Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
and dividing everything by 2 to simplify a bit:
. Upon analyzing that equation, it looks like we need values for x, y,
, and
. And here's what we were given:
and
In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find
at the instant that
= .5.
Solving for x and y:
and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
so
and now we can fill in our derivative. Remember the derivative was found to be
so
and
and
and multiplying by the reciprocal of the left gives us:
so

The greatest common factor is 2
B because in commutative property of addition the numbers switch but they do not change the sign nor the numbers. hope this helped
Answer:
W=191,000MWH S=27,000MWH
Step-by-step explanation:
OK, let's W be wind electricity generated and S, solar electricity generate.
TOTAL GENERATED: <u>218,000mwh = W + S </u>
RELATION BETWEEN W AND S: <u>W = 2,000mwh + 7S</u>
We have now two equations:
218,000 = W + S
W = 2,000 + 7S
Put th value of W into the 1st equation in order to find S:
218,000 = 2,000 + 7S + S
218,000 = 2,000 + 8S
218,000 - 2,000 = 8S
216,000 = 8S
S = 216,000/8
S = 27,000mwh
Now, we find W.
W = 2,000 + 7*27,000mwh
W = 2,000 + 189,000mwh
W = 191,000mwh
Answer:
4x^4y^6
Step-by-step explanation:
(4x²y³)²=
4x^4y^6