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
Answer:a.35 degrees b. 145 degrees
Step-by-step explanation: angle 2 and angle 6 are equal they are corresponding
Angle 2 and angle 8 are supplementary they equal 180. So 180-35=145
Step-by-step explanation:
The sum of complementary angles is 90°,
Let 1st be 30x then other is 5x,
30x+5x=90°
➡️ 35x=90°
➡️ x=90°/35=(18/7)°
THUS THE FIRST ANGLE =30*18/7=540/7°
AND SECOND =5*18/7=90/7°
Answer:
Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole.