HELPPP!
Use the mid-point rule with n = 2 to approximate the area of the region bounded by y equals the cube root of the quantity 16 minus x cubed y = x, and x = 0.
Please explain the answer

Answers

Answer 1

Answer:

The approximate area of the region using the midpoint rule with n = 2 is about 2.8418 square units.

Step-by-step explanation:

We want to use the midpoint rule with n = 2 to approximate the area of the region bounded by the graphs of:

[tex]\displaystyle y=\sqrt[3]{16-x^3}, y=x\text{ and } x=0[/tex]

This is shown in the graph below. Our area of interest is between the green, red, and blue lines.

First, find the intersection point of the two graphs:

[tex]\displaystyle x=\sqrt[3]{16-x^3}\Rightarrow x=2\Rightarrow (2, 2)[/tex]

Therefore, we will want to approximate from x = 0 to x = 2.

Note that the red graph (cubic root) is greater than the linear function for all x in the interval [0, 2].

Since the cubic function is greater than the linear function for all x in [0, 2], the area of the region will be the linear function subtracted from the cubic function. Hence:

[tex]\displaystyle \text{Area}=\int_{0}^2\sqrt[3]{16-x^3}-x\, dx[/tex]

We will let:

[tex]f(x)=\sqrt[3]{16-x^3}-x[/tex]

The midpoint rule is given by:

[tex]\displaystyle \text{Area}\approx \sum_{i=1}^nf\left(\frac{x_{i-1}+x_i}{2}\right)\Delta x[/tex]

Since the area is on the interval [0, 2] and n = 2, find the width:

[tex]\displaystyle \Delta x=\frac{2-0}{2}=1[/tex]

Hence, our x-coordinates are x₀ = 0, x₁ = 1, and x₂ = 2.

Therefore, by the midpoint rule:

[tex]\displaystyle \text{Area}\approx \sum_{i=1}^2f\left(\frac{x_{i-1}+x_i}{2}\right)(1)[/tex]

Substitute:

[tex]\displaystyle \text{Area}\approx (1)\left(f\left(\frac{0+1}{2}\right)+f\left(\frac{1+2}{2}\right)\right)[/tex]

Evaluate:

[tex]\displaystyle \text{Area}\approx\displaystyle f\left(0.5\right)+f(1.5)[/tex]

Evaluate:

[tex]\displaystyle \text{Area}\approx(\sqrt[3]{16-(.5)^3}-(.5))+(\sqrt[3]{16-(1.5)^3}-(1.5))}\approx 2.8418[/tex]

Hence, the approximate area of the region is about 2.8418 square units.

Notes:

The exact area is 2.80436... square units.

HELPPP! Use The Mid-point Rule With N = 2 To Approximate The Area Of The Region Bounded By Y Equals The
Answer 2

Answer:

2.8147

Step-by-step explanation:

See the attached writeup!

It's a windy explanation because really short explanations are impossible.  If you're using a textbook, its explanation may be shorter, but probably unclear.


Related Questions

find the vertex of the graph of the following quadratic equations y= -3x^2 -12x-13

Answers

by using the rule -b/2a —> 12/-6= -2

Answer:

Step-by-step explanation:

The vertex is a point. The x value is defined as x = - b / 2a where

a = -3

b = - 12

x = - -12/ 2* -3

x = 12 / - 6

x = -2

what is y when x = - 2?

y = -3(-2)^2 - 12(-2) - 13

y = -12 + 24 - 13

y  = -1

Does the graph agree? It should

The equation is written as

y = -3(x + 2)^2 - 1

$5000 grew to $9000 at the compound interest of 12% per annum what was the years taken for the investment​

Answers

Answer:

1year?hehehehehehehehehe

Please find the answer! <3 tyvm have a great day/night!!!

Answers

Answer:

96

Step-by-step explanation:

area is B*H*L

6*8*2 = Area

96 = Area

A circle has radius 6 cm. Suppose an arc on the circle has length 31 cm. Answer the
following:
a. The fraction of the whole circle represented by this arc is
b. The measure of the central angle defined by the arc is
degrees.
C. The area of the sector defined by the arc is
cm2. (Express answer
in terms of r or pi).

