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3 years ago

An isosceles triangle has an angle of 9x+1 and another of 88, find x

Mathematics

1 answer:

CaHeK987 [17]3 years ago

7 0

Answer:

Step-by-step explanation:

2(9x+1)+88=180

9x+1+44=90

9x=90-45=45

x=5

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

Using the volume formula of a cylinder

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

The length of a rectangle is 7 ft longer than twice the width. If the perimeter is 92 ft find the length and width of the rectan

user100 [1]

Width of the rectangle is 13 ft and length of the rectangle is 33 ft

Step-by-step explanation:

Step 1:

Given perimeter of the rectangle = 92 ft. Let the width be x, then the length of the rectangle = 2x + 7. Use the formula for perimeter of a rectangle = 2(length + width) to find the dimensions.

92 = 2(2x + 7 + x) = 2(3x + 7) = 6x + 14

⇒ 92 = 6x + 14

⇒ 78 = 6x

⇒ x = 78/6

∴ x = 13 ft

⇒ Width of the rectangle = 13 ft

∴ Length of the rectangle = 2x + 7 = 26 + 7 = 33 ft

4 0

3 years ago

If the radius of a circle is 24 feet, what is the diameter? PLZ HRLP I HAVE TO SUMBIT IN 30 MIN

Romashka-Z-Leto [24]

Answer:

d=2r= 2·24=48ft

Step-by-step explanation:

6 0

3 years ago

Find X and Y and show please show calculations

torisob [31]

Answer:

Y = 90

X = 52

Step-by-step explanation:

Y is on a straight line. The sum of the angles on a straight line is 180.

The only other angle (that is marked) on this straight line, is a 90 degree one. So, <y + 90 = 180.

<y = 90.

Now <x + 38 = 90

so, x = 52

6 0

3 years ago

If it takes 1 person 2/3 of a minute to prepare a bag how long would it take 4 peiple to prepare a bag?

Anna11 [10]

Answer:

1/6 of a minute.

Step-by-step explanation:

4 0

3 years ago