Answer: 3 pounds
Step-by-step explanation:
The equation can be set up according to slope form: y=mx+b where x represents cost per round.
$70 = $7.51x + $47.47
Subtract 47.47 to both sides: $22.53 = $7.51x
Divide both sides by 7.51: 3 = x
Answer:
The area is growing at a rate of 
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3 
and we identify such as the following differential rate:
Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find 
.
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):
We now apply the derivative operator with respect to time (
) to this equation, and use chain rule as we find the quadratic form of the radius:
![\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5BA%3D%5Cpi%5C%2Cr%5E2%5D%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%5Cpi%5C%2C%2A2%2Ar%2A%5Cfrac%7Bdr%7D%7Bdt%7D)
Now we replace the known values of the rate at which the radius is growing ( ), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :
which we can round to one decimal place as:
Answer:A chord with length 24 cm at 5 cm from the center gives a radius of 13 cm, using a half-length of 12 cm and the distance of 5 cm in Pythagoras’s theorem to find the radius.
Using the same radius and Pythagoras's theorem again, a chord 10 cm from the circle with radius 13 cm has a half-length of sqrt(69), or a full length of double that, so 2*sqrt(69).
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Answer:
Levi must sell more than 80000 cars per month for the new job to be better than the current job.
Step-by-step explanation:
New Job;
He receives $800 per month plus a commission of 2% or 0.02 of the total price of the cars.
Now, let the total amount he receives in a month be "y" and let the amount of cars sold be x.
Thus;
y = 800 + 0.02x - - - -(eq1)
Current Job:
He receives $1200 per month plus a commission of 1.5% or 0.015 of his total sales.
Thus;
y = 1200 + 0.015x - - - (eq2)
Substituting 800 + 0.02x for y into eq(2) gives;
800 + 0.02x = 1200 + 0.015x
0.02x - 0.015x = 1200 - 800
0.005x = 400
x = 400/0.005
x = 80000
This means Levi must sell more than 80000 cars per month for the new job to be better than the current job.
Answer:
-1/2
or -2/4
Step-by-step explanation:
they are the same
