the sum of three numbers is 144. the third number is 4 times the first. the second number is 6 more than the first. what are the
1 answer:
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Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
Then, an antiderivative of this is:
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and
Since this this function is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
Answer:
Length: 6 m
Width: 4 m
Step-by-step explanation:
Area: 24
Width: 2L - 8 m
Length: ?
Formula: A = W * L
Replace the variables:
24 = (2L - 8) * L
24 = 2 - 8L
0 = 2 - 8L - 24
or
2 - 8L - 24 = 0
Solve; if you don't know how to solve it using this method, let me know. It's the expression
1.
2.
3.
4.
5. (L-6) (2L+4)
6. L-6 = 0 AND 2L+4 = 0
L - 6 =0
L = 6
---------------------------------
2L = -4
L =
L = -2
Since the length cannot be negative, the only real value is 6.
Area: 24
Width: 2L - 8 m
Length: 6 m
Calculate width:
W = 2L - 8
W = 2(6) - 8
W = 12 - 8
W = 4 m