Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
![\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bw%5Cell%5D)
By the Product Rule:
Since we know that dl/dt = 6 and that dw/dt = 5:
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Answer:
78.88%
Step-by-step explanation:
We have been given that
The z-score formula is given by
For 
For 
Now, we find the corresponding probability from the standard z score table.
For the z score -1.25, we have the probability 0.1056
For the z score 1.25, we have the probability 0.8944
Therefore, the percent of the trees that are between 20 and 30 years old is given by
0.8944 - 0.1056
= 0.7888
=78.88%
Answer:
a; she will have $8812
b: It will be enough for her trip
Step-by-step explanation:
In this question, we are tasked with calculating how much a certain value in a savings account that is earning an interest that is compounded annually will be worth.
To calculate this, we use the compound interest formula;
A = P(
Where A is the amount after that number of years which of course we want to calculate
P is the principal amount which is the amount we are investing which is $6439 according to the question
r is the interest rate which is 4% = 4/100 = 0.04
t is the time which is 8 years
n is 1 which is the number of times interest will be compounded annually
We plug these values as follows;
A = 6439(1 + 0.04/1)^8
A = 6439(1.04)^8
A = $8,812.22
This amount is greater then the needed $8,500 for the trip and of course it will be enough
Answer:
The friend caught the ball at 2 feet.
Step-by-step explanation:
1. False; the ball was not still in the air at 1 second the x-component of the vertex is 0.5.
2. False; the x-component of the vertex is 0.5
3. True; the ball was tossed at a height of 2 feet (when x=0, y=2), it is safe to assume the ball was caught at the same height.
4. False; when x = 0, y = 2.
First you need to distribute the -8
So you would get -8x-8 now distribute the 3 so it would be 3x-6
-8x-8+3x-6=-3+2 is how it should look
Now combine the -8x and 3x cause their like terms and also -8 and -6
-5x-14=-3x+2 now add -3 to both sides
-2x-14=2 and add 14 to both sides
-2x=12 all left to do is divide both by -2
X=-6
