Ratio of two volume cylinders (Geometry)

If two similar cylinders have heights of 75cm and 25cm. What is the
ratio of the volume of the larger cylinder to the volume of the smaller
cylinder? Can someone please explain in detail. Thank you!

Answers

Answer 1

Answer: The ratio of the lengths is 75 : 25 or 3 : 1

The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2
(In working out the area the radius is squared)

The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3
(In working out the volume the radius is cubed)

Hopefully this explains it

Answer 2

Answer: V1 = π* ( r1)^2 * 75;
V2 = π* ( r2)^2 * 25;

V1/V2 = (r1/r2)^2 * 3.

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Find the 30th term of the following sequence. 1, 7, 13, 19, ... 174 175 180 181.

Answers

Checking if the sequence is an arithmetic sequence 7 - 1 = 6 13 – 7 = 6 Therefore the sequence is arithmetic, with a_0 = 1 and d = 6 a_n = a_0 + (n-1)d a_30 = 1 + (29)(6) = 175 Therefore the 30th term is 175.

the rule is : 6n - 5 to find the 30th term replace n with 30 6× 30 - 5 = 175

The three sides of a triangle are tangent to a unique circle called the incircle. On the coordinate plane, the incircle of ABC has its center at the origin. The lines whose equations are x+4y=6s(qrt17), 2x+(sqrt5)y=-18, and 2(sqrt2)x=y+18 contain the sides of ABC. What is the length of the radius of the incircle?sqrt= square root

A. 2 units
B. 3 units
C. 6 units
D. 8 units

Answers

We are looking for the length of a radius.

If we can find the coordinates of the two endpoints of a radius, then we can find its length.

A tangent to a circle intersects the circle at a single point.

A radius of the circle drawn to the point of tangency is perpendicular to the tangent.

We know the center of the circle is the origin. That means we know one endpoint of every radius.

We use one side of the triangle which is given as an equation.

We find its slope. Then using that slope and the coordinates of the origin,

we can find the equation of the radius that is perpendicular to that side.

We then solve the equations simultaneously to find the coordinates of the point of tangency. The point of tangency is the other endpopint of the radius.

Knowing two endpoints of a radius, we can find its length. That will give us the answer since we are looking for the length of the radius.

Let's use the first given equation.

Find its slope.

$x + 4y = 6 √(17)$

$4y = -x + 6 √(17)$

$y = -(1)/(4)x + (3√(17))/(2)$

The slope of the side of the triangle is -1/4.

The slope of the radius perpendicular to that side is 4.

The equation of the line that contains the radius is

$y - y_1 = m(x - x_1)$

We are told the circle is centered at the origin, so one point on the line containing the radius is (0, 0).

$y - 0 = 4(x - 0)$

$y = 4x$

The line containing the radius is y = 4x.

Now we use the equation of the line containing the side of the triangle and the equation of the line containing the radius as a system of equations to find their point of intersection. That point is the other endpoint of the radius.

$x + 4y = 6 √(17)$

$y = 4x$

Multiply the first equation by 4 and subtract the x-term from both sides.

$16y = -4x + 24 √(17)$

$y = 4x$

Add the equations and solve for y.

$17y = 24 √(17)$

$y = (24 √(17))/(17) = (24)/(√(17))$

Now replace y with the value we found, and solve for x in the second equation.

$(24 √(17))/(17) = 4x$

$(6 √(17))/(17) = x$

$x = (6 √(17))/(17) = (6)/(√(17))$

The coordinates of the point of intersection are

$((6)/(√(17)), (24)/(√(17)))$

This point of intersection is one endpoint of the radius.

The other endpoint of the radius is the origin.

Now we need to find the the length of the radius.

$r = √((x_2 - x_1)^2 + (y_2 - y_1)^2)$

$r = \sqrt{((6)/(√(17)) - 0)^2 + ((24)/(√(17)) - 0)^2}$

$r = \sqrt{(36)/(17) + (576)/(17)}$

$r = \sqrt{(612)/(17)}$

$r = √(36)$

$r = 6$

Answer: The radius is 6 units long, choice C.

Answer:

Step-by-step explanation:

edge21

What is 0.16326530612 as a fraction

Answers

There is an easy steps on how to convert a decimal into a fraction. First is you need to divide it by one(I will reduce it to 3 decimal places so that it would be easily be divided later, it goes 0.163/1). Next is you need to multiply both side by 10 until the decimal number would be gone(goes like this, 163/1000). Lastly simply fit until it became a simplified fraction. So the answer to it is (4/25)

1. A rectangular picture 6cm by 8cm is enclosed by a frame 1/2cm wide. Calculate the area of the frame. A.15sq cm B. 20 sq cm C. 13 sq cm D. 16 sq cm E. 17

Answers

Answer:

The area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Step-by-step explanation:

Length of rectangular picture frame = 6 cm

Width of rectangular picture frame = 8 cm

Area of rectangular picture frame = 6×8 cm² = 48 cm²

Length, excluding 1/2 cm wide frame of rectangular picture = (6–1/2-1/2) = 5 cm

Width, excluding 1/2 cm wide frame of rectangular picture = (8–1/2-1/2) = 7 cm

Area, excluding 1/2 cm wide frame of rectangular picture = 5×7 cm² = 35 cm²

Area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Therefore, the area of 1/2 cm wide frame = 48 - 35 = 13 cm²

It is given that y is directly proportional to x raise to power n and write down the value of n when y metre square is area of a square of length x metre