Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 8x − x2 x = 0 y = 16

Answer:

  1,456

Step-by-step explanation:

The sum of n terms of a geometric sequence with first term a1 and common ratio r is given by ...

  Sn = a1·(r^n -1)/(r -1)

For your series with a1=4, r=3, and n=6, the sum is ...

  S6 = 4·(3^6 -1)/(3 -1) = 2·728 = 1,456

Answer:

[tex]|AB|=30[/tex]

Step-by-step explanation:

From the diagram,

AO=OC=16 units, all radii of a circle are equal.

BO=OC+BC

BO=16+18

BO=34

A tangent to a circle will always meet the radius at right angles.

We use the Pythagoras Theorem to obtain:

[tex]|AB|^2+|AO|^2=|BO|^2[/tex]

[tex]|AB|^2+16^2=34^2[/tex]

[tex]|AB|^2+256=1156[/tex]

[tex]|AB|^2=1156-256[/tex]

[tex]|AB|^2=900[/tex]

Take positive square roots to get:

[tex]|AB|=\sqrt{900}[/tex]

[tex]|AB|=30[/tex]

The answer is:

B. [tex]d\leq 1,640ft[/tex]

From the statement we know that the cheetah can reach a speed of 70 mph, but it can be maintained for no more than 1,640 feet.

The expression "no more than" means that at least it can be reached but never exceeded, it involves that the distance can be less or equal than 1,640 feet but never more than that.

So, the correct option is:

B. [tex]d\leq 1,640ft[/tex]

Have a nice day!

Answer:

[tex](-7, -4)[/tex]

[tex](-4, 2)[/tex]

[tex](-4, 1)[/tex]

Step-by-step explanation:

We know that the point (-6, 1) belongs to the main function g(x)

The transformation

[tex]y = g (x + 1) -5[/tex]

add 1 to the input variable (x) and subtract 5 to the output variable (y)

So the point in the graph of [tex]y = g (x + 1) -5[/tex] is

[tex]x + 1 =-6\\x = -7[/tex]

[tex]y= 1-5\\y = -4[/tex]

The point is:  [tex](-7, -4)[/tex]

The transformation

[tex]y = -2g(x -2) +4[/tex]

subtract two units from the input variable (x), multiply the output variable (y) by -2 and then add 4 units

So the point in the graph of [tex]y = -2g(x -2) +4[/tex] is

[tex]x -2 =-6\\x = -4\\\\y = -2(1)+4\\y = 2[/tex]

The point is:  [tex](-4, 2)[/tex]

The transformation

[tex]y=g(2x+2)[/tex]

Multiply the input variable (x) by 2 and then add two units

So the point in the graph of   [tex]y=g(2x+2)[/tex] is

[tex]2x +2 =-6\\2x = -8\\x=-4[/tex]

[tex]y=1[/tex]

The point is:  [tex](-4, 1)[/tex]

Final answer:

The transformation y=g(x+1)-5 results in the point (-7, -4), the transformation y=-2g(x-2)+4 gives the point (-4, 2), and the transformation y=g(2x+2) results in (-4, 1) on their respective graphs.

Explanation:

If the point (-6, 1) is on the graph of y=g(x), then we need to find the corresponding points for the given transformations of the function g(x).

For the function y=g(x+1)-5, the x-coordinate will be shifted left by 1, and the y-coordinate will be 5 less than the original y value. Therefore, the new point will be (-7, -4).

In the case of y=-2g(x-2)+4, the x-coordinate will be shifted right by 2, and the y value will be scaled by a factor of -2 and increased by 4. If g(x) was 1 when x was -6, then for x-2, g(x) would be 1 when x is -4. So, we plug in the original x value of -6 into this transformation to get (-4, -2*1+4), which simplifies to (-4, 2).

For y=g(2x+2), we find the new x-coordinate by setting 2x+2 = -6, which gives x = -4. The new point does not change the y-coordinate as there's no vertical shift, so the point is (-4, 1).

