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3 years ago

What is the first step when finding the volume of a pyramid?

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

4 0

Step-by-step explanation:

B. Find the area of the base so as to calculate the volume of the prism

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The width of a triangle is six more than twice the height. The area of the triangle is 88in2. Find the height and base of the tr

malfutka [58]

For this case we have that by definition, the area of a triangle is given by:

$A = \frac {b * h} {2}$

Where:

b: It is the base of the triangle

h: It is the height of the triangle

According to the statement data we have:

$b = 6 + 2h$

Substituting we have:

$88 = \frac {(6 + 2h) * h} {2}\\176 = 6h + 2h ^ 2\\2h ^ 2 + 6h-176 = 0$

We divide between 2 on both sides:

$h ^ 2 + 3h-88 = 0$

We factor by looking for two numbers that, when multiplied, are obtained -88 and when added together, +3 is obtained.

These numbers are +11 and -8.

$(h + 11) (h-8) = 0$

We have two roots:

$h = -11\\h = 8$

We choose the positive value.

Thus, the base of the triangle is: $b = 6 + 2 (8) = 22$

Answer:

The base of the triangle is 22 units.

5 0

4 years ago

Read 2 more answers

.............helppppppppppppppppppp

raketka [301]

Answer:

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8 0

3 years ago

Read 2 more answers

Using Cramer’s Rule, what is the value of x in the system of linear equations below?

MArishka [77]

We have to solve the system of equations by Cramer's rule.

The coefficient matrix is given by

$D=\begin{bmatrix}3&4\\8 &-2\end{bmatrix}$

Let us find the determinant of coefficient matrix.

$|D|= -6-32=-38$

For X-matrix

$D_x=\begin{bmatrix}15&4\\40 & -2\end{bmatrix}$

Now, we find its determinant

$|D_x|=-30-160=-190$

For Y-matrix

$D_x=\begin{bmatrix}15&3\\ 40&8\end{bmatrix}$

Now, we find its determinant

$|D_y|=120-120=0$

Therefore, the value for x is given by

$x=\frac{D_x}{D}\\\\x=\frac{-190}{-38}\\\\x=5$

The value for x is 5.

8 0

3 years ago

Find the equation of the line that passes through points A and B.<br>A (1,7)<br>B (-3,-1)

Mila [183]

Equation of a line is -> m= y2 - y1 all over x2 - x1. Therefore, -1 - 7= -8 and -3 - 1= -4. -8 divide -4= 2 so the gradient is 2.

7 0

4 years ago

Read 2 more answers

The focus of a parabola is (0, - 2) The directrix of the parabola is the line y = - 3 What is the equation of the parabola

777dan777 [17]

Answer:

Option B: $\textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}}$

Step-by-step explanation:

When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:

$\textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}}$

Here, we are given the focus: (h, k) = (0, -2)

Directrix: y = c = -3.

We substitute in the formula to get the equation of the parabola.

$(x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y$

$\implies x^2 + 4 - 9 = 2(- 2 + 3)y$

$\implies x^2 - 5 = 2(1) y$

$\implies 2y = x^2 - 5$

Dividing by 2, throughout we get:

$\textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}}$ which is the required answer.

5 0

3 years ago