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ivolga24 [154]
2 years ago
5

Region R is bounded by the curves y = √x, y = 1, and x = 4. A solid has base R, and cross sections perpendicular to the x-axis a

re squares. The volume of this solid is
A. 4/3
B. 8
C. 7/6
D. 15/2

Mathematics
2 answers:
zlopas [31]2 years ago
8 0
The answer is B. hope this helped
Korolek [52]2 years ago
7 0

The cross sections have side length equal to the vertical distance between y = √x and y = 1, or |√x - 1|. The two curves meet at the point (1, 1), and y = √x meets x = 4 at (4, 2), so we'll be integrating with respect to x on the interval [1, 4]. Over this interval, √x ≥ 1, so |√x - 1| = √x - 1.

A cross section of thickness ∆x has volume

(√x - 1)² ∆x = (x - 2√x + 1) ∆x

Then the volume of the solid is

\displaystyle \int_1^4 (x - 2\sqrt x + 1) \, dx = \boxed{\frac76}

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Pavlova-9 [17]

If \frac{6}{10} is multiplied with a fraction less than 1, out of the given options \frac{1}{2} would be the answer.

Explanation:

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  • If \frac{6}{10} is multiplied with 1, we get the value \frac{6}{10}. Since the fraction must be lesser than 1, \frac{6}{10} cannot be an answer. So option 1 cannot be the answer.
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4 0
3 years ago
What is the value of x
My name is Ann [436]
X=3



Explanation:

A straight line equals 180°, and they give you the one angle of 56°, so you know 56+ the other equation has to equal 180

56+4x+112=180
168+4x=180

Subtract 168 from both sides

4x=12

Divide 4 from both sides

X=3


You can check by filling it in.


56+4*3+112=

12+56+112=180
5 0
2 years ago
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Ivenika [448]

Answer:

0.\overline{369} = \frac{41}{111}

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}

4 0
3 years ago
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