These transformations illustrate the dependence of y on x and show how function composition and arithmetic operations alter the input-output pairs in a function's graph.

Answer:

12 5/8 tons were delivered by the third truck

Step-by-step explanation:

25 = 6 4/8 + 5 7/8 + x

25 = 12 3/8 + x

- 12 3/8

12 5/8 = x

Answer:

6 3/4

Step-by-step explanation:

5 7/8 * 2 +6 1/2 + X = 25

Do the algebra.

x = 6 3/4

Final answer:

To calculate the flux of the vector field through the given surface, set up a double integral using the dot product of the field and the unit normal vector. Choose the order of integration and determine the limits of integration based on the given triangle in the xy-plane. The double integral will be evaluated to find the flux.

Explanation:

To set up a double integral for calculating the flux of F=3xi+yj+zk through the given surface, we need to determine the limits of integration and the order of integration. Since the triangle in the xy-plane has vertices (0,0), (0,2), and (2,0), the limits of integration for x and y will be from 0 to 2. The order of integration can be either dx dy or dy dx, but let's choose dx dy for this problem.

Therefore, the integrand is the dot product of F and the unit normal vector n to the surface: (3x, y, 1) • (-5, -2, 1). So the integrand is -15x-2y+z.

The limits of integration are x = 0 to x = 2 and y = 0 to y = 2 - x. The double integral to find the flux is:

∫∫R (-15x-2y+z) dx dy, where R represents the region defined by the triangle in the xy-plane.

Answer:

  x = -5

Step-by-step explanation:

We don't know what equation solver you're supposed to use. Here are the results from one available on the web.

4 - 2(x + 7) = 3(x + 5)

4 - 2x - 14 = 3x + 15

-2x - 3x = 15 + 14 - 4

-5x = 25

x = 25/(-5)

Answer: A, inside the circle.

Step-by-step explanation: Because the radius is wider than 4, (4,-1) would be just inside the circle instead of outside. Using the radius, you could determine that all points on the circle extend 5 units from its center, which means that the overall circumference would be past (4,-1).

Hope this helps,

LaciaMelodii :)

Answer:

a)

[tex]y=400(2.5)^{x}[/tex]

b)

3,814,698

c)

16.08 weeks

Step-by-step explanation:

a)

The question presented here is similar to a compound interest problem. We are informed that there are 400 rice weevils at the beginning of the study. In a compound interest problem this value would be our Principal.

P = 400

Moreover, the population is expected to grow at a rate of 150% every week. This is equivalent to a rate of interest in a compound interest problem.

r = 150% = 1.5

The compound interest formula is given as;

[tex]A=P(1+r)^{n}[/tex]

We let y be the weevil population in any given week x. The formula that can be used to predict the weevil population is thus;

[tex]y=400(1+1.5)^{x}\\\\y=400(2.5)^{x}[/tex]

b)

The weevil population 10 weeks after the beginning of the study is simply the value of y when x = 10. We substitute x with 10 in the equation obtained from a) above;

[tex]y=400(2.5)^{10}\\\\y=3814697.3[/tex]

Therefore, the weevil population 10 weeks after the beginning of the study is approximately 3,814,698

c)

We are simply required to determine the value of x when y is

1,000,000,000

Substitute y with 1,000,000,000 in the equation obtained in a) above and solve for x;

[tex]1000000000=400(2.5)^{x}\\\\2.5^{x}=2500000\\\\xln(2.5)=ln(2500000)\\\\x=\frac{ln(2500000}{ln(2.5)}=16.0776[/tex]

Answer:

The solutions of linear equations in the procedure

Step-by-step explanation:

Part 1) we have

x+y=-1 ----> equation A

-6x+2y=14 ----> equation B

Solve the system by elimination

Multiply the equation A by 6 both sides

6*(x+y)=-1*6

6x+6y=-6 -----> equation C

Adds equation C and equation B

6x+6y=-6

-6x+2y=14

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

6y+2y=-6+14

8y=8

y=1

Find the value of x

substitute in the equation A

x+y=-1 ------> x+1=-1 ------> x=-2

The solution is the point (-2,1)