Answers

Answer:

[tex]Fraction = \frac{31}{38}[/tex]

[tex]\theta = 296.18^\circ[/tex]

[tex]Area = 29.62 \pi[/tex]

Step-by-step explanation:

Given

[tex]r = 6[/tex]--- radius

[tex]L = 31[/tex] --- arc length

Solving (a): Fraction represented by the arc

First, calculate the circumference (C)

[tex]C = 2\pi r[/tex]

So, we have:

[tex]C = 2 * 3.14 * 6[/tex]

[tex]C = 38[/tex] --- approximated

So, the fraction represented by the arc is:

[tex]Fraction = \frac{L}{C}[/tex]

[tex]Fraction = \frac{31}{38}[/tex]

Solving (b): Measure of the center angle

Using arc length formula, we have:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

This gives

[tex]31 = \frac{\theta}{360} * 2 * 3.14 * 6[/tex]

[tex]31 = \frac{\theta}{360} * 37.68[/tex]

Make [tex]\theta[/tex] the subject

[tex]\theta = \frac{360 * 31}{37.68}[/tex]

[tex]\theta = 296.18^\circ[/tex]

Solving (c): The area of the sector

This is calculated as:

[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]Area = \frac{296.18}{360} * \pi * 6^2[/tex]

[tex]Area = \frac{296.18}{360} * \pi * 36[/tex]

Divide 360 and 36

[tex]Area = \frac{296.18}{10} * \pi[/tex]

[tex]Area = 29.618 * \pi\\[/tex]

[tex]Area = 29.62 \pi[/tex] --- approximated

What is the volume of a rectangular prism that has a length of 18 inches, a width of 1 foot, and a height of 14 inches?

Answers

Answer:

The volume is 252 inches.

Step-by-step explanation:

Volume is length x width x height so
18 x 1 x 14 is 252

Answer:

3024

Step-by-step explanation:

l * w * h

18 in. * 12 in. * 14 in.

there are 12 inches in 1 foot.

HELP ME WITH THIS PLS! MATH :)

Answers

Answer:

(-7,5)

Step-by-step explanation:

the question was cut off, but I'm assuming that you want to find the location of Denver. Looking at the coordinate plane, Denver, would sit at (-7,5) as you find what x and y values they meet up at. Hopefully this answers your question

If we are looking for the location of Dallas (that is all I see), the coordinates would be as follows.

(2,-4)

Hope this helps.

please tell me where i have to graph this!! also please tell me if i open the dot or not. (NO FILE ANSWERS!!)

Answers

Answer:

Graph at 0 with open circle and arrow pointing right. Right now, all you need to do is open circle

Step-by-step explanation:

Dot at 0 bc 0 is only number in equation

Open circle because there is no "or equal to", so it doesn't include zero

pointing right because right is greater than

Help pls I’ll mark you brainliest

Answers

Answer:

9

Step-by-step explanation:

9

25 points! Please help!

Answers

Answer: 15 minutes

Explanation:

Answer:

17.5(D)

Step-by-step explanation:

So, lets see:

Every 5 minutes, Raul answers 22 questions.

The test has 77 questions.

We must figure out the time it takes to answer all 77 questions.

To do this, lets first divide the total questions by the questions answered per 5 minutes:

77 / 22

=

3.5

I got 3.5 knowing that 3x22 is 66, and half(0.5) of 22 is 11, and 11 plus 66 is 77.

So, the 3.5 is how many times he answrs 22 questions in five minutes.

To make a bit more sense, basically we have to multiply the 5 minutes by the 3.5:

3.5*5

=

17.5

We know that 3 times 5 is 15. Half(0.5) of 5 is 2.5, so 15+2.5 is 17.5.

So the answer is that for the 77 quesitons, it takes 17.5 minutes

HOPe this helps!

csc^ 2 theta- csc^ 2 theta sec^ 2

Answers

Answer:

-csc²θ(tan²θ)

Step-by-step explanation:

csc²θ-csc²θ(sec²θ)

-csc²θ(-1+sec²θ)

-csc²θ(tan²θ)

Question in screenshot

Answers

Answer:

See below

Step-by-step explanation:

[tex]y = {u}^{ \frac{3}{2} } \\ \\ \therefore \: \frac{dy}{du} = \frac{3}{2} {u}^{ \frac{3}{2} - 1 } = \boxed{\frac{3}{2} {u}^{ \frac{1}{2}} } \\ \\ u = 8x + 3 \\ \\ \frac{du}{dx} = 8.1 + 0 = \boxed{8}[/tex]

For all x -4 which of the following is equivalent to the expression below?
x2 + 12x + 32 / x + 4

A. X + 3
B. X + 8
C. X + 11
D. X + 16
E. X + 28

Answers

A and e

Step-by-step explanation:

i did this on khan so I know it

The expression (x² + 12x + 32)/(x + 4) is equivalent to (x+8) option (B) (x+8) is correct.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]=\rm \dfrac{x^2 + 12x + 32} { x + 4}[/tex]

[tex]=\rm \dfrac{(x+4)(x+8)} { x + 4}[/tex]

As it is given, x ≠ -4

We can cross the term (x+4) from the numerator and denominator.

