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3 years ago

What is the volume of the rectangular prism

Mathematics

1 answer:

maria [59]3 years ago

6 0

Answer:

$\frac{23}{3}$ cubic units

Step-by-step explanation:

To find the volume, we can multiply the base by the height. $\frac{4}{3}$ * $\frac{23}{4}$ is $\frac{92}{12}$ , or $\frac{23}{3}$ . So the volume is $\frac{23}{3}$ cubic units.

You might be interested in

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

Please help me in this question

weqwewe [10]

Question is: how many 84s will fit in 5376? Let's think about some easy multiples:

84 * 100 = 8400, so it's too big
84 * 10 = 840, so it might work

84 | 5376 | 10
-840

84 | 4536 | 10
-840

84 | 3696 | 10
-840

84 | 2856 | 10
-840

84 | 2016 | 10
-840

84 | 1176 | 10
-840

84 | 336

We can't fit any more 840 in 336, so we check how many 84s are in 336 and what's the remainder:

84 | 336 | 4
- 336

So there's no remainder. Now we add all the partial quotients to get the final result:

10 + 10 + 10 + 10 + 10 + 10 + 4 = <u>64

</u>It's correct, I checked it with calculator. I just hope you'll be able to read something from that, it's quite difficult to do partial dividing with no pencil and paper :)

3 0

3 years ago

A car dealership decreased the price of a certain car by 13%. The original price was $45,400.

ira [324]

Answer:

5902

Step-by-step explanation:

Solution: 13% off 45400 is equal to (13 x 13) / 100 = 5902.

5 0

3 years ago

What figure is comprised of two rays that share a common end point called a vertex?

KIM [24]

This would be called an ANGLE.

Hopefully this helps!

5 0

3 years ago

A square field has an area of 100 square meters. What is the length of the square? Show how you got the work please.

Goryan [66]

Answer:

The length of the square is 10 meters.

Step-by-step explanation:

First, you need to know that a square has four equal sides, and that finding the area of a square means multiplying one side by another side. This means that if you know the area of the square, all you have to do is find the square root of the area to find a side length. So, by using a calculator, you can find that the square root of 100 is 10, which is the length of one side of the square.

8 0

3 years ago

Read 2 more answers