Part 2) we have

-4x+y=-9 -----> equation A

5x+2y=3 ------> equation B

Solve the system by elimination

Multiply the equation A by -2 both sides

-2*(-4x+y)=-9*(-2)

8x-2y=18 ------> equation C

Adds equation B and equation C

5x+2y=3

8x-2y=18

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

5x+8x=3+18

13x=21

x=21/13

Find the value of y

substitute in the equation A

-4x+y=-9 ------> -4(21/13)+y=-9 ----> y=-9+84/13 -----> y=-33/13

The solution is the point (21/13,-33/13)

Part 3) we have

-x+2y=4 ------> equation A

-3x+6y=11 -----> equation B

Multiply the equation A by 3 both sides

3*(-x+2y)=4*3 ------> -3x+6y=12

so

Line A and Line B are parallel lines with different y-intercept

therefore

The system has no solution

Part 4) we have

x-2y=-5 -----> equation A

5x+3y=27 ----> equation B

Solve the system by elimination

Multiply the equation A by -5 both sides

-5*(x-2y)=-5*(-5)

-5x+10y=25 -----> equation C

Adds equation B and equation C

5x+3y=27

-5x+10y=25

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

3y+10y=27+25

13y=52

y=4

Find the value of x

Substitute in the equation A

x-2y=-5 -----> x-2(4)=-5 -----> x=-5+8 ------> x=3

The solution is the point (3,4)

Part 5) we have

6x+3y=-6 ------> equation A

2x+y=-2 ------> equation B

Multiply the equation B by 3 both sides

3*(2x+y)=-2*3

6x+3y=6

so

Line A and Line B is the same line

therefore

The system has infinite solutions

Part 6) we have

-7x+y=1 ------> equation A

14x-7y=28 -----> equation B

Solve the system by elimination

Multiply the equation A by 7 both sides

7*(-7x+y)=1*7

-49x+7y=7 -----> equation C

Adds equation B and equation C

14x-7y=28

-49x+7y=7

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

14x-49x=28+7

-35x=35

x=-1

Find the value of y

substitute in the equation A

-7x+y=1  -----> -7(-1)+y=1 ----> y=1-7 ----> y=-6

The solution is the point (-1,-6)

Answer:

That is true

Step-by-step explanation:

The ratio is a one-to-one measure, literally a ratio of the sides in reduced form.  The area is that one-to-one ratio squared.

Our numbers are already squared, so in order to find the one-to-one we have to take the square roots of both of them.  

[tex]\frac{\sqrt{4} }{\sqrt{64} } =\frac{2}{8} =\frac{1}{4}[/tex].

Answer:

True

step-by-step explanation:

Just in case you needed a second opinion.

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

Side DF is opposite the marked angle, and the hypotenuse is EF, so ...

  sin(60°) = (√3)/2 = DF/(14√3) . . . . . to solve, multiply by the denominator

  DF = (√3)/2·(14√3) = 7·3 = 21

__

Likewise,

  Cos = Adjacent/Hypotenuse

Side DE is adjacent to the marked angle, so ...

  cos(60°) = 1/2 = DE/(14√3) . . . . . to solve, multiply by the denominator

  DE = (1/2)(14√3) = 7√3

Answer:

[tex]t=2.47\ s[/tex]  

The ball takes 2.47 seconds to touch the ground

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is:

[tex]h(t) = h_0 + s_0t -16t ^ 2[/tex]

Where [tex]h_0[/tex] is the initial height, [tex]s_0[/tex] is the initial velocity and t is the time in seconds.

