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3 years ago

Write the following using index notation: a) 4x4

Mathematics

1 answer:

Sonbull [250]3 years ago

8 0

Answer:

$4^{2}\\$

Step-by-step explanation

4 is multiplied 2 times. That means it has an index of 2, therefore, the answer is 4 squared.

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3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall

Katen [24]

Answer:

The volume of the toy is $V=5.23\ ft^3$

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

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

In this problem, the wide of the toy is equal to the diameter of the hemisphere

$D=2\ ft$

$r=2/2=1\ ft$ ----> the radius is half the diameter

substitute

$V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3$

step 2

Find the volume of the cone

The volume of the cone is given by

$V=\frac{1}{3}\pi r^{2}h$

we know that

The radius of the cone is the same that the radius of the hemisphere

$r=1\ ft$

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

$h=4-1=3\ ft$

substitute the given values

$V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3$

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

$V=(\frac{2}{3} \pi+\pi)\ ft^3$

$V=(\frac{5}{3}\pi)\ ft^3$

assume

$\pi=3.14$

$V=\frac{5}{3}(3.14)=5.23\ ft^3$

5 0

3 years ago

If x + 5 = 15 then x = 10

77julia77 [94]

Yes u are correct x is 10

6 0

2 years ago

Read 2 more answers

How would I set up question one?

Darina [25.2K]

A straight line is 180 degrees:

25x + 8 + 9x + 2 = 180

Combine like terms:

34x + 10 = 180

Subtract 10 from both sides:

34x = 170

Divide both sides by 34:

X = 5

Now solve the smaller angle:

9x + 2 = 9(5) + 2 = 45 + 2 = 47

They angle with the y is a vertical angle to 47 so needs to also equal 47:

7y + 5 = 47

Subtract 5 from both sides:

7y = 42

Divide both sides by 7:

Y = 6

Answer: x = 5, y = 6

8 0

2 years ago

B<br> Which of the following regions is best described as hot and<br> humid with low elevations?

Diano4ka-milaya [45]

Answer:

Region C

Step-by-step explanation:

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5 0

2 years ago

Read 2 more answers

A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the dia

Anettt [7]

Answer:

d = 13.8 feet

Step-by-step explanation:

Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is

$V=\pi r^2h$

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet. Filling in then gives us:

$6000=(3.141592654)(r^2)(40)$

Simplify on the right to get

$6000=125.6637061r^2$

Divide both sides by 125.6637061 to get that

$r^2=47.74648294$

Taking the square root of both sides gives you

r = 6.90988299

But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8

5 0

2 years ago