What is 6/4 as a percentage? -Reese in 6th grade

Kwame bought a car for $25,000. The value of the car is decreasing at a rate of 6.5% each year. Write a function that represents

sweet-ann [11.9K]

<h3>The function that represents the price P of the car after x years is:</h3>

$P = 25000(0.935)^x$

Solution:

The decreasing function is given as:

$y = a(1 - r)^t$

Where,

y is future value

a is initial value

r is decreasing rate in decimal

t is time period

From given,

a = 25000

$r = 6.5 \% = \frac{6.5}{100} = 0.065$

number of years = x

future value = P

Therefore,

$P = 25000(1 - 0.065)^x\\\\P = 25000(0.935)^x$

Thus the function is found

8 0

3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

3 years ago

Spending on wars is essentially categorized as government purchases. How do increases in spending on the war in Afghanistan affe

DanielleElmas [232]

With the spending on wars, the aggregate demand falls and the curve will shift towards the left because the production of other goods will reduce in the economy.

Explanation:

When the government of a country spends on the war or the making of the weapons for the war, then the overall working of the economy is affected because the production of goods and services reduces compared to the normal production of goods and services.

With the fall in the production of the goods and the services, the demand also reduces because the overall income of the economy falls. The resources are used to produce war weapons and not consumer goods thus leading to fall in employment, income and so on. Thus the demand curve will shift to the left.

8 0

2 years ago

A pyramid and a cone are both 8 centimeters tall and have the same volume.

Brrunno [24]

Answer:

Step-by-step explanation:

D

6 0

3 years ago

Read 2 more answers

75 points and I’ll give brainlyist and pleas show work

IRISSAK [1]