Find the volume created by revolving the region bounded by y = x^2 and y = √x about the line x = 2 using a different method. show steps

Answer:

sin2x = 16/65

cos2x = -63/65

tan2x = -16/63

Explanation:

the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:

Therefore, we can calculate the value of the hypotenuse as:

With the hypotenuse, we can calculate sin(x) and cos(x) as follows:

We type the negative sign because the question says that sin(x) is negative.

Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)

Therefore, replacing the values, we get:

So, the answers are:

sin2x = 16/65

cos2x = -63/65

tan2x = -16/63

Answer:

2830.6875 hours of sleep per year (7.45 should be 7.75)

Step-by-step explanation:

To find your average sleep per year, you need to covert avg hours per day, to days per year.

Note that 45 minutes is not equivalent to .45 hours, but actually .75 hours since there are only 60 minutes in an hour.  ( 45 / 60 == .75 )

Simply, the amount of days per year is 365.25 (to account for leap years).

So perform this calculation:

(7.75 hrs / day ) * ( 365.25 days / year ) == 2830.6875 hrs / year

Meaning, on average you get 2830.6875 hours of sleep per year.

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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The graph of the inequality 8x ≤ 56 on the number line has a closed circle on 7 and a line extending to the left, representing all values of x less than or equal to 7.

To graph the solution to the inequality 8x ≤ 56 on a number line, you would first find the boundary point by solving for x:
8x = 56
x = 7
Then you would draw a filled-in circle at 7 on the number line to represent the boundary point.
Next, you would determine which side of the number line to shade. Since the inequality is less than or equal to, we would shade to the left of the boundary point (since values less than or equal to 7 satisfy the inequality).

Finally, you would draw an arrow to the left of the filled-in circle to indicate that all values to the left of 7 (including 7) satisfy the inequality.
The final graph should look like this:
<---|======================o---->
   0      7                   10
First, let's solve the inequality:
8x ≤ 56
To find the value of x, divide both sides by 8:
x ≤ 7
Now, let's graph the solution on the number line. Since x is less than or equal to 7, you'll place a closed circle on the number 7 to show that it is included in the solution. Draw a line extending to the left from the closed circle, indicating all the numbers less than 7 are also part of the solution.
Your answer: The graph of the inequality 8x ≤ 56 on the number line has a closed circle on 7 and a line extending to the left, representing all values of x less than or equal to 7.

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Answer:

Bond

Step-by-step explanation:

A promissory note or a promise to repay a certain amount of money at some point in the future is basically a bond.

A bond is a debt security that represents a loan made by an investor to a borrower, which is usually a corporation or government agency. It is a fixed-income investment, meaning that the borrower promises to pay a specific amount of interest over a set period of time and return the principal amount of the loan on the date of maturity. Bonds are issued for various purposes, such as raising capital, funding new projects, or refinancing debt.

CD (Certificate of Deposit) is a savings instrument issued by a bank or credit union that generally pays a fixed rate of interest over a set term. Mutual fund is an investment vehicle that pools money from multiple investors to purchase a portfolio of securities, such as stocks, bonds, or both. Stock is an ownership share in a company that represents a claim on part of the company's assets and earnings.

40% of 250 is 250 × 40/100 = 25 × 4 = 10

Answer:

m (Slope) = 3

Step-by-step explanation:

Slope formula:

m = (y2 - y1) / (x2 - x1)

= (24 - 3) / (9 -2)

= 21 / 7

=3

Answer:

There are 24 different trip possibilities.

Step-by-step explanation:

Here the first thing we need to find is all the individual events, such that each event (or selection) will have a given number of options.

The first event is the selection of the location.

Here the options are: Phoenix, Las Vegas, San Diego, or Los Angeles (4 options)

The second event is the selection of how you go there.

The options are flying or driving (2 options)

The third event is the selection of how many days you will stay there. The options are 3 days, 4 days, and 5 days (3 options).

The total number of different trip possibilities is equal to the product between the number of options for each event.

P = 4*2*3 = 24

There are 24 different trip possibilities.

Answer:

All worked out by Kepler some years ago. A circular orbit is a special (and very unlikely) case of an eliptical orbit.

Step-by-step explanation:

Answer:

\(h = \frac{2A}{b +B } \)

Height= 16 feet

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

f(5) = 13

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² - 12

x = 5

Step 2: Evaluate

Answer:

13

Step-by-step explanation:

replace the x with 5.

5^2-12=

25-12=13

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

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Answer:

Step-by-step explanation:

The parenthesis can cancel because the lack of anything you can do in them, so that will leave you with 7m + 3 + 7m + 6

Next step is to add like numbers, you should start by adding 7m + 7m, which would be 14m.

Next would be to add 3 + 6, which is nine.

To end this equation, simply put 14m + 9

There is no one-number answer because we do not know what m is. So the equation 14m + 9 is the final answer.

Let two consecutive numbers are : x,x+1

Sum of these numbers is -11, then

x+x+1=−11

⇒2x=−11−1=−12

⇒x=−6

and other consecutive number is x+1=−6+1=−5

The answer is -6 and −5

The slope of Line 1 is equal to 1.

The slope of Line 2 is equal to 1/2.

Line 1 and Line 2 are neither parallel nor perpendicular.

