The length of the rectangle is 3 feet less than twice its width.

A new computer loses 1/2 of its value every year. Which graph could represent the relationship between the year and the computer

Igoryamba

Let's first consider: the fact that a new computer loses 1/2 of its value

⇒ third choice and fourth choice are eliminated

⇒ because of the graph project the computer's value as growing over

years

Now let's try to set up an equation:

After 1st year ⇒ Computer's value = $total_.value*\frac{1}{2}$

After 2nd year ⇒ Computer's value = $total_.value*\frac{1}{2}*\frac{1}{2}=total_.value*(\frac{1}{2} )^2$

After 3rd year ⇒ Computer's value = $total_.value*\frac{1}{2}*\frac{1}{2}* \frac{1}{2}=total_.value*(\frac{1}{2})^3$

..... (Hopefully you see a pattern)

After x year ⇒ Computer's value = $total_.value*(\frac{1}{2})^x$

Therefore, the equation is: $total_.value*(\frac{1}{2})^x$

⇒that means the graph has to exponentially decreasing as it has

an exponent (meaning the function is exponential) and a base less

than 1 (meaning that the function is decreasing)

Answer: Choice (1)

Hope that helps!

5 0

2 years ago

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func

nadya68 [22]

Answer:

a) C(1,000)=288,491.11 $

b) c(1,000)=288.49 $/u

c) dC/dx(1,000)=349.74 $/u

d) x=100 u

e) c=220 $/u

Step-by-step explanation:

(a) Find the total cost at a production level of 1000 units.

$C(x) = 2,000 + 160x + 4x^{3/2}\\\\C(1,000)=2,000 + 160(1,000) + 4(1,000)^{3/2}\\\\C(1,000)=2,000+160,000+126,491.11= 288,491.11$

(b) Find the average cost at a production level of 1000 units.

$c(x)=C(x)/x\\\\c(1,000)=C(1,000)/1,000=288,491.11/1,000=288.49$

(c) Find the marginal cost at a production level of 1000 units.

$\frac{dC}{dx} =0+160+4*(3/2)x^{3/2-1}=160+6x^{1/2}\\\\dC/dx|_{1,000}=160+6*(1,000)^{1/2}=160+189.74=349.74$

(d) Find the production level that will minimize the average cost.

$c=2,000x^{-1}+160+4x^{1/2}\\\\dc/dx=2,000(-1)x^{-2}+0+4(1/2)x^{-1/2}=0\\\\-2,000x^{-2}+2x^{-1/2}=0\\\\2x^{-1/2}=2,000x^{-2}\\\\x^{-1/2+2}=1,000\\\\x^{3/2}=1,000\\\\x=1,000^{2/3}=100$

(e) What is the minimum average cost?

$c(x) = 2,000/x + 160 + 4x^{1/2}\\\\C(100)=2,000/100 + 160 + 4(100)^{1/2}=20+160+40=220$

5 0

3 years ago

What is the answer I need help

Softa [21]

Answer: A 8040 is exactly divisible by 67 the quotient is 120

3 0

2 years ago

ZABC and ZQRS are supplementary angles.

SVEN [57.7K]

THEOREM:

• Supplementary angle —» The sum of two angles is equal to 180°.

ANSWER:

By supplementary angle property,

So, m∠QRS + m∠ABC = 180°

m∠QRS + 41° = 180°
m∠QRS = 180° - 41°
m∠QRS = 139°

3 0

3 years ago

Read 2 more answers

Jeff is 18 years older than Joe, and Jeff is also 2 1/2 times as old as Joe. How old is Joe?

Yuri [45]

7 years

First of all, half of 18 is 9, and if you divide 18 by 2.5, it results in 7.2. I hope this helps!

6 0

3 years ago