [31]
3 years ago
15

Brent purchased a used vehicle that depreciates under a straight-line method. The initial value of the car is $7500, and the sal

vage value is $500. If the car is expected to have a useful life of another 7 years, how much will it depreciate each year?
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
5 0
Let the value of the vehicle be described by the equation
V = a + bx
where x =  number of years since purchase
a,b are constants.

When x = 0, V = $7500. Therefore
a + b*0 = 7500
a = 7500

When x = 7, V = $500. Therefore
7500 + 7b = 500
7b = 500 -7500 = -7000
b = -7000/7 = -1000

The equation is
V = 7500 - 1000x

The slope of this equation is the depreciation rate, and it is -$1000 per year.

Answer: $1000 depreciation per year.

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It would be 39,858,075 by 2100. The population goes up by x3 every 10 years.
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What is the value of x?<br><br><br><br> Enter your answer in the box.<br><br><br> °
pashok25 [27]

Answer:

x = 127 degrees

Step-by-step explanation:

The sum of the interior angles is (n-2)180, so in this case it would be

(6-2)180

(4)180

720

Then you can substitute the given angle measurements to get the equation:

112+133+128+100+120+x = 720

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8 0
3 years ago
A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i
sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0
3 years ago
find the measure of the arc or angle indicated. assume that lines which appear to be diameters are actual diameters just enter t
konstantin123 [22]

Answer:

I think D

if wrong correct me plssssssss

have a nice day

And good luck if you have exam

#Captainpower

8 0
3 years ago
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