11.
Given:
Differentiate with respect to x, we get
The given point is (3,9)
Substitute x=3 in the derivative, we get
Hence the slope is 3.
12.
Given:
Differentiate with respect to x, we get
The given point is (0,4)
Substitute x=0 in the derivative, we get
Hence the slope is 0.
Answer:
The average rate of change is 0
Step-by-step explanation:
You don't really have to do any math for this problem. The vertex lies at the center of [-2,11] so it means that the slope going across the interval line (x=1) is 0. (i used desmos to graph it)
check image if u wanna do the work
Answer:
Step-by-step explanation:
Solving for x means you have to factor. First factor out the GCF of 2 to get:
and now we'll factor using the regular old method of ac and then factoring by grouping. In our polynomial, a = 3, b = 1, c = -6. Therefore, a times c is 3 * -6 which is -18. We need some combinations of the factors of 18 that will add to give us 1, the b term in the middle. The factors of 18 are:
1, 18
2, 9
3, 6 and that's it. Hm...it seems that won't work, so let's throw this into the quadratic formula, going back to the original and a = 6, b = 2 and c = -12:
and
and
and
and
which finally simplifies to
No wonder that didn't factor using the traditional method of factoring! We could have found that out by finding first the value of the discriminant, but oh well!
1.25 gallons
so we know 0.5 gallons makes 1 pound, and we know that there are at least 2 pounds of butter made.
so we know that there is 1 full gallon of cream used.
however, there is also .5 pounds of butter, so we need to find out the other half.
to do this, we need to split the .5 gallons of cream in half, making 0.25
then, we add 1 + 0.25 gallons to equal 1.25 gallons of cream needed to make 2.5 pounds of butter
The answer is 1.74 I just used a calculator
