D. Solve the following problems:

Approximately how many times as great is the volume of a grapefruit with a diameter 16 cm as the volume of a lime with a diamete

SIZIF [17.4K]

Answer: The volume of the grapefruit is approximately 8 times as great as the volume of the lime.

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere. This is:

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

Where "r" is the radius.

Volume of the grapefruit

You know that its diameter is 16 centimeters.

Since the radius is half the diameter, you get that its volume is:

$V_g=\frac{4}{3}\pi (\frac{16\ cm}{2}) ^3\\\\V_g= 2,144.66\ cm^3$

Volume of the lime

According to the information given in the exercise, the diameter of the lime is 8 centimeters.

As it was explained above, the radius is half the diameter. Knowing that, you get that volume of the lime is the shown below:

$V_l=\frac{4}{3}\pi (\frac{8\ cm}{2}) ^3\\\\V_l= 268.08\ cm^3$

In order to find approximately how many times as great is the volume of theat grapefruit as the volume of that lime, you need to divide the volumes calculated above. Then:

$\frac{2,144.66\ cm^3}{268.08\ cm^3}\approx8\ times$

8 0

3 years ago

A photographer is 6 feet tall and cast a shadow that is 2 feet long. He is photographing a palm tree with a shadow that is 7 fee

Novay_Z [31]

Answer: The height of the tree is 21 feet.

Step-by-step explanation:

Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.

Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.

Then we will have a relationship like:

Tg(angle) = shadow/height

height = shadow/Tg(angle)

Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K

Tg(angle) = K

Then we have the equation:

Height = Shadow/K

We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:

6ft = 2ft/K

K = 2ft/6ft = (1/3)

Now we know that the shadow of the tree is 7ft long, then the height will be:

height = 7ft/(1/3) = 7ft*3 = 21ft

The tree is 21 ft tall.

6 0

3 years ago

2x - 2y = -8 x + 2y = -1 (-3,1) O (-14, 1) (0,4) (1,5)

trasher [3.6K]

Answer:

2x - 2y = -8

x + 2y = -1

3x = -9

x = -3

-3 + 2y = -1

2y = 2

y = 1

(-3, 1) is the solution

Step-by-step explanation:

6 0

2 years ago

How to subtract fractions

frosja888 [35]

You need to first make denominator in the fractions you have equal, then simply subtract numenators.

example:
2/3 - 1/2
first step is to make denominators equal.
for this example, the denominator will be equal to 6 which is 2x3
so, 2/3 = 4/6 and 1/2 = 3/6
so, the expression now becomes:
4/6 - 3/6
simply subtract numenators and the denominator will be 6 as well.
4/6 - 3/6 = 1/6

another example:
3/4 - 1/2
here the denominator can be equal to 4 in all terms
1/2 = 2/4
so, the new expression is now:
3/4 - 2/4 = 1/4

5 0

3 years ago

A 14 foot ladder is placed against a wall. It is placed 5 feet from the base of the wall.

Vladimir [108]

Answer:

c = 18.47

Step-by-step explanation:

This would create a triangle in which the length of the wall would be the missing side. We can use the Pythagorean Theorem to find this:

1. $a^{2}$ + $b^{2}$ = $c^{2}$