Answer:
It's the third option: (x^2 - 5)(x - 7).
Step-by-step explanation:
x^3 – 7x^2 – 5x + 35
= x^2(x - 7) - 5(x - 7) The (x - 7) is common so we have:
(x^2 - 5)(x - 7).
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:
i don't speak spanish
Step-by-step explanation:
Always follow the rules of BOMDAS. (If you don't know them or maybe learned differently tell me).
Firstly multiply 4(1/2) and then substract
8 - 4(1/2)
8 - 2
6
Hope this helps :).
Answer:
Torrance spends 16$ on his brother
Step-by-step explanation:
You have 100$
So, we have
x (brother) + x (sister) + x (mother) = 100
But, since 10$ less will be spent on the sister than the brother, it becomes (x - 10) and twice + 6$ is spent on the mom, it also becomes (2x + 6)
Our equation then becomes
(x - 10) + x + (2x + 6) = 100
X will end up equaling 26. This is how much is spent on the sister.
(x - 10) will be substituted for (26 - 10), which equals 16.
I'm not sure if this is right so you might want to check with somebody (since I may be wrong) I hope this helps you understand how to basically do it though. <3
