Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0 , y=cos (7x) , x=π/14 , x=0 about the axis x=3

Answer:

  155°

Step-by-step explanation:

∠EYV is half the difference of arcs EV and EH

  (1/2)(EV -EH) = ∠EYV

  (1/2)(EV -85°) = 35° . . . . fill in the given values

  EV -85° = 70° . . . . . . . . .multiply by 2

  EV = 155° . . . . . . . . . . . . add 85°

Answer:

N=920 (1+0.03)^4t

where N=number of cars serviced after t years

Step-by-step explanation:

Apply the compound interest equation

N=P( 1+r/n)^nt

where N ending number of cars serviced , P is the number of cars serviced in 2012, r is the interest rate, n is the number of compoundings per year, and t is the total number of years.

Matching parts of the exponential function

Initial number of cars serviced=920

The quarterly rate of growth = if interest is compounded quarterly, n=4

r=12% ÷ 4 = 0.03 or 3%

The growth rate is given by (1 +r/n) = 1+0.03 = 1.03

number of compoundings for t years= nt= 4t

The compound period multiplied by the number of years = 920(1.03)^4t

Answer:

The number of the 2 kg blocks is 10

The number of the 5 kg blocks is 20

Step-by-step explanation:

Let the number of the 2 kg blocks be x and the number of the 5 kg blocks be y.

The total number of blocks in terms of x and y is;

x + y

We are informed that he has a total of 30 blocks, implying that;

x + y = 30

The total weight of the bar in terms of x and y will be;

2x + 5y

We are also informed that the total weight of the bar is observed to be 120, implying that;

2x + 5y = 120

We therefore have two equations in two unknowns.;

x + y = 30

2x + 5y = 120

We can solve these equations simultaneously via elimination method;

multiply the first equation by 2;

2x + 2y = 60

2x + 5y = 120

Subtracting the first equation from the second one yields;

5y - 2y = 120 - 60

3y = 60

y = 20

But x + y = 30, implying that;

x = 30 - 20

x = 10

By Green's theorem,

[tex]\displaystyle\int_C\cos y\,\mathrm dx+x^2\sin y\,\mathrm dy=\iint_D\left(\frac{\partial(x^2\sin y)}{\partial x}-\frac{\partial(\cos y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

where [tex]D[/tex] is the region with boundary [tex]C[/tex], so we have

[tex]\displaystyle\iint_D(2x+1)\sin y\,\mathrm dx\,\mathrm dy=\int_0^5\int_0^4(2x+1)\sin y\,\mathrm dy\,\mathrm dx=\boxed{60\sin^22}[/tex]

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)+sin^2(x)cot^2(x)\implies sin^2(x)+\underline{sin^2(x)}\cdot \cfrac{cos^2(x)}{\underline{sin^2(x)}} \\\\\\ sin^2(x)+cos^2(x)\implies 1[/tex]

Answer:

  (9x -2)(9x +2)

Step-by-step explanation:

Each of the terms in the difference is a perfect square, so the "perfect square trick" applies. The factors are the sum and difference of the square roots of the given terms.

  81x² - 4 = (9x +2)(9x -2)

Answer:

x = ±[tex]5\sqrt{2}[/tex]

Step-by-step explanation:

We have been given the quadratic equation;

[tex]50-x^{2}=0[/tex]

The first step is to subtract 50 from both sides of the equation;

[tex]50-x^{2}-50=0-50[/tex]

[tex]-x^{2}=-50[/tex]

Multiplying both sides by -1 yields;

[tex]x^{2}=50[/tex]

The final step is to obtain square roots on both sides;

[tex]\sqrt{x^{2} }=\sqrt{50}\\x=+/-\sqrt{50}[/tex]

Therefore, x = ±[tex]5\sqrt{2}[/tex]

Check the picture below.

Answer:C

Step-by-step explanation:

The constant and the variable relationship is p<9.That means it is "Alva spent less than 9%"

Answer:

it is c

Step-by-step explanation:

The compound inequality representing the range of possible values for 'x' (side length BC) in the triangle ABC, given that side lengths AB=13 and AC=21, is 8 < x < 34.

In the triangle ABC with side lengths, AB=13, AC=21, and BC=x, we use the triangle inequality theorem which states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute difference between them. Applying this theorem to your specific situation, we get the compound inequality 8 < x < 34. This inequality represents the range of possible values for the side length x is BC.

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For triangle ABC with sides AB = 13, AC = 21, and BC = x, the range of possible values for x is[tex]\( 8 < x < 34 \)[/tex] based on the triangle inequality theorem.

