.I want a way to solve such a problem​

well, first off, when it comes to volumes by rotation, we'd want to graph them, Check the picture below.  Our rotation over the axis will give us a "washer", so we'll be using the washer method.

now, our axis of rotation is the y-axis or namely x = 0, x = 0 is a vertical line, meaning we have to put the functions in y-terms, that is in f(y) form

[tex]y = x^2\implies \pm\sqrt{y}=x\implies \boxed{\pm\sqrt{y}=f(y)} \\\\\\ y = 4x\implies \cfrac{y}{4}=x\implies \boxed{\cfrac{y}{4}=g(y)}[/tex]

if we look at the picture, the parabola is the farthest from the axis of rotation and the line is the closest, or namely R² and r² respectively.

the way I get the area for R² and r², is by using the same I do with "area under the curve", so if I say call the axis of rotation h(y), the way I get the area is

R => f(y) - h(y)

r => g(y) - h(y)

so let's proceed.

[tex]\textit{area under the curve}\\ \begin{array}{llll} \sqrt{y}- 0\implies &\sqrt{y}\\ \frac{y}{4}-0\implies &\frac{y}{4} \end{array}\qquad \qquad \begin{array}{llll} \stackrel{R^2}{(\sqrt{y})^2}-\stackrel{r^2}{\left( \frac{y}{4} \right)^2}\\[-0.5em] \hrulefill\\ y\qquad -\qquad \frac{y^2}{16} \end{array}[/tex]

now, we want to get the area enclosed by both, and thus we'd need their points of intersection, setting both to [tex]\sqrt{y}=\cfrac{y}{4}[/tex]  which in short gives us the bounds of 0 and 16.

[tex]\pi \displaystyle\int_{0}^{16}\left( y - \cfrac{y^2}{16} \right)dy\implies \pi \int_{0}^{16}y\cdot dy-\pi \int_{0}^{16}\cfrac{y^2}{16}\cdot dy\\\\\\\pi \cdot \left. \cfrac{y^2}{2} \right]_{0}^{16}-\pi \cdot \left. \cfrac{y^3}{48} \right]_{0}^{16}\implies 128\pi -\cfrac{256\pi }{3}\implies \boxed{\cfrac{128\pi }{3}}[/tex]

Answer:

D

Step-by-step explanation:

BH is perpendicular to AC since an orthocenter is a point at which the three altitudes of a triangle intersect. The altitude of a triangle is that line that passes through its vertex and is perpendicular to the opposite side. Since you know that BH is an altitude due to Point H being an orthocenter, you know that BH is perpedendicular to AC.

Answer:

= 130°

Step-by-step explanation:

a far away exterior angle is equal to the sum of two far interior angles

50+80 = x

Answer:

78300 rounded to the nearest hundred is 78300.00 it would basically be the sam thing as 78300

Step-by-step explanation:

Hope this helps :)

Answer:

A. x²- 4x+ 1

option A is the answer

Answer:

C) (0,3)

Step-by-step explanation:

It would be that answer because I found the answer in a website. Its Math-way

Answer:

Step-by-step explanation:

Graph each line on the same plane and take the point of their intersection.

Given linear equations:

See the attached  to confirm the answer is the point (0, 3)

Answer:

LCM of 6 and 9 are 18

1/6 = 1×3/6×3

= 3/18

= 3×10/18×10

= 30/180

1/9 = 1×2/9×2

= 2/18

=2×10/18×10

= 20/180

therefore rational no.s between 1/6 & 1/9 are

21/180,22/180,23/180,24/180,25/180,26/180,27/180,28/180,29/180

Step-by-step explanation:

sorry if im wrong

Answer:

1/18.

Step-by-step explanation:

-1/6 = -3/18 and 1/9 = 2/18

so one rational number between these values is  1/18.

Answer:

It is B

Step-by-step explanation:

Using the midpoint formula, the coordinates of endpoint H are (4, -6).

The midpoint formula is given as: [tex](x_m, y_m) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]

Where,

[tex](x_m, y_m)[/tex] = coordinates of the midpoint

[tex](x_1, y_1)[/tex] = coordinates of the first point

[tex](x_2, y_2)[/tex] = coordinates of the second point

Given the following:

[tex](x_m, y_m)[/tex] = M( 6,-4)

[tex](x_1, y_1)[/tex] = G(8,-2)

[tex](x_2, y_2)[/tex] = H(?, ?)

Plug in the values into the midpoint formula

[tex]M(6, -4) = (\frac{8 + x_2}{2}, \frac{-2 + y_2}{2} )[/tex]

Solve for the x-coordinate and y-coordinate separately

[tex]6 = \frac{8 + x_2}{2}[/tex]

[tex]6 \times 2 = 8 + x_2\\\\12 = 8 + x_2\\\\12 - 8 = x_2\\\\4 = x_2\\\\\mathbf{x_2 = 4}[/tex]

[tex]-4 = \frac{-2 + y_2}{2}\\\\-8 = -2 + y_2\\\\-8 + 2 = y_2\\\\-6 = y_2\\\\\mathbf{y_2 = -6}[/tex]

Therefore, using the midpoint formula, the coordinates of endpoint H are (4, -6).

