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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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Ms. Fontanges wants to put a line of bricks along the back edge of her yard. She needs 35 feet of bricks. The bricks she wants t
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Answer:

$41.16

Step-by-step explanation:

Length of bricks required = 35 feet, length of brick sold = 10 inches, cost of 10 inches brick = $0.98 per brick

Total number of brick required to build the back yard = Length of bricks required ÷ Length of brick sold

1 ft = 12 inches

Number of brick required = (35 * 12) ÷ 10

Number of bricks required = 42 bricks

Cost of brick required = Per length cost of brick * Number of bricks required

Cost of brick required = 0.98 * 42

Cost of brick required = $41.16

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5 0
2 years ago
The area, A, of a triangle is one-half the product of the triangle's base and height. A = A = (12)(5) A = ( b+ h) A = A = (b·h)
polet [3.4K]

Answer:

A = (1/2) * b * h

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as obtuse, scalene, right angle, equilateral and isosceles triangle.

The area of a triangle is half the product of the base of the triangle and the triangle height. The area is given by the formula:

A = (1/2) * b * h

A = (1/2)bh  = 0.5bh

Where A is the area of the triangle, b is the bae of the triangle and h is the height of the triangle.

8 0
3 years ago
A rectangular retaining wall has an area of
Veronika [31]

Answer:

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Step-by-step explanation:

Given as :

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The Height of wall = ( W - 2 ) feet

Now, Area of Rectangle = Height  width

Or , 15 ft² = ( W - 2 ) ft × W ft

Or,  15 = W² - 2 W

Or,   W² - 2 W - 15 = 0

Or,  W² - 5 W + 3 W - 15 = 0

Or, W ( W - 5 ) + 3 ( W - 5 ) = 0

So , ( W - 5 ) ( W + 3 ) = 0

So, W = 5 , - 3

∴ The width of wall = W = 5 feet

And The Height of wall = ( W - 2 ) = 5 - 2 = 3  feet

Hence The height of wall is 3 feet and length of wall is 5 feet. Answer

8 0
3 years ago
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