= (x+8)

Thus, the expression (x² + 12x + 32)/(x + 4) is equivalent to (x+8) option (B) (x+8) is correct.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

5th grade math. correct answer will be marked brainliest

Answers

Answer:

C

Step-by-step explanation:

The focus of a parabola is (2, 5) and the directrix is y = 1. What is the equation of the parabola?

Answers

Answer:

y = 0.125x² - 0.5x + 3.5

Hope that this helps!

Answer:

y = 0.125x² - 0.5x + 3.5

Step-by-step explanation:

I dont know if its correct hope it helped

R 408 344 525.2 What i want to know this money is a millions or thousand?​

Answers

Answer:

million

Step-by-step explanation:

please answer ive been having such a bad day today

Answers

Answer:

A - y = 2x + 1

Step-by-step explanation:

2(2) + 1 = 5

2(4) + 1 = 9

2(6) + 1 = 13

Hope this helps <3

Which term describes a fraction that has a polynomial in its numerator and denominator?

Answers

Rational expression refers to a fraction in which the numerator and denominator are polynomials.

Answer:

Rational expression

Step-by-step explanation:

One term of a geometric sequence is a4=135. The common ratio is r=3. Write an explicit rule for the nth term.

Answers

Answer:

[tex]a_{n} = 5 * 3^{n-1}[/tex]

Step-by-step explanation:

To find the nth term of a geometric sequence, you have the general formula:

[tex]a_{1} *r^{n-1}[/tex]

where a1 is the first term and r is the common ratio. In order to find the 4th term, we can substitute what we have(n is 4 because we are looking for the fourth term):

135 = [tex]a_{1} * 3^{4 - 1}[/tex]

135 = [tex]a_{1} * 3^3[/tex]

135 = [tex]27a_{1}[/tex]

[tex]a_{1} = 5[/tex]

Now, we can substitute the first term back in:

[tex]a_{n} = 5 * 3^{n-1}[/tex]

What is a,b,c and d please help me

Answers

Step-by-step explanation:

Edit:

a is 18

b is 36

c is 18

d is 18 times sqr root of 3

Answers:

a = 18b = 36c = 18d = 18*sqrt(3)

sqrt is shorthand for "square root"

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

Explanation:

The smaller triangle on the left is a 45-45-90 triangle (aka isosceles right triangle). One special property of such triangles is that the legs are the same length, meaning a = c. Another special feature is that the hypotenuse is exactly sqrt(2) times that of the leg.

In other words, if x is the leg length, then x*sqrt(2) is the length of the hypotenuse. That means mean a = 18 in order for the hypotenuse to be 18*sqrt(2). This then leads to c = 18 as well.

--------------

The smaller triangle on the right side has a = 18 as the shorter leg, opposite the smallest angle (30 degrees). The hypotenuse b is twice that of the short leg, and this works because we're dealing with a 30-60-90 triangle. Therefore b = 2a = 2*18 = 36.

The longer leg d is equal to sqrt(3) times the short leg, ie,

d = a*sqrt(3)

d = 18*sqrt(3)

You could use the pythagorean theorem to solve for d like so:

a^2 + d^2 = b^2

18^2 + d^2 = 36^2

d^2 = 972

d = sqrt(972)

d = 18*sqrt(3)

I skipped a bunch of steps, but you get the idea.

Find the product of (√2 + √5) (√7 - √5)

PLs help( a guy answered to this image (linked below) said I have to find that to find the answer) pls solve for me! THx :))))

Answers

Answer:

[tex](\sqrt 2 + \sqrt 5)(\sqrt 7 - \sqrt 5) = \sqrt{14} - \sqrt{10} +\sqrt{35} - 5[/tex]

Step-by-step explanation:

Given

[tex](\sqrt 2 + \sqrt 5)(\sqrt 7 - \sqrt 5)[/tex]

Required

Solve

We have:

[tex](\sqrt 2 + \sqrt 5)(\sqrt 7 - \sqrt 5)[/tex]

Open bracket

[tex](\sqrt 2 + \sqrt 5)(\sqrt 7 - \sqrt 5) = \sqrt{2*7} - \sqrt{2*5} +\sqrt{5*7} - \sqrt{5* 5}[/tex]

[tex](\sqrt 2 + \sqrt 5)(\sqrt 7 - \sqrt 5) = \sqrt{14} - \sqrt{10} +\sqrt{35} - 5[/tex]

Is the function shown in the graph one-to-one?


