The formula for the volume of a cone is V= 1/3pir^2h where V represents the volume, r represents the radius of the base, h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?

Answer:

That makes no sense because there is no A and those measurements are not clear.

Step-by-step explanation:

Answer:

2s = 16

Step-by-step explanation:

In the choir, there are 16 altos and s sopranos.

Let the number of altos be a.

=> a = 16

There are twice as many sopranos as altos.This means that:

a = 2s

Since the number of altos, a, is 16, the equation that represents this situation is:

2s = 16

An equation representing the number of sopranos in a choir, given the number of altos is s = 2 x 16, which simplifies to s = 32.

The question asks us to write an equation to represent the number of sopranos in a choir based on the number of altos. Given that there are 16 altos and the number of sopranos is twice as many, we can represent the number of sopranos as s. The relationship between the altos and sopranos can be expressed mathematically as s = 2 × 16. Therefore, the equation that represents this situation is s = 32, where s stands for the number of sopranos in the choir.

The height of the cone (h) is approximately 12.8 centimeters to the nearest tenth of a centimeter.

To find the height of the cone (h) to the nearest tenth of a centimeter, we can follow these steps:

Calculate the radius (r) of the base:

The formula for the circumference of a circle is C = 2πr.

We are given the base circumference C = 44 cm.

Solving for r, we get: r = C / (2π) ≈ 7.07 cm (round to two decimal places).

Use the Pythagorean theorem to find the height (h):

The Pythagorean theorem states that a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

In this case, the slant height (16.2 cm) is the hypotenuse, and the radius (7.07 cm) and the height (h) are the legs.

Therefore, we can write the equation: 16.2² = 7.07² + h².

Solve for the height (h):

Rearranging the equation to isolate h, we get: h² = 16.2² - 7.07² ≈ 163.97 cm².

Taking the square root of both sides, we get: h ≈ 12.8 cm.

Round the height to the nearest tenth of a centimeter:

Rounding 12.8 cm to the nearest tenth gives us: h ≈ 12.8 cm (to the nearest tenth).

Therefore, the height of the cone (h) is approximately 12.8 centimeters to the nearest tenth of a centimeter.

Final answer:

The height of the cone is calculated using the base radius, found from the given base circumference, and applying the Pythagorean theorem with the slant height as the hypotenuse. The height comes out to be approximately 14.6 cm.

Explanation:

To calculate the height of the cone (h) given its slant height and base circumference, we first need to find the base radius (r) using the formula for the circumference of a circle: C = 2πr. Given that the base circumference is 44 cm, solving for r we get:

r = C / (2π)
 = 44 cm / (2 * 3.1416)
 ≈ 7 cm

Next, we use the Pythagorean theorem in the right-angled triangle formed by the radius, slant height, and the height of the cone. The slant height is the hypotenuse of the triangle, 16.2 cm in this case, and the opposite side to the angle at the cone's base is the height we need to find.

Using the formula h = √(slant height)^2 - (radius)^2, we substitute the values into the equation:

h = √(16.2 cm)^2 - (7 cm)^2
 = √262.44 cm^2 - 49 cm^2
 = √213.44 cm^2
 ≈ 14.6 cm

Therefore, the height of the cone, rounded to the nearest tenth, is 14.6 cm.

Answer:

Step-by-step explanation:

Given:

The volume of a cylinder is 30π cubic units.

A cone shares the same base.

The height of the cone is twice the height of the cylinder.

We need to determine the volume of the cone.

Height of the Cone:

Let h denote the height of the cylinder.

Let H denote the height of the cone.

Since, it is given that, the height of the cone is twice the height of the cylinder, we have;

H=2h

Volume of the cylinder:

The formula to determine the volume of the cylinder is

V=πr^2h

Since, volume of the cylinder is 30π , we get;

30π=πr^2-------(1)

Volume of the cone:

The formula to determine the volume of the cone is

v=1/3πr^2H

Substituting H=2h , we get;

v=1/3πr^2(2h)

v=1/3πr^2h

Substituting equation (1), we get;

V=2/3(30π)

v=20π

Thus, the volume of the cone is 20π

Answer:

The answer is 20pi

Step-by-step explanation:

Answer: B.) x = 6

Step-by-step explanation:

Pythagoras Theorem a^2 +b^2 =c^2

Additionally divide 8 by 2 since it's an isosceles triangle and it's in the middle.

[tex]\sqrt{52}[/tex] ^2 - 4^2= x^2

52 - 16 = x^2

x^2 = 36

Square root both sides = 6

Answer:

60

Step-by-step explanation:

AB is 4 of 5 parts BC is i of 5 parts

75 divided by 5 = 15

75 minus 15=60

Answer: A, (y-1)^2/49-x^2/81=1

The given equations are both hyperbola equations with the center shifted to (0,1). They represent different graphs due to differences in their denominators. Hyperbola equations result in a graph of two separate curves, each one a mirror image of the other.

The equations (y-1)^2/49-x^2/81=1 and (y-1)^2/7-x^2/9=1 are both in the form of the hyperbola equation. This type of equation represents a graph that consists of two separate curves, each one a mirror image of the other, positioned about a central point called the center of the hyperbola. In these particular equations, the center of the hyperbola is shifted from the origin to the point (0,1).

Hyperbola equations are generally in the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 - (x-h)^2/b^2 = 1

However, even though these equations are in the form of hyperbolas, they do not represent identical graphs. In the first equation, the y term is divided by 49 and the x term by 81, whereas in the second, these denominators are 7 and 9. These denominator values affect the shape and orientation of the hyperbolae, leading to different graphical representations for each equation.

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Answer:

R = $ 40

Step-by-step explanation:

Answer:

$40 dollars

i ready

The area of the bedroom is 40 square feet, 10 square feet less than the area of the kitchen.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Given, Gavin is moving into a new apartment that has a kitchen with an area of 50 square feet.

Also given that the area of the kitchen is 10 square feet more than the area of the bedroom.

Let, The area of the bedroom be 'x' square feet.

Therefore, x + 10 = 50.

x = 50 - 10.

x = 40 square feet.

So, The area of the bedroom is 40 square feet.

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Final answer:

The area of the bedroom is 40 square feet, calculated by subtracting 10 square feet from the kitchen's area of 50 square feet.

Explanation:

To find the area of the bedroom, we start with the area given for the kitchen, which is 50 square feet. The problem states that the kitchen is 10 square feet larger than the bedroom. Therefore, to find the area of the bedroom, we subtract the difference from the kitchen area.

Area of bedroom = Area of kitchen - 10 square feet

Area of bedroom = 50 square feet - 10 square feet

Area of bedroom = 40 square feet

Answer:

50

Step-by-step explanation:

The inside of a triangle equals 180 and so you subtract the other two values(100 and 30) to 180 and you get 50.

Answer:

50

Step-by-step explanation:

The sum of the angles of a triangle add to 180

A+B+C = 180

A + 100+ 30 = 180

A + 130= 180

Subtract 130 from each side

A+130-130= 180-130

A = 50

Answer:

B and C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A= very light

B= heavy

C= REALLY HEAVY

Answer:

1.) not safe

2.)

[tex]18 \sqrt{3} [/tex]

Step-by-step explanation:

1.) given the length of the ladder = 15ft.

and the height to the top of ladder when leaned against a wall is 14.8ft. This all forms a right triangle.

with what we are given we can solve for the angle it creates from the ground to the leaned ladder by using the SOHCAGTOA. Whike we do this keep in mind its not safe for a ladder to create an angle more than 70 degrees.

in this case if we are solving for the angle where the height is opposite we will use SOH. because we know the oposite and the hyp. Sin(theta) = opp/hyp

[tex] \sin(theta) = \frac{14.8}{15} [/tex]

[tex]sin^{ - 1} ( \frac{14.8}{15} ) = 81 \: degrees[/tex]

therefore not safe.

2.)

your givin 90 and 60. remember all interior angles add up to 180.

therefore 30 would be the unknown angle.

knowing that we use the chart at the top.

across from 30 is 6. so we put that by x. (remember we are doing this to find the height for our area of a triangle formula = base time height devide by 2.)

we need to find the height so since we kmow what x is we know what is across from 60 which is

[tex]6 \sqrt{3} [/tex]

so we plug that into our formula for area of triangle and u should get 18

[tex] \sqrt{3} [/tex]

Answer:

Tn = 64-4n

Step-by-step explanation:

The nth term of an AP is expressed as:

Tn = a+(n-1)d

a is the common difference

n is the number of terms

d is the common difference

Given the 6th term a6 = 40

T6 = a+(6-1)d

T6 = a+5d

40 = a+5d ... (1)

Given the 20th term a20 = -16

T20 = a+(20-1)d

T20 = a+19d

-16 = a+19d... (2)

Solving both equation simultaneously

40 = a+5d

-16 = a+19d

Subtracting both equation

40-(-16) = 5d-19d

56 = -14d

d = 56/-14

d = -4

Substituting d = -4 into equation

a+5d = 40

a+5(-4) = 40

a-20 = 40

a = 20+40

a = 60

Given a = 60, d = -4, to get the nth term of the sequence:

Tn = a+(n-1)d

Tn = 60+(n-1)(-4)

Tn = 60+(-4n+4)

Tn = 60-4n+4

Tn = 64-4n

Answer:

50 degrees

Step-by-step explanation:

It would be 50 degrees because angle CGD is directly across so the angle measures would be the same

Answer:

360 x 1/10 = 360/10 simplify is 36

36 degrees is 1/10

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

Set the factors equal to 0.

(5k - 3)(9 + k) = 0

The zero product property states that if two terms being multiplied have a product of zero, then at least one of them must be zero.  In our case, this means we can set both (5k - 3) and (9 + k) equal to 0:

5k - 3 = 0

5k = 3

k = 3/5

9 + k = 0

k = -9

The value of k is 3/5 and -9.

Answer:

3

Step-by-step explanation:

49 divided by (5+2) - 2 x (1+1)

49 divided by 7 - 2 x 2

7-4

3

Answer:

C (x,-y)

Step-by-step explanation:

Answer:

x,-y

Step-by-step explanation:

It cannot transform across x axis unless it goes down to negative y.

In a graph we have 4 areas to fit a description of reflect accross an axis.

As this was x axis it can only be reflection negative y or reverse.

We cannot reverse this as the object has the positive y side of x

The image is the reflection or the transformation, and so this image is now negative y.

x-y= x object | y image = positive x = negative y.

Answer:

Point C

Step-by-step explanation:

Answer:

3. C

Step-by-step explanation:

X before Y

Answer:

Step-by-step explanation:

(-3,1) (5,3)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{3-1}{5-(-3)}\\\\=\frac{2}{5+3}\\\\=\frac{2}{8}\\\\=\frac{1}{4}[/tex]

= 0.25

The correct value of the h function is; h= -9.8t² + 45t + 1

Answer:

Using the discriminant, no real solution exists and the baseball will not hit the roof.

Step-by-step explanation:

We are told the height is expressed as;h= -9.8t² + 45t + 1

Also that the Astrodome has a maximum height of 63.4 m

Thus, to find out if the baseball hit at a velocity of 45 m/s will hit the roof, we'll replace h with 63.4m.

Thus;

63.4 = -9.8t² + 45t + 1

Subtract 63.4 from both sides to give;

-9.8t² + 45t + 1 - 63.4 = 0

-9.8t² + 45t - 62.4 = 0

Using quadratic formula, we have;

t = -45 ± √{(45² - (4 * (-9.8) * (-62.4)}

t = -45 ± √(2025 - 2446.08)

t = -45 ± √(-421.08)

The discriminant is -421.08

This value is less than 0.

Thus, no real solution exists and the baseball will not hit the roof.

Answer:

Discriminant = 84

The polynomial has two real distinct roots

Step-by-step explanation:

Given: [tex]f(x)=3x^2+12x+5[/tex]

To find: discriminant of the given function and number of distinct real zeros

Solution:

For a polynomial [tex]f(x)=ax^2+bx+c[/tex] , discriminant is given by [tex]D=b^2-4ac[/tex]

If [tex]D>0[/tex], then the polynomial has two real and distinct roots.

If [tex]D=0[/tex] then the polynomial has two real and equal roots.

If D<0 then roots are not real.

Here, in [tex]f(x)=3x^2+12x+5[/tex]

a = 3, b = 12 and c = 5

[tex]D=(12)^2-4(3)(5)=144-60=84[/tex]

As D > 0, the polynomial has two real distinct roots.

Answer:

The discriminant of F is 84

F has 2 distinct real number zeros

Step-by-step explanation:

The measure of Arc DE is 39 degree.

The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.

Given:

From figure:

m<APB + m<APE = 180 (Linear pair)

4w+ 8 + 4w + 4= 180

8w + 12= 180

8w = 168

w = 21

Also, <APB = <PED + <DPC (Vertical opposite angle)

4w+ 8 = <PED + 2w+ 11

92 = <PED + 53

<PED = 39

So, the measure of Arc DE is 39 degree.

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Answer:

Semicircle radius is 4.5

Radius x radius x 3.14 = area of circle but you divide by 2

4.5 x 4.5 = 20.25 x 3.14 = 63.585/2=31.7925 for semicircle

To find the line for the triangle subtract 16 from the other side which is 8 so the triangle is 8 by 3.

8 x 3 = 24/2=12 for triangle

6 + 3 = 9 the missing side.

9 x 8 = 72 so the rectangle is 72

72 + 12 = 84 + 31.7925 = 115.7925 so that is the area

Circumference is the perimeter for the circle. 9 x 3.14 = 28.26

Perimeter of triangle is 19.544

8 + 9 = 17 x 2 = 34

28.26 + 34 = 62.26 + 19.544 = 81.804

Area is 115.7925 and perimeter is 81.804

Step-by-step explanation:

Answer:

The two numbers are 5 and 12, the lesser is 5.

5 is the lesser number, therefore the answer. Hope this helped! :D

Answer:

35x+5=10

Step-by-step explanation:

We can solve it, but we can't actually use the interactive system they want you to use.  Let's see if we can guide you through it.

My guess is you can control the lines by dragging the two points on the line.

Let's make the green line y = 2x + 3

When x=0 we get y=3, point (0,3).   That's the y intercept, 3 up on the y axis.  Drag one green point there.

When x=2 we get y=7, point (2,7), two to the right, seven  up.  Drag the other green point there.   The green line is now y = 2x + 3.

Similarly the red line is made y = -3x + 3.    When x=0, y=3, point (0,3).  [Surprise!]   When x=2, y=-3, point (2,-3).  Drag the red points to (0,3) and (2,-3).

We already saw where they meet, at (0,3), x=0, y=3, the y intercept of both lines.

Answer: x=0, y=3