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ycow [4]
2 years ago
13

The base of a solid is bounded by the curve y = sqrt (x+1) the x-axis and the line x = 1. the cross sections, taken perpendicula

r to the x-axis, are squares. find the volume of the solid.
a. 1
b. 2
c. 2.333
d. none of these
(will vote brainlest, like and rate)
Mathematics
1 answer:
Andrei [34K]2 years ago
3 0

See attached for a sketch of some of the cross sections.

Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).

If the thickness of each cross section is ∆x, then the volume of each cross section is

∆V = (√(x + 1))² ∆x = (x + 1) ∆x

As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,

\displaystyle \int_{-1}^1 (x+1) \, dx = \left(\frac{x^2}2 + x\right) \bigg|_{-1}^1 = \boxed{2} ~~~~ (B)

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One root of f(x) = x + 10x2 – 25x – 250 is x = -10. What are all the roots of the function? Use the Remainder Theorem.
Natalka [10]

Answer:

-10

-5

5

Step-by-step explanation:

From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250

The Remainder Theorem is going to take a bit to solve.

You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.

The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.

However just to get the roots, the graph shows that

x = -10

x = - 5

x = 5

The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give

f((10) = 10^3 + 10*10^2 - 25*10 - 250

f(10) = 1000 + 1000 - 250 - 250

f(10) = 2000 - 500

f(10) = 1500 which is  not 0.

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

f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250

f(1) = 1 + 10 - 25 - 250

f(1) = -264 which again is not zero

3 0
3 years ago
Read 2 more answers
Hugo is mixing blue paint with red paint to create purple paint. The ratio of blue to red is 3 to 2. How many pints of blue pain
AysviL [449]
From my calculations I got :
- 24 pints of blue paint
- 16 pints of red paint
3 0
3 years ago
The table shows the heights of 40 students in a class b.) explain why your answer (a) is an estimate
Damm [24]

Answer:

whatssssssssssssssssssss

7 0
3 years ago
Let m = 4 and n = 5
finlep [7]

the answer is c because 4(4)+4(5)=36 and 2(4)^2=16 that 36-16=20 and mn (4*5)=20 so that gives you answer c

 

4 0
3 years ago
Read 2 more answers
Bryan and Jadyn had barbeque potato chips and soda at a football party. Bryan ate 4 oz of chips and drank 1 cup of soda for a to
Inga [223]

Answer:

1 oz of chips has 140 mg of sodium, and 1 cup of soda has 40 mg of sodium.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the amount of sodium in 1oz of chips.

y is the amount of sodium in 1 cup of soda.

Bryan ate 4 oz of chips and drank 1 cup of soda for a total of 600mg of sodium.

This means that 4x + y = 600, also y = 600 - 4x

Jadyn ate 1 oz of chips and drank 4 cups of soda for a total of 300mg of sodium.

This means that:

x + 4y = 300

From the first equation, we have that y = 600 - 4x. So

x + 4(600 - 4x) = 300

x + 2400 - 16x = 300

15x = 2100

x = \frac{2100}{15}

x = 140

y = 600 - 4x = 600 - 4*140 = 40

1 oz of chips has 140 mg of sodium, and 1 cup of soda has 40 mg of sodium.

4 0
3 years ago
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