What is the measure of angle ABC of a circle

The volume of a cylinder of height 8 cm is 72π cm3 Find the radius of the cylinder.

SVEN [57.7K]

Answer:

3 cm

Step-by-step explanation:

Divide the volume by the height

72π/8 = 9π

Now we have the surface area. The surface area is π $r^{2}$ , so we reverse it.

Divide the number by π:

9π/π=9

Now we find the square root

3 x 3 is 9, so 3 is the square root and radius.

8 0

2 years ago

Let $X,$ $Y,$ and $Z$ be points such that $\frac{XZ}{XY} = \frac{ZY}{XY} = \frac{1}{2}.$ If $Y = (1, 7)$, $Z = (-1, -7)$, then w

BlackZzzverrR [31]

Answer:

Coordinates of point X = (-3, -21)

The sum of the coordinates of X = - 24

Step-by-step explanation:

There are 3 points, X, Y and Z.

Let the coordinates of point X be (x, y)

Y = (1, 7)

Z = (-1, -7)

(XZ/XY) = (ZY/XY) = (1/2)

The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate system is given as

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

Therefore,

XZ = √[(x + 1)² + (y + 7)²]

XY = √[(x - 1)² + (y - 7)²]

ZY = √[(-1 - 1)² + (-7 - 7)²] = √(4 + 196) = 14.14

From the relation

(XZ/XY) = (ZY/XY) = (1/2)

We can deduce that

(XZ/XY) = (1/2)

(ZY/XY) = (1/2)

XZ = ZY

(XZ/XY) = (1/2)

XY = 2XZ

√[(x - 1)² + (y - 7)²] = 2(√[(x + 1)² + (y + 7)²]

Square both sides

(x - 1)² + (y - 7)² = 4[(x + 1)² + (y + 7)²]

x² - 2x + 1 + y² - 14y + 49 = 4[x² + 2x + 1 + y² + 14y + 49]

x² - 2x + 1 + y² - 14y + 49 = 4x² + 8x + 4 + 4y² + 56y + 196

3x² + 10x + 3 + 3y² + 70y + 147 = 0

3x² + 3y² + 10x + 70y + 150 = 0 (eqn 1)

(ZY/XY) = (1/2)

XY = 2ZY

√[(x - 1)² + (y - 7)²] = 2(14.142)

Square both sides

(x - 1)² + (y - 7)² = 4(200) = 800

x² - 2x + 1 + y² - 14y + 49 = 800

x² + y² - 2x - 14y - 750 = 0 (eqn 2)

XZ = ZY

√[(x + 1)² + (y + 7)²] = 14.142

Square both sides

(x + 1)² + (y + 7)² = 200

x² + 2x + 1 + y² + 14y + 49 = 200

x² + y² + 2x + 14y - 150 = 0 (eqn 3)

Rewriting the 3 equations together,

3x² + 3y² + 10x + 70y + 150 = 0

x² + y² - 2x - 14y - 750 = 0

x² + y² + 2x + 14y - 150 = 0

Make (x² + y²) the subject of formula in equation 3

(x² + y²) = -2x - 14y + 150

Substituting this into eqn 1

3x² + 3y² + 10x + 70y + 150 = 0

3(x² + y²) + 10x + 70y + 150 = 0

(x² + y²) = -2x - 14y + 150

3(-2x - 14y + 150) + 10x + 70y + 150 = 0

-6x - 42y + 450 + 10x + 70y + 150 = 0

4x + 28y + 600 = 0

x + 7y = -150

Substitute this into this expression (x² + y²) = -2x - 14y + 150

x = -7y - 150

(x² + y²) = -2x - 14y + 150

(-7y - 150)² + y² = -2(-7y - 150) - 14y + 150

49y² + 2100y + 22500 + y² = 14y + 300 - 14y + 150

50y² + 2100y + 22050 = 0

y² + 42y + 441 = 0

y = -21

x = -7y - 150 = -7(-21) - 150 = 147 - 150 = -3

Point X's coordinate = (x, y) = (-3, -21).

The sum of X's coordinate = -2 - 21 = -24

Hope this Helps!!!

6 0

3 years ago

What is the area of the shape below? Hint: use the formula: A =1/2 h (b1 + b2) *

Inga [223]

Answer:

B. 172.5 yd squared

Step-by-step explanation:

FIrst, we must find half of the height, which is 15/2 or 7.5.

Next we have to multiply 7.5 times (15+8) which is B.

5 0

3 years ago

PLZ HELP THIS IS TIMED!!!!

mihalych1998 [28]

Answer:

For the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let $a_1=\frac{-2}{3}$ , $a_2=-4$ , $a_3=-24$ ,...

First find the common ratio

$r=\frac{a_2}{a_1}$ here $a_1=\frac{-2}{3}$ and, $a_2=-4$

$=\frac{-4}{\frac{-2}{3}}$

$=\frac{4\times 3}{2}$

$=\frac{12}{2}$

$r=6$

$r=\frac{a_3}{a_2}$ here $a_2=-4$ and $a_3=-24$

$=\frac{-24}{-4}$

$=6$

$r=6$

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

$a_n=a_1r^{n-1}$

The formula which describes the given geometric sequence is

$f(x)=a_1r^{x-1}$ for x=1,2,3,...

$=\frac{-2}{3}6^{x-1}$ for x=1,2,3,...

Now verify that $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of $a_1$ in $f(x)=a_1r^{x-1}$ for x=1,2,3,...

we get $f(1)=-\frac{2}{3}(6)^{1-1}$

$=-\frac{2}{3}(6)^0$

$=-\frac{2}{3}$

Therefore $f(1)=-\frac{2}{3}$

put x=2 we get $f(2)=-\frac{2}{3}(6)^{2-1}$

$=-\frac{2}{3}(6)^1$

$=-\frac{12}{3}$

Therefore $f(2)=-4$

put x=3 we get $f(3)=-\frac{2}{3}(6)^{3-1}$

$=-\frac{2}{3}(6)^2$

$=-\frac{2(36)}{3}$

Therefore $f(3)=-24$

Therefore the sequence is f(1),f(2),f(3),...

Therefore the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

7 0

3 years ago

Read 2 more answers

Write the equation of the line that has a slope of 2 and passing through (3,-4) point

wel

Answer:

$y=2x-10$

Step-by-step explanation:

We know that the line has a slope of 2 and it passes through the point (3, -4).

So, we can use the point-slope form:

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

Where m is the slope and (x₁, y₁) is a point.

So, let’s substitute 2 for m and (3, -4) for (x₁, y₁). This yields:

$y-(-4)=2(x-3)$

Solve for y. Distribute the right:

$y+4=2x-6$

Subtract 4 from both sides. Therefore, our equation is:

$y=2x-10$

4 0

3 years ago