In triangle ABC, the relationship among its side lengths is governed by the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

For the given triangle with side lengths AB = 13, AC = 21, and BC = x, we can express this relationship as a compound inequality. Let \[tex]( a \), \( b \), and \( c \)[/tex]  represent the lengths of the sides of the triangle. According to the triangle inequality theorem, we have:

[tex]\[ a + b > c \][/tex]

Substitute the given values:

[tex]\[ 13 + x > 21 \][/tex]

Now, solve for[tex]\( x \)[/tex]

[tex]\[ x > 8 \][/tex]

Similarly, for the other pair of sides:

[tex]\[ 21 + x > 13 \][/tex]

Solving for \( x \):

[tex]\[ x > -8 \][/tex]

However, since side lengths cannot be negative, we disregard the second inequality. Therefore, the compound inequality representing the range of possible values for [tex]\( x \) is \( 8 < x < 34 \).[/tex] This means that any value of [tex]\( x \)[/tex] between 8 and 34 (exclusive) will satisfy the conditions for the given triangle.

Answer:

  2 cm and 6 cm

Step-by-step explanation:

The product of the dimensions must be 12 cm². (All answer choices meet that requirement.)

Opposite sides of a rectangle are the same length, so the sum of the two dimensions must be half the perimeter, 8 cm. The sums of the answer choices are ...

Only the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.

6

×

2

Explanation:

For the rectangle

Length

=

ℓ

Breadth

=

b

Area is  

12

cm

2

ℓ

b

=

12

Perimeter is  

16

cm

2

(

ℓ

+

b

)

=

16

ℓ

+

b

=

8

Substitute  

b

=

12

ℓ

from first equation

ℓ

+

12

ℓ

=

8

ℓ

2

+

12

=

8

ℓ

ℓ

2

−

8

ℓ

+

12

=

0

Use quadratic formula (

x

=

−

b

±

√

b

2

−

4

a

c

2

a

) to find  

ℓ

ℓ

=

−

(

−

8

)

±

√

(

−

8

)

2

−

(

4

×

1

×

12

)

2

×

1

ℓ

=

8

±

√

16

2

ℓ

=

8

±

4

2

ℓ

1

=

8

+

4

2

=

6

ℓ

2

=

8

−

4

2

=

2

If  

ℓ

1

is taken as length then  

ℓ

2

is the breadth of the rectangle.

-288/5 or - 57.6 I used a calculator so I cannot solve step by step

Answer:

21 classes

Step-by-step explanation:

Let’s set up equations for both memebers and non-members!

Let c = classes

To find how many classes it would take to make the two things even, we set them equal.

10c+100 = 15c

Solving for c,

5c = 100

So c = 20.

Since you need 20 classes to break even, to save money as a member, you need 21 classes.

Answer:

2.9%

Step-by-step explanation:

The problem says the stations are 260 feet apart.  Assuming that this is the horizontal distance between them, then the grade is:

7.5 / 260 × 100% = 2.9%

This is less than the maximum of 3.5%, so it meets the standards.

Answer:

B. 0.12

Step-by-step explanation:

To obtain this probability, you need to multiply the two probabilities.. since it's comprised of two events: one that he's in the brass section, one that he plays trombone.  The probably of him playing trombone only happens if he's in the brass section.

So, you have the possibility he's in the brass section: 0.50

The possibility he's playing trombone, if he's in the brass section: 0.24

P = 0.5 * 0.24 = 0.12

Answer:

B: 0.12

Step-by-step explanation:

ap3x

Answer:

Step-by-step explanation:

If Thaddeus drives the whole 16 hours, the distance between them is ...

  distance = speed · time

  distance = 20 mi/h · 16 h

  distance = 320 miles.

It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...

  (45 mi)/(5 mi/h) = 9 h

The rest of the 16 hours is the time that Thaddeus drove: 7 hours.

___

Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...

  distance = speed · time

  365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)

  45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms

  (45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x

_____

Comment on the solution

You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.

To solve the problem, we need to set up two equations based on the information given in the problem. Solving the equations simultaneously gives Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.

First, we'll define the variables. Let's say the time Thaddeus has been driving is T hours, and the time Ian has been driving is I hours. The total distance they covered is the sum of the distances each one traveled, which is 365 miles. Thaddeus travels at a rate of 20 mph, while Ian travels at 25 mph. This is represented by the equation 20T + 25I = 365.

