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3 years ago

What is the mathematical formula for finding the volume of a pyramid

Mathematics

1 answer:

Marta_Voda [28]3 years ago

3 0

Volume of a pyramid= 1/2 * base area * height

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When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

aleksandr82 [10.1K]

Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

We have to sum 528 and three times the number, so we have $528+3x$

Then, we have to subtract this number from $x^2$ , so we have

$x^2-(3x+528)$

The result is 120, so the equation is

$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

$x = \dfrac{3-51}{2} = \dfrac{-48}{2} = -24$

But we know that x is positive, so we only accept the solution $x = 27$

6 0

3 years ago

Match each graph with the correct slope of the line. drag and drop the answer

OLEGan [10]

Answer/Step-by-step explanation:

✔️Slope of the first graph:

Using two points on the line, (0, 1) and (3, 2),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{3 - 0} = \frac{1}{3}$

Slope = ⅓

✔️Slope of the second graph:

Using two points on the line, (0, 0) and (1, 1),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{1 - 0} = \frac{1}{1} = 1$

Slope = 1

✔️Slope of the third graph:

Using two points on the line, (0, 1) and (2, 2),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{2 - 0} = \frac{1}{2}$

Slope = ½

3 0

3 years ago

Read 2 more answers

Who was part of the triumvirate after Caesar’s death? (3 people)

Anon25 [30]

Answer: Octavian (the future emperor Augustus), Mark Antony, and Lepidus. i hope this helped

Step-by-step explanation:

5 0

3 years ago

(1) Calculate the circumference of the<br>circles below in terms of π

Mademuasel [1]

Answer:12.57

Step-by-step explanation:

C=2πr

=2·π·2

=12.56637

3 0

3 years ago

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Let u = <-7, -2>. Find 8u.

Evgen [1.6K]

<8 * (-7), 8 * (-2)>

<-56, -16>

Hope it helps, good work!

8 0

3 years ago