We know that the initial height is:

[tex]h_0 = 4.5\ ft[/tex]

The initial speed is:

[tex]s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s[/tex]

So the equation is:

[tex]h (t) = 4.5 + 37.62t -16t ^ 2[/tex]

The ball hits the ground when when [tex]h(t) = 0[/tex]

So

[tex]4.5 + 37.62t -16t ^ 2 = 0[/tex]

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

[tex]at^2 +bt + c[/tex]

The quadratic formula is:

[tex]t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]

In this case

[tex]a= -16\\\\b=37.62\\\\c=4.5[/tex]

Therefore

[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]

[tex]t_1=-0.114\ s\\\\t_2=2.47\ s[/tex]  

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground

It would take approximately B. 2.47 seconds

The answer is:

Benji requires 90mL per injection.

From the statement we know that dog's weight is 12 kg, and daily injections are required for 3 days, the dose rate is 7.5 mg/kg, so we need to calculate how many mL per injection does Benji require.

We have that:

[tex]Weight=12Kg\\\\Dose=7.5\frac{mL}{Kg}[/tex]

If the dose rate is 7.5 mL per each Kg, how many mL are required for 12 Kg? We can set it up using the following relation:

[tex]7.5mL=1Kg\\x=12Kg\\\\x=\frac{7.5mL*12Kg}{1Kg}=\frac{90mL.Kg}{1Kg}=90mL[/tex]

Hence, we have that there are needed 90 mL per injection.

Have a nice day!

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Final answer:

To determine the probability of the instructor finishing grading before 11:00 P.M., calculate the expected time to grade 40 exams, determine the standard deviation, and then use the z-score to find the corresponding probability from the standard normal distribution.

Explanation:

To tackle these statistics problems, there are several concepts we need to apply including expected value, standard deviation, the central limit theorem, hypothesis testing, and probability. Since only one problem can be answered at a time, I'll focus on the first one you've mentioned about the grading times for exams.

The instructor's time to grade each paper is a random variable with an expected value of 6 minutes and a standard deviation of 6 minutes. When considering the grading of 40 papers, we can use the central limit theorem which suggests that the sum of these independent random variables will be approximately normally distributed given the large number of papers (n=40).

We first calculate the expected total time to grade 40 exams by multiplying the individual exam time's expected value by the number of exams: 6 minutes/exam * 40 exams = 240 minutes. Then, we calculate the standard deviation for the total grading time: 6 minutes/exam * √40 ≈ 37.95 minutes.

To find the probability that the instructor finishes grading before 11:00 P.M., we need to calculate the number of minutes from 6:50 P.M. to 11:00 P.M., which is 250 minutes. Next, we convert this problem into a z-score problem where we find the z-score corresponding to 250 minutes. Finally, we look up this z-score in a standard normal distribution table (or use statistical software) to find the corresponding probability.

Answer: Yes you can using the sum of internal angles in a triangle they add up to 180, so if you add the two given angle measures and them substract the result from 180 you will have the measure of the third angle. Hope this helps. :)

Step-by-step explanation:

Answer:

y = 20

Step-by-step explanation:

x+y+z = 50

x/y = 1/4 so y = 4x

Substitute y = 4x into  x+y+z = 50

x + 4x + z = 50

5x + z = 50

y/z = 4/5 --> 4z = 5y so z =5/4 y

Substitute z =5/4 y into 5x + z = 50

5x + 5/4 y = 50

You can solve for x from these 2 equations

5x + 5/4 y = 50

y = 4x

Substitute y = 4x into 5x + 5/4 y = 50

5x + 5/4 (4x) = 50

5x + 5x = 50

10x = 50

  x = 5

y = 4x = 4 (5) = 20

Answer

y = 20

The sum of the numbers x, y, and z is 50. The ratio of x to y is 1:4, and the ratio of y and z is 4:5

The value of y =20

Given :

The sum of the numbers x, y, and z is 50

The ratio of x to y is 1:4, and the ratio of y and z is 4:5.