Next, we know that the total time they have been driving is 16 hours, which gives us another equation, T + I = 16. Now we have a system of linear equations that we can solve simultaneously to find the values of T and I. The solution gives T = 7 hours and I = 9 hours. Hence, Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.

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So amplitude is the length from the highest (or lowest) point from the mid-line of the function

In this case the mid-line is y = 1

The highest point, which has a y of 3 is 2 units away from the mid-line. This means that the amplitude is 2!

Hope this helped!

The amplitude of the function graphed will be 2.

The amplitude of a function is the amount by which the graph of the function travels above and below its midline, i.e. it is the height from the mean value of the function to its maximum or minimum.

We have,

A graph,

The highest value = 3,

Lowest value = -1

So,

From the definition mentioned above,

Amplitude [tex]=\frac{3+|-1|}{2}[/tex]

We get,

Amplitude = 2

Hence, we can say that the amplitude of the function graphed will be 2.

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Answer:

  x = 21

Step-by-step explanation:

From the rules of secants (and tangents), you know that ...

   x^2 = 7·(7 +56)

   x = √(7·63) = √441 = 21

_____

When secant lines intersect, the product of distances from the point of intersection to the two points on the circle is a constant. The tangent line is a degenerate case where the two points of intersection are the same point (hence the product of distances is x^2). For the other secant, the near distance is 7, and the far distance is 7+56  = 63.

Interestingly, this property holds whether the secants intersect inside the circle or outside (as here). That makes it easier to remember, since there's really only one rule, not three.

Answer: The slope is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The slope can be calculated with the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then, knowing that the line passes through the points (2,1) and (-1,-1), we can substitute the coordinates into the formula.

In this case:

[tex]y_2=-1\\y_1=1\\x_2=-1\\x_1=2[/tex]

Therefore, the slope of the line that passes through the points (2,1) and (-1,-1) is:

[tex]m=\frac{-1-1}{-1-2}\\\\m=\frac{-2}{-3}\\\\m=\frac{2}{3}[/tex]

[tex]S[/tex] is a closed surface with interior [tex]R[/tex], so you can use the divergence theorem.

[tex]\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+9\,\vec k\implies\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(x)}{\partial x}+\dfrac{\partial(y)}{\partial y}+\dfrac{\partial(9)}{\partial z}=2[/tex]

By the divergence theorem, the flux of [tex]\vec F[/tex] across [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over [tex]R[/tex]:

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

Convert to cylindrical coordinates, setting

[tex]x=u\cos v[/tex]

[tex]y=y[/tex]

[tex]z=u\sin v[/tex]

The integral is then

[tex]\displaystyle2\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}\int_{y=0}^{y=8-u\cos v}u\,\mathrm dy\,\mathrm du\,\mathrm dv=\boxed{16\pi}[/tex]

The flux of a vector field across a surface is calculated using a surface integral, which involves integrating the dot product of the vector field and the differential area element over the surface. For closed surfaces, the outward orientation is used. Electric flux, the flux of the electric field across a surface, is mentioned as an example.

The flux of a vector field across a surface can be calculated using a surface integral. For the given vector field F(x, y, z) = x i + y j + 9 k and the surface S defined as the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8, the flux is evaluated by integrating F·dS over the surface S.

The orientation of the surface is important in this process. For a closed surface, the positive (outward) orientation is used. The normal vector at any point on the surface points from the inside to the outside, and this outward normal is used to compute the flux through a closed surface.

Conceptually, this is like breaking the surface up into infinitesimally small patches dA and summing up the contributions of the vector field F (in this case, x i + y j + 9 k) through each patch - this is referred to as electric flux in the context of electric fields. This calculation embodies the concept of electric flux, which is defined as the scalar product of the electric field and the area vector.

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Answer: Hence, Fourth option is correct.

Step-by-step explanation:

Since we have given that

Number of computers expected to sell = 40  millions

Cost price of internet advertising = $5 million

According to the graph, we can see that

40 millions is the y-coordinate and $5 million is the x-coordinate.

so, Horizontal axis - y- axis is the "Number of computers".

Vertical axis - x- axis is the "Advertising cost ":

Hence, Fourth option is correct.

Horizontal axis will have number of computers in millions and vertical axis will have advertising dollars in millions.

Given information:

The graph of computer production and advertising amount spent is given in the question.

Total number of computer sell = 40 millions

Cost of internet advertising = $5 million

Now , by looking the graph one can conclude that, Y coordinate of the graph is 40 million and the X coordinate of the graph is $5 million.

Hence, from the above conclusion one can write as:

Horizontal axis (X-axis) is the number of computers and the Vertical axis is (Y-axis) the advertising cost of computers.

