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2 years ago

How many integers $n$ satisfy the inequality $3n^2 - 4 \le 44$?

Mathematics

2 answers:

FromTheMoon [43]2 years ago

8 0

Answer:

7 integers

Step-by-step explanation:

The inequality to solve is $3n^2-4$

We can do algebra and solve this:

$3n^2-4$

If we solve $3n^2-48=0$ , we will get the intercepts. So:

$3n^2-48=0\\3(n^2-16)=0\\n^2-16=0\\n^2=16\\n=4,-4$

Since, the inequality is less than, the solution set is all numbers between -4 and 4. So

-4 < n < 4

*note: -4 and 4 is NOT included, so the integers in the range are:

-3, -2, -1, 0, 1 , 2, 3

Which is 7 integers.

Softa [21]2 years ago

8 0

Answer:

Step-by-step explanation:

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Answer:

0.08 cubic feet.

Step-by-step explanation:

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble.

The original statue in Vienna is 7 feet tall.

First we will convert this to inches as one relation is given in inches.

1 feet = 12 inches

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Let the amount of marble used for 84 inches statue be = x

We can relate both the conditions in the following way:

$\frac{10}{16} =\frac{84}{x}$

$10x=16\times84$

$10x=1344$

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2 years ago

A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.

Wewaii [24]

Answer:

The sphere has a diameter of 32 in. CORRECT: the diameter of a sphere doubles its radio, so if the radio equals 16,the diameter measures the double, in this case, 32.
The radius' lenght is one half the length of the diameter. CORRECT: , by definition, the diameter is the maximum distance between two opposite points on the surface of the sphere, and its lenght equals twice the radius because the radius is the distance between the center of the sphere and any point of the frontier of the sphere (then, one colud imagine that the distance between two opposite points in a sphere can be united by two radius, or a diameter).
The volume (V) of a sphere can be calculated as $\frac{4\pi r^3}{3}$ , where r is the radio. In this case, the volume of the sphere will be $\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}$ , which is also equal to $\frac{16384\times\pi}{3}$ .

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2 years ago

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A container has the shape of an open right circular cone, as shown. The height of the container is 10 cm and the diameter of the

SVETLANKA909090 [29]

A) Volume = (1/12)pi*h^3, with height = 5cm.

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does that make sense?

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2 years ago

8. Peter and his partner are conducting a physics experiment on pendulum motion. Their 30-cm

katrin2010 [14]

Answer: 90/pi degrees

Step-by-step explanation:

It forms a 15cm arc from a circle of radius 30 cm.

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-sirswagger21

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2 years ago

Daniel deposited $500 into a savings account and after 8 years, his investment is worth $807.07. The equation A = d(1.005)12t mo

shtirl [24]

Answer:

Step-by-step explanation:

The equation A = d(1.005)^12t modelling the value of Daniel’s investment shows a monthly compounded interest. This means that the interest is compounded 12 times in a year.

We can confirm by inputting the given values

t = 8 years

d = 509

Therefore,

A = 500(1.005)12 × 8

A = 500(1.005)^96

A = $807.07

Therefore, the true statements are

Increases

Exponential

Never Decrease

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2 years ago