The sum of the numbers x, y, and z is 50

The equation becomes [tex]x+y+z=50[/tex]

The ratio of x to y is 1:4

[tex]\frac{x}{y} =\frac{1}{4} \\4x=y\\y=4x[/tex]

Now use the second ratio . the ratio of y and z is 4:5

[tex]\frac{y}{z} =\frac{4}{5}\\5y=4z\\Replace \; y=4x\\5(4x)=4z\\20x=4z\\z=5x[/tex]

Replace y=4x  and z=5x in the first equation

[tex]x+y+z=50\\x+4x+5x=50\\10x=50\\x=5[/tex]

Now we replace x with 5  and find out y

[tex]y=4x\\y=4(5)\\\y=20[/tex]

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According to the recursive formula,

[tex]a_2=a_1+4[/tex]

[tex]a_3=a_2+4=(a_1+4)+4=a_1+2\cdot4[/tex]

[tex]a_4=a_3+4=a_2+2\cdot4=a_1+3\cdot4[/tex]

and so on, with the general formula

[tex]a_n=a_1+(n-1)\cdot4[/tex]

Then

[tex]a_n=-2+4(n-1)=4n-6[/tex]

and the answer is C.

Answer:

C. an = 4n -6

Step-by-step explanation:

Only one of the offered choices gives a1=-2 for n=1.

___

The recursive formula tells you ...

a2 -a1 = 4

The only choices that increase by 4 when n increases by 1 are choices C and D. Of these, choice D gives a1=4·1+6 = 10 ≠ -2.

Choice C gives a1 = 4·1 -6 = -2, as required.

Answer:

Step-by-step explanation:

The base is defined as x. The height is said to be 3 less than 2x, so is (2x-3).

The formula for the area of a triangle is ...

  A = (1/2)bh

Filling in the given values, we have ...

  17.5 = (1/2)x(2x-3)

  35 = 2x^2 -3x . . . . multiply by 2

  2x^2 -3x -35 = 0 . . . . put in standard form

  (2x +7)(x -5) = 0 . . . . . factor

The base is 5 meters; the height is 2·5-3 = 7 meters.

The base and height of the triangle satisfying the given conditions are approximately 4.3 and 5.6 meters, respectively.

The area of a triangle is given by the formula 1/2 * base * height. Here, the area is 17.5 square meters, the base of the triangle is x, and the height of the triangle is 3 meters less than twice its base, therefore the height is 2x-3. Plugging these values into the formula, we get 17.5 = 1/2 * x * (2x - 3).

To solve this equation for x, first simplify the right-hand side, yielding 17.5 = x*(2x - 3). Multiplying this out gives 17.5 = 2x^2 - 3x. Then, rearrange to get the equation in standard quadratic form, resulting in 2x^2 - 3x - 17.5 = 0.

Through using quadratic formula we can find the solution(s) to be approximately x = 4.3 or x = -2.0. Since a negative value for x ? the base of a triangle ? is not possible, we discard that solution. Thus, the base of the triangle is 4.3 meters, and the height would then be 2*4.3 - 3 = about 5.6 meters.

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Answer:Answer: All real numbers greater than -1. Step-by-step explanation: We have to find the range of: y= 2e^x-1. We know that e^x lies in (0,∞). Hence, 2e^x lies in (0,∞). Hence, 2e^x-1 lies in (-1 ...

Step-by-step explanation:Answer: All real numbers greater than -1. Step-by-step explanation: We have to find the range of: y= 2e^x-1. We know that e^x lies in (0,∞). Hence, 2e^x lies in (0,∞). Hence, 2e^x-1 lies in (-1 ...

Answer:

B. All real numbers greater than –1.

Step-by-step explanation:

We have been given a function [tex]y=2e^x-1[/tex]. We are asked to find the range of our given function.  

We know that the range of an exponential function [tex]f(x)=c\cdot n^{ax+b}+k[/tex] is [tex]f(x)>k[/tex].

Upon looking at our given function, we can see that [tex]k=-1[/tex], therefore, the range of our given function would be [tex]y>-1[/tex] that is all real numbers greater than [tex]-1[/tex].

