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3 years ago

A sphere has a surface area of 60 square feet. Which choice is the best approximation of its radius? Use 3.14 to approximate pi.

Mathematics

1 answer:

timurjin [86]3 years ago

4 0

Answer:

Radius is 2.18

Step-by-step explanation:

We have been given the surface area of sphere 60 square feet

And formula for area of sphere is $4{\pi}r^2$

using ${\pi}=3.14$

On substituting the values $60=4\cdot 3.14\cdot r^2$ we get:

$60=4\cdot 3.14\cdot r^2$

On simplification we get:

$4.77= r^2$

$\sqrt{4.77}= r$

$2.18= r$

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Solve the following problem. PV=$24,122; n = 70; i = 0.024; PMT ?; PMT = $ (Round to two decimal places.)

Ira Lisetskai [31]

Answer:

The payment per period is $714.82.

Step-by-step explanation:

Given information: PV=$24,122; n = 70; i = 0.024

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Substitute PV=$24,122; n = 70; i = 0.024 in the above formula.

$PMT=\frac{24122\times 0.024}{1-(1+0.024)^{-70}}$

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3 years ago

The Chimera Ant population is 7,500 and grows 3% each year. What will the population be after 3 years.

Mashutka [201]

8175 because the 3 percent of 3 years is 675

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3 years ago

A small boat traveled 29.5 miles upstream in 2 hours. The same boat took 3 hours to travel 59.25 miles downstream. If the speed

mel-nik [20]

Answer:

boat speed: 17.25 mph
current: 2.5 mph

Step-by-step explanation:

Upstream, the speed of the current (c) subtracts from the speed of the boat (b) to give the net speed. Downstream, the speed of the current adds. We can make use of the relation ...

speed = distance/time

b-c = 29.5/2 = 14.75 . . . . . miles/hour

b+c = 59.25/3 = 19.75 . . . .miles/hour

Subtracting the first equation from the second, we get ...

(b+c) -(b-c) = 19.75 -14.75

2c = 5

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Then either equation can be used to find b:

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The speed of the boat in still water is 17.25 miles per hour; the speed of the current is 2.5 miles per hour.

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3 years ago

Victor stands 20 meters from a building that is 45 meters tall. He looks up at the roof edge of the building. What is the measur

Gwar [14]

We know that the height of the building is 45m, and the distance between the building and victor is 20m. Since the problem does not state the height of Victor, we can assume that horizontal line of sight of Victor coincides with the base of the building. This gives us a right triangle with angle x and sides 45m and 20m, as you can see in the diagram.

Now, to find the value of the angle x, we will need a trigonometric function that relates the opposite side of our angle x with the adjacent side of it; that trigonometric function is tangent. Remember that $tangent (\alpha) = \frac{oppositeside}{adjacentside}$

We know for our diagram that the opposite side of Victor's angle of inclination, x, is the height of the building (45m), and the adjacent side of it is the distance between Victor and the building (20m). Now we can replace the values in our tangent equation to get:

$tan(x)= \frac{45}{20}$

But we need to find the value of x not the value of tangent, so we are going to use the inverse function of tangent, arctangent (arctan)

$x=arctan( \frac{45}{20} )$ to solve the equation for x:

$x=66$

We can conclude that Victor's angle of inclination from he stands to the top of the building is 66°.

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4 years ago