In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

For line 1, we have the following:

Slope (m) = (2 - 4)/(-2 - 0)

Slope (m) = -2/-2

Slope (m) = 1.

For line 2, we have the following:

Slope (m) = (1 - 2)/(-4 + 2)

Slope (m) = -1/-2

Slope (m) = 1/2

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The computation of the angle given simply shows that the value of angle x is 109°.

From the information given, it can be noted that two numbers are given and there's a subtraction sign between the numbers given.

Therefore, in this scenario, one simply just has to subtract the numbers. Therefore, thus goes thus:

x = 304 - 115

x = 189

The value of x is 189°.

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Answer:

The correct answer would be 10^0.

Step-by-step explanation:

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Answer: 45

Step-by-step explanation: 2 1/4 = 2hr and 15 min

1/3 of 2hr and 15 min = 45

Amount of time spent by Nathan's family watching the video is 3/4 hour or 45 minutes.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Given that,

Nathan’s family spent 2 and 1/4 hours visiting national monument near their home.

They watched a video in the visitor center for 1/3 of that time.

Total time spent by Nathan's family in the monument = 2 + 1/4 hours

                                                                                         = 9/4 hours

Fraction of time spend in watching the video = 1/3

Time spend in watching the video = 1/3 × 9/4

                                                         = 3/4 hour

                                                         = 45 minutes

Hence the time spent is 3/4 hour.

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Answer:

2s

Step-by-step explanation:

sq pool so total length = 4s

so need 4s/2 = 2s tiles

1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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Note that sides AD and BE are perpendicular on the same side AC. So the angles CAD and CBE, both are equal to 90 degrees.

Beig the corresponding angles, ADC and BEC are also equal.

And the angle ACD is the common angle in both the triangles.

Therefore by the AAA criteria, the triangles CAD and CBE are similar.

So their corresponding sides must be proportional,

The volume of a triangular prism is given by:

Solve for t:

Answer:

13 feet

Step-by-step explanation:

See attached worksheet

Answer:

L to M is 90 degrees

Step-by-step explanation:

Hope this helps!

Answer:

180

Step-by-step explanation:

i straight line is equal to 180

Answer:

The number is 39

Step-by-step explanation:

Let the number at the tens place be x and the number at ones place be y.

Hence, The number is 10x + y.

From the question, the digit at ones place (y) is three times the digit at tens place (x). That is, y is three times x. This means

y = 3x ...... (1)

Also, When 54 is added to the number, its digits are reversed (That is, the resulting number would be 10y + x). This means

10x + y + 54 = 10y + x ...... (2)

Put the value of y = 3x from equation (1) into equation (2) to solve for x

Then,

10x + y + 54 = 10y + x

10x + 3x + 54 = 10(3x) + x

13x + 54 = 30x + x

13x + 54 = 31x

31x - 13x = 54

18x = 54

x = 54/18

x = 3.

Now, Put the value of x = 3 into equation (1) to solve for y

y = 3x

y = 3(3)

y = 9.

Hence, x = 3 and y = 9.

Since the number is 10x + y

Substitute the values of x and y.

Then,

10x + y = 10(3) + 9

=30 + 9

= 39

Hence, the number is 39.

Answer:

it might be 125 cuz it takes 10 100'to make 1000

Answer:

93+30=123 so e equals 123

Step-by-step explanation:

To check, do 123-30=93

The water level drop each​ hour by 0.0384 inch

Firstly, the deacrease in water level is takes as per the question

Decrease = 3/8 inches

Decrease=0.375 inches

Then the time interval is calculated

From 10 pm to  7:45 hours will be 9.45 hours

Time interval= (9 + 45/60) hours

Time interval=9.75 hours

Now, the drop in water level per hour is determined, to do so, total water level decreased is divided by the time taken to decrease that water level

that is 0.375/9.75 inches/hour

= 0.03846 inches/hour

Therefore, if between 10 P.M. and 7:45 A.M.​, the water level in a swimming pool decreased by 3/8 inches and the water level decreased at a constant​ rate, the water level drop each​ hour is 0.03846

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Answer:

I don't know the answer sorry

Answer:

t ≥ 10

Step-by-step explanation:

Since the student needs at least 10 hours of driving time, they need greater than or equal to 10 hours to pass.

let's firstly get the EQUATion, of the graph before we get the inequality.

so we have a quadratic with two zeros, at -6 and 8, hmmm and we also know that it passes through (-2 , 10)

\(\begin{cases} x = -6 &\implies x +6=0\\ x = 8 &\implies x -8=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +6 )( x -8 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=10 \end{cases}\)

\(a ( -2 +6 )( -2 -8 ) = 10\implies a(4)(-10)=10\implies -40a=10 \\\\\\ a=\cfrac{10}{-40}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{1}{4}(x+6)(x-8)=y\implies -\cfrac{1}{4}(x^2-2x-48)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12=y \end{array}}~\hfill\)

now, hmmm let's notice something, the line of the graph is a solid line, that means the borderline is included in the inequality, so we'll have either ⩾ or ⩽.

so hmmm we could do a true/false region check by choosing a point and shade accordingly, or we can just settle with that, since the bottom is shaded, we're looking at "less than or equal" type, or namely ⩽, so that's our inequality

\({\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12\geqslant y \end{array}}\)