Answer:

60

Step-by-step explanation:

We have been given the matrix;

[tex]\left[\begin{array}{ccc}5&8\\-5&4\end{array}\right][/tex]

For a 2-by-2 matrix, the determinant is calculated as;

( product of elements in the leading diagonal) - (product of elements in the other diagonal)

determinant = ( 5*4) - (8*-5)

                     = 20 - (-40) = 60

Answer:

c. 60

Step-by-step explanation

math

I hope this helps with you

Answer:

  17.8 hours

Step-by-step explanation:

Serena's bonus on $1200 sales is 15%×$1200 = $180. In order to make $500 for the week, then she must have at least ...

  $500 - 180 = $320

in hourly pay.

At $18 per hour, that requires she work $320/($18/h) = 17.77_7 h.

Serena must work a minimum of about 17.8 hours to make $500.

_____

Comment on the answer

The exact result of the computation is 17 7/9 hours. Many payroll departments record hours to the nearest 1/4 or 1/10 hour. For Serena's pay to be at least $500, she must work 17.8 (rounded to tenths) or 18.0 (rounded to quarters) hours.

diameter and height i think

Answer:

they describe diameter and height

26-diameter

34-height

The inverse of the function f(x) = 3x + 5 is [tex]f^{-1}(x) = \dfrac{x - 5}{3}[/tex]

How to determine the inverse of the function

From the question, we have the following parameters that can be used in our computation:

f(x) = 3x + 5

Express the function as an equation

So, we have

y = 3x + 5

Swap the occurrence of x and y in the equation

This gives

x = 3y + 5

Subtract 5 from all sides

3y = x - 5

So, we have

[tex]y = \dfrac{x - 5}{3}[/tex]

Express as an inverse function

[tex]f^{-1}(x) = \dfrac{x - 5}{3}[/tex]

[tex]f^{-1}(x) = \dfrac{x - 5}{3}[/tex]

Verifying the relationship [tex]f^{-1}(f(x))[/tex] and [tex]f(f^{-1}(x))[/tex]

We have

[tex]f^{-1}(f(x)) = \dfrac{3x + 5 - 5}{3}[/tex]

[tex]f^{-1}(f(x)) = \dfrac{3x }{3}[/tex]

[tex]f^{-1}(f(x)) = x[/tex]

Also, we have

[tex]f(f^{-1}(x)) = 3 * \dfrac{x - 5}{3} + 5[/tex]

[tex]f(f^{-1}(x)) = x - 5 + 5[/tex]

[tex]f(f^{-1}(x)) = x[/tex]

Hence, the inverse of the function is [tex]f^{-1}(x) = \dfrac{x - 5}{3}[/tex]

Question

Find the inverse of the function below and write it in the form y = f^-1(x)

Verify the relationshipsf(f^-1(x)) and f^-1(f(x))=x​

f(x)=3x+5

Answer:

Cortex layer

Step-by-step explanation:

The fibrous protein core of the hair, formed by elongated cells containing melanin pigment, is the cortex layer

Answer:

The fibrous protein core formed by elongated cells that contains melanin pigment is the cortex.

Answer:

Choice B is correct;  (10, 60)

Step-by-step explanation:

For Lisa to make a profit, the function R should assume a value greater than 0;

R > 0

We are to determine the interval of x values for which the above expression will be true.

From the graph, R(x) = 0 when x = 10. As x increases from 10 to 60, the value of R(x) remains positive, that is;

R(x) ≥ 0 for values of x in the interval (10, 60)

The domain that she should use in order to only model selling prices for which she will make a profit is thus;

(10, 60)

Answer:

  24

Step-by-step explanation:

Mack can choose any of the 4 for the first visit, any of the remaining 3 for the second visit, either of the remaining 2 for the third visit, then visit the last one. There are 4·3·2·1 = 24 ways Mack can do this.

_____

The number 4·3·2·1 is "four factorial", written as 4! (with an exclamation point). It is the number of ways 4 objects can be ordered, called the number of permutations of 4 objects.

Answer:

first u should find the radius .radius is half of diameter 12/2=6 so surface area of sphere is 4*3.142*6*6=452.448 square in