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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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What is 2 X (6+ 2 + 8) -4
VladimirAG [237]

Answer:

The correct answer is 32x - 4

Step-by-step explanation:

1) Simplify 6 + 2 to 8.

2x(8 + 8) - 4

2) Simplify 8 + 8 to 16.

2x \times 16 - 4

3) Simplify 2x × 16 to 32x.

32x - 4

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>32x</u><u> </u><u>-</u><u> </u><u>4</u>.

4 0
3 years ago
If f(x) = 2x^3 - 14x^2 + 38x -26 and x-1 is a factor of f(x) find all of the zeros of f(x) algebraically.
Anestetic [448]

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26

f(1) = 2 - 14 + 38 - 26

f(1) = -12 + 38 = + 26

f(1) = 26 - 26

f(1) = 0

=========================

next perform a long division

x -1  || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

          2x^3 - 2x^2

          ===========

                    -12x^2 + 28x

                     -12x^2 +12x

                     ==========

                                  26x -26

                                  26x - 26

                                 ========

                                      0

Now you can factor 2x^2 - 12x + 26

                                 2(x^2 - 6x + 13)

The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

     =============

                 2

x  = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

1

3 +/- 2i

8 0
3 years ago
Please help me, I don't understands this question
Rudik [331]
It would be none because the same would be the reciprocal which would be (-7, -8.75)
8 0
3 years ago
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
olga_2 [115]

Answer:

7\pi cm^2

Step-by-step explanation:

The area of a circle is given by A=\pi r^2

For circle B, the radius is 3 cm, it has an area of \pi *3^2=9\pi cm^2

Circle D also has a radius of 1 cm. Its area is \pi *1^2=\pi cm^2

Circle P also has a radius of 1 cm and area \pi*1^2=\pi cm^2

The area of the shaded region is then 9\pi -\pi-\pi=7\pi cm^2

5 0
3 years ago
Which of the following numbers is irrational?
love history [14]
the square root of three when multiplied by itself if the number three it is more precisely call the principal square root of three the square root of three is an irrational number approved the irrationality
6 0
3 years ago
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