To find the area of the curve subject to these constraints, we must take the integral of y = x ^ (1/2) + 2 from x=1 to x=4
Take the antiderivative: Remember that this what the original function would be if our derivative was x^(1/2) + 2
antiderivative (x ^(1/2) + 2) = (2/3) x^(3/2) + 2x
* To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^(1/2) + 2
To find integral from 1 to 4:
Find anti-derivative at x=4, and subtract from the anti-derivative at x=1
2/3 * 4 ^ (3/2) + 2(4) - (2/3) *1 - 2*1
2/3 (8) + 8 - 2/3 - 2 Collect like terms
2/3 (7) + 6 Express 6 in terms of 2/3
2/3 (7) + 2/3 (9)
2/3 (16) = 32/3 = 10 2/3 Answer is B
If Point T is on the line segment S U, then ST + TU = SU, Hence the length of SU is 16.
<h3>What is addition?</h3>
The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
If Point T is on the line segment S U, then ST + TU = SU
Given;
S T = 6 and T U = 10
Substitute
SU = ST + TU
SU = 6 + 10
SU = 16
Hence the length of SU is 16.
Learn more about lines;
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Answer:
-19
Step-by-step explanation:
-20 + 55 + 10 + -15 = 30
30 - 11 = 19
-19
The first one has one solution because the lines intersect at one point.
The second one also has one solution because the lines only intersect at one point.
Cross multiply then solve the equation.