Yes, there exists one input for every output.

No, there exists more than one input for at least one output.

Yes, there exists one output for every input.

No, there exists more than one output for at least one input.

Answers

Yes, there exists one input for every output.

Please can somebody help me

Answers

Answer:

Rectangle: bh or l · w

Circle: pi(r)²

can anyone help please

Answers

Answer:

x = 0, x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given

8x² - 12x = 0 ← factor out 4x from each term

4x(2x - 3) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

Researchers surveyed 250 college students at one time. They were asked if they were taking any engineering classes and whether or not they felt depressed. If 75 students reported taking at least one engineering class and 15 of those students said they were depressed, what is the incidence of depression in this group

Answers

Answer:

the  incidence of the depression is  1 ÷ 5

Step-by-step explanation:

Given that

There is 250 college students that are surveyed

In the case when 75 students reported for minimum ne engineering class

And, out of this 15 students would be depressed

We need to find out the incidence of the depression

So

= 15 ÷ 75

= 1 ÷ 5

Hence, the  incidence of the depression is  1 ÷ 5

A tutoring company would like to understand if most students tend to improve their grades (or not) after they use their services. They sample 220 of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year. Write the null and alternative hypotheses in words.

Answers

Answer:

Null hypothesis :

Grades have not improved for a majority of students

Alternative hypothesis :

Grades have improved for a majority of students

Step-by-step explanation:

The null and alternative hypothesis for this scenario who see the null hypothesis take a midpoint between improvement and decline ; which can be expressed as ;

H0 : p = 0.5

This means that the performance of students is at a centre point where it could swing either way (decline or improve).

To test of grade has improved students, the, the proportion of f students who have proved should be greater. Which is what the test intends.

H1 : p > 0.5

please help will give brainliest

Answers

Answer:

4

Step-by-step explanation:

The number of kids who like vanilla is 13 the number of kids who like strawberry is 9

13-9=4

hope this helps!!

Picture Below
(i have to make this 20 characters so I'm doing this now)

Answers

Answer:

H.

Step-by-step explanation:

16x^2 is the big square area and the -10x comes from subtracting the smaller area from the big one

Answer:

H. is the answer

hope this helps

have a good day :)

Step-by-step explanation:

There are 15 red, 14 green, and 9 yellow balls in a bag. What is the minimum number of balls that Bob needs to take out of the bag (without looking) so that at least 12 the balls are the same color?

Answers

26 balls

Step-by-step explanation:

have to at least take 11 red, 10 green 5 yellow so have 12 balls in bag

The experiment proceeded as normal, with the experimental group hearing about the potential presence of a gun as the confederates left the study and the control group not hearing about the gun. Unfortunately, word spread around campus about a man with a gun who stole a laptop during a study. Unknown to the study researchers, many potential participants participated in the research anyway, and kept an eye out for a gun, knowing that they might be asked about it. The researchers found that those in the experimental group did not differ from those in the control group about the likelihood of a gun. That is, the mean score that a gun was present during the second interview was similar for the experimental group (M = 67%, SD = 12.4%) and the control group (M = 63%, SD = 11.16%).

Maturation
Regression to the mean
Selection
Mortality
Instrumentation
Testing
History
Interactions
Diffusion
No Threat

Answers

Answer:

The answer is "The threat to internal validity is mortality".

Step-by-step explanation:

It signifies that while in terms of your study, persons were "morning." It usually signifies when people leave the studies. There will be only likely if indeed the experiment lasts a long period that it'll be a substantial danger to validity and reliability because the chance for drops increases. Eight content validity risks are history, maturity, instrument, test, choice, average regress, human engagement, and mortality.

If A = –2p + 7 and B = p2 + 3p – 5, find an expression that equals A – 3B in
standard form.

Answers

Answer:

-3p^2 - 11p + 22

Step-by-step explanation:

A - 3B becomes (-2p + 7) - 3*(p^2 + 3p - 5).

Perform the indicated multiplication, obtaining:

                            (-2p + 7) - 3p^2 - 9p + 15, and then:

                              -2p + 7 - 3p^2 - 9p + 15, or (combining like terms):

                             

                                 -3p^2 - 11p + 22

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