Learn more about midpoint formula on:

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Answer:

B. 70

Step-by-step explanation:

If 199.50 PHP gets you 2.85KG of rice.

A kilogram of rice would cost = Total Amount / Total Weight.

199.50/2.85

= 70PHP

Answer:

$1650 is the answer hope it helps

Answer:

1

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - 4 / 0 - -2

2 / 2 = 1

Answer:

60

Step-by-step explanation:

→ Work out the change in distance

160 - 40 = 120

→ Work out the change in time

3 - 1 = 2

→ Apple speed = distance over time

120 ÷ 2 = 60

Answer:

[tex]\frac{\sqrt{6} }{4}[/tex], 1.538..., [tex]\frac{19}{7}[/tex], [tex]\sqrt{29}[/tex]

Step-by-step explanation:

Solve them each on the calculator and then put in order

[tex]\frac{\sqrt{6} }{4}[/tex] = 0.6123...

19/7 = 2.714

[tex]\sqrt{29}[/tex] = 5.385...

Answer:

14 minutes

Step-by-step explanation:

For every two minutes the temperature increases by 15 c. since 8 equals 55, 10 is 70, 12 is 85, and 14 is 100.

Answer:

14

Step-by-step explanation:

Answer: - 0.3

Step-by-step explanation:

Correct me if I am incorrect.

Squaring a number means multiplying the same number by itself.

For example,

[tex]\\2 \cdot 2 =2^2\\\\a\cdot a =a^2~~ \\\\ (a+1)(a+1) =(a+1)^2 \\\\ (x^{10}+1)(x^{10}+1) =(x^{10}+1)^2[/tex]

Answer:

  (7, -4)

Step-by-step explanation:

Rotation 180° causes both coordinates to change sign. It is the same as reflection across the origin, or  reflection across both the x- and y-axes.

The image point is (7, -4).

Answer:

$20,000

Step-by-step explanation:

20,000 / 0.07 = 1400

The average distance is 300 yards

The ratio is given as:

Driver : 2-iron = 5 : 4

When the iron driver is 240 yards, we have:

Driver : 240 = 5 : 4

Express as fraction

Driver/240 = 5/4

Multiply both sides by 240

Driver= 300

Hence, the average distance is 300 yards

Read more about ratio at:

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#SPJ1

Answer:

Ez 1+1=3 Duh

Step-by-step explanation:

The equation of the distance of the plane from the city in Ecuador is a

linear  equation that has a constant rate of change.

Reasons:

The equation that estimates the distance of the plane from the city in

Ecuador is d = 2565 - 500·t

Where;

d = The distance in miles from the city in Ecuador

t = The time in hours after taking off from the city in Pennsylvania

Required:

The meaning of -500 in the context of the problem.

Solution:

By using dimensional analysis, we have;

Given that d is in miles and t is in hours, 2,565 is in miles, and 500 × t is in

miles.

Therefore, -500 is in miles per hour, which is the speed of the plane.

The -500 therefore, in the context, is the number of miles, the rate, by

which the plane becomes closer to the city in Ecuador every hour.

Learn more rate of change here:

https://brainly.com/question/1388646

We can  analice through a  dimensional evaluation, every term in any equation.

Solution is:

The term - 500 × t

represents, the quantity of miles travel in the time t

Looking carefully each term in the equation:

d = 2565 - 500×t

And knowing:

We are able to answer the question.

Then in the expression

d = 2565 - 500×t

As d is in miles, we must understand that 2565 is the total distance of the trip, also in miles, should and the product  -500×t must also be in miles. According to that, the number 500 is necessarily in miles/hours (the speed of the plane),  and the negative sign for 500 means that the total distance 2565 miles should be subtracted from the total time of travel.

For instance if t = 1 hour

d = 2565 miles - 500 (miles)/hour × 1 (hour)

As we can see we are able to determine the total time of fly, as the total distance between the cities is 2565, and 500 is the speed of the plane (constant during the whole trip).

For the whole trip

d = 2565 miles    then total fly time is:

2565 (miles)/ 500 (miles/hour)×t

To get .  t = 5.13 h

Related link:https://brainly.com/question/8956323

we need the image to solve the problem

The least common multiple is the smallest expression that can be divided by both of the given expressions.

x^2 - 16 = (x - 4)(x + 4)

x^2 + 4x - 32 = (x + 8)(x - 4)

Both of the factored versions of the expressions have an (x - 4) in them. Thus, that will automatically be included in the LCM. Next, we have to include the (x + 4) and the (x + 8) in our LCM.

LCM = (x - 4)(x + 4)(x + 8)

Hope this helps! :)

Answer:

Step-by-step explanation:

Factorize the given expressions:

The LCM is the product of all unique  factors of both expressions: