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4 years ago

What is the measure of angle X?

Mathematics

1 answer:

grandymaker [24]4 years ago

6 0

Answer: I would say c. or d.

Step-by-step explanation:

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Three water storage containers have the same volume in the shape of a cylinder, a cone, and a sphere. The base radius of the cyl

fredd [130]

Answer:

- The ratio of the height of the cone to the height of the cylinder is 3:1

- The ratio of the height of the cone to radius of the sphere is 4:1

Step-by-step explanation:

Note that the radii of all the structures are the same.

Let the height of the cone be H and the height of the cylinder be h

The volume of each of the shapes are given below as

Volume of cylinder = πr²h

Volume of a cone = (1/3)πr²H

Volume of a sphere = (4/3)πr³

1) The ratio of the height of the cone to the height of the cylinder

To obtain this, we equate the volume of those two structures

Volume of the cone = Volume of the cylinder

(1/3)πr²H = πr²h

πr² cancels out on both sides and we're left with

(H/3) = h

H = 3h

(H/h) = (3/1)

So, The ratio of the height of the cone to the height of the cylinder is 3:1

2) The ratio of the height of the cone to radius of the sphere

Similarly equating the volumes of the cone and the sphere

(1/3)πr²H = (4/3)πr³

(1/3)πr² cancels out on both sides and we're left with

H = 4r

(H/r) = (4/1)

The ratio of the height of the cone to radius of the sphere is 4:1

Hope this Helps!!!

8 0

4 years ago

Find the missing lengths of the sides

Ket [755]

ANSWER

The correct answer is C

EXPLANATION

The given triangle is a right triangle. Since two angles are equal, it is a right isosceles triangle.

This implies that, x=8 units.

Using Pythagoras Theorem,

${y}^{2} = {8}^{2} + {8}^{2}$

This implies that:

${y}^{2} = 64 + 64$

${y}^{2} =128$

Take positive square root,

${y} = \sqrt{128}$

${y} = 8 \sqrt{2}$

The correct answer is C

5 0

3 years ago

Read 2 more answers

In this fulcrum, for the weights to be balance, what do the distances d1 and d2 have to be if the overall length is 12 feet?

mel-nik [20]

For the fulcrum to balance, the product of weight and distance on both sides of the fulcrum must be the same.

Let d1= x. since total distance is 12, we can write d2 = 12 - x

for the fulcrum to balance:

60x = 50(12 - x)

60x = 600 - 50x

110x = 600

x = 5.45

Thus, d1= 5.45
and
d2= 12 - d1 = 12 - 5.45 = 6.55

d1 = 5.45
d2 = 6.55

5 0

3 years ago

Read 2 more answers

How to solve 45 45 90 triangle given hypotenuse?

statuscvo [17]

From the Special Triangle Theorem, the hypotenuse is equal to the side lengtht times the Sqrt(2).
So hypotenuse H = xSqrt(2), x=H/Sqrt(2).
Using numbers, if H = 7, then x = 7/Sqrt(2) = 7Sqrt(2)/2 to rationalize it.

4 0

3 years ago

a farmer is buying fencing to surround a square field of area 3600m^2. What length of fencing does he need to buy?

kirill115 [55]

Answer:

240 m

Step-by-step explanation:

The area of a square field is 3600 m².

We need to find the length of fencing he needs to buy. It means we need to find the perimeter of the field.

The area of a square field is given by :

A = side²

So,

$s=\sqrt{3600} \ m\\\\s=60\ m$

Length of fencing = perimeter

= 4(s)

= 4(60)

= 240 m

So, he would need to buy 240 m of fencing.

8 0

3 years ago