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2 years ago

The volume of this cylinder is 32π yd2. Find the height.

1 answer:

6 0

The radius of the can is
4 inches.

Explanation:
The formula for volume of a cylinder is:
V=πr2h

Since we know the volume and the height of the can, we can determine the radius.
32
π
=
π
r
2
×
2
Cancelling the similar terms on either side, we get.
32
π
=
π
r
2
×
2
32
=
r
2
×
2
Divide both sides by
2
.
16
=
r
2
Square both sides, remembering that the result has to be a positive integer.
4
=
r
Hence the radius of the cylindrical can is
4
inches.

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Find an equation of the line in the form ax+by=c whose x-intercept is 12 and y-intercept is 4, where a, b, and c are integer

Lostsunrise [7]

Answer:

The equation of the line in $ax+by=c$ form where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0 is:

$x+3y=12$

Step-by-step explanation:

Given:

x-intercept = 12

y-intercept = 4

To find the equation of line in the form $ax+by=c$ where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0.

Solution:

The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as $(x,0)$

Thus, on point of the line is (12,0)

The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as $(0,y)$ .

Thus, on point of the line is (0,4)

Using the two points we can find the slope of the line using the slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

So, slope of the line can b given as:

$m=\frac{4-0}{0-12}$

$m=\frac{4}{-12}$

$m=-\frac{1}{3}$

The slope intercept form of the equation of he line is given as:

$y=mx+b$

where $m$ represents slope of the line and $b$ represents the y-intercept.

So, the equation of the line can be given as:

$y=-\frac{1}{3}x+4$

Multiplying each term by 3 to remove fraction.

$3y=3.-\frac{1}{3}x+4(3)$

$3y=-x+12$

Adding $x$ both sides.

$3y+x=-x+x+12$

$3y+x=12$

Thus, the equation of the line in $ax+by=c$ form where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0 is:

$x+3y=12$

8 0

3 years ago

What are the coordinates of the point on the directed line segment from (-6, -3) to

melamori03 [73]

Given:

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.

To find:

The coordinates of that point.

Solution:

Section formula: If point divides a line segment in m:n, then the coordinates of that point are

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get

$Point=\left(\dfrac{6(5)+5(-6)}{6+5},\dfrac{6(8)+5(-3)}{6+5}\right)$

$Point=\left(\dfrac{30-30}{11},\dfrac{48-15}{11}\right)$

$Point=\left(\dfrac{0}{11},\dfrac{33}{11}\right)$

$Point=\left(0,3\right)$

Therefore, the coordinates of the required point are (0,3).

3 0

3 years ago

What does X = In question 2

OverLord2011 [107]

Answer:

Step-by-step explanation:

10/5=2/1 or 2

4+2=6

6 0

3 years ago

8. While solving the equation log,(8x) – log,(x2 - 1) = log, 3, Karla found possible solutions at x=3

TiliK225 [7]

The possible solution to the equation given is 3 and -1/3

<h3>Laws of logarithm</h3>

Given the logarithmic expression given as:

log,(8x) – log,(x^2 - 1) = log, 3

Applying the product and quotient rule will give:

log(8x/x^2-1) = log3

8x/x^2-1 = 3

Cross multiply

8x = 3x^2 - 3

3x^2 - 8x - 3 = 0

3x^2 -9x + x - 3 = 0

3x(x-3)+1(x-3)

x - 3 = 0 and 3x = -1

x = 3 and -1/3

Hence the possible solution to the equation given is 3 and -1/3

Learn more on logarithm here: brainly.com/question/25710806

3 0

2 years ago

A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under

Ierofanga [76]

Answer:

[8i + 54j + 72k] joules per newton metre square.

Step-by-step explanation:

F(x,y,z) = z2i + 3xyj + 3y2k

F(3,0,0) = 0

F(3,3,1) = 1(2i) + 3(3)(3)j + 3(3)(2k)

= 2i + 27j + 18k

F(0,3,1) = 1(2i) + 3(0)(3)j + 3(3)(2k)

= 2i + 18k

The sum = [4i + 27j + 36k]

Since the particle moves back to the origin, we multiply the above Work Done by 2:

[8i + 54j + 72k]

And since work done is the product of Force and Distance, the S.I. unit is Joules/newton metre square

4 0

3 years ago