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Hi the answer is 344

Answer:

140

Step-by-step explanation:

54-75=-21

-21+81=60

60-(-27)=87 or 60+27=87

87+53=140

The answer is c. This is the ONLY possible answer.

Answer:

  KM = 20

Step-by-step explanation:

Point V is the midpoint of KM, so ...

  KV = VM

  2.5z = 5z -10

  10 + 2.5z = 5z . . . . . add 10

  10 = 2.5z . . . . . . . . . subtract 2.5z

This is sufficient to answer the question:

  KV = VM = 2.5z = 10

  KM = KV + VM = 10 + 10

  KM = 20

_____

In this case, it is not necessary to find the value of z. If you wanted to, you could divide by the coefficient of z in the last equation:

  10/2.5 = z = 4

Answer: the answer is 6

Step-by-step explanation: 3 times 2 is 6 then 6 times 1 is still 6

Answer: [tex]3!=6[/tex]

Step-by-step explanation:

The factorial function has the following symbol: "!" (As you can observe, it is an exclamation mark).

 The factorial functions are applied to the numbers greater than zero. Then, the factorial of a positive integer "n" is representend as:

[tex]n![/tex]

Since you need to simplify 3!, you has to multiply all the positive  integer numbers that are between the number 3 and and the number 1.

Therefore, for 3! you get the following result:

[tex]3!=3*2*1\\3!=6[/tex]

Answer:

  x = 11°

Step-by-step explanation:

The parallel lines suggest we look to the relationships involving angles and transversals. The angle marked 33° and ∠CAB are alternate interior angles, hence congruent:

  ∠CAB = 33°

5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:

  5x = 2x + 33°

  3x = 33° . . . . . . . . . subtract 2x

  x = 11° . . . . . . . . . . . divide by 3

Answer:

Equation 1:  r = 4 +( 3 * cos theta  )

Equation 2: r = sqrt ( 5² * sin(2 theta) )

Step-by-step explanation:

GRAPH 1:  

The first graph is a dimpled limacon.

General equation for dimpled limacon:

r = a + b cos theta                     ∴ if dimple is along the x- axis

r = a + b sin theta                      ∴ if dimple is along the y-axis

y-intercept : { a, -a }  = { 4, -4 }   ∴ the points at which limacon intersects y-axis

Negative side of x-axis = ( a – b ) ⇒ 1

Positive side of x-axis = ( a + b ) ⇒ 7

Subtract the value of a from sum of a and b to find b:

b = 7 – 4 ⇒ 3

Equation1:  r = 4 +( 3 * cos theta  )

GRAPH 2:  

The second graph is a lemniscates.  

General equation for lemniscates is:

r² = a² cos(2theta)                        ∴ if petals of graph are on coordinate axis

r² = a² sin(2 theta)                ∴ if petals of graph are not on coordinate axis

now, according to the graph:

a = 5 ⇒ a² = 25

angle of graph:  cos2θ, simply divide 360° by 2:

[tex]\frac{360}{2}[/tex] ⇒ 180°

The petals cannot be on coordinate axis, we start from 45° and then the next petal will be on:

45° + 180° = 225°

Since the graph is not on the coordinate axis, so

r² = 5² sin(2 theta)   ⇒    r = sqrt ( 5² * sin(2 theta) )      

Equation 2: r = sqrt ( 5² * sin(2 theta) )      

Explanation:

It is the average (mean) of the absolute values of the differences between a set of numbers and their mean.

Example: consider the set {1, 2, 4}. The mean is computed in the usual way: the sum divided by the number of contributors —

mean = (1 + 2 + 4)/3 = 7/3 = 2 1/3

Then the deviations are ...

1 -2 1/3 = -1 1/3 . . . . the absolute value of this is 1 1/3

2 -2 1/3 = -1/3 . . . . . the absolute value of this is 1/3

4 -2 1/3 = 1 2/3 . . . . the absolute value of this is 1 2/3

The mean of these absolute values is their sum divided by the number of them:

(1 1/3 +1/3 +1 2/3)/3 = (3 1/3)/3 = 1 1/9

The MAD of {1, 2, 4} is 1 1/9.

_____

Your graphing calculator or spreadsheet program may have a function that will calculate this for you.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is g(x) = (1/4 x)^2

It has a horizontal stretch of 4. Since it is horizontal it goes inside the parentheses and becomes the reciprocal of 4  which is  1/4

Hope this helped!

~Just a girl in love with Shawn Mendes