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Naddika [18.5K]
3 years ago
6

The height of a triangle is 4 times its base. The area of the triangle is 288 square. Find the base and the height of the triang

le
Mathematics
1 answer:
Vanyuwa [196]3 years ago
7 0
\bf \textit{area of a triangle}\\\\
A=\cfrac{1}{2}bh\qquad 
\begin{cases}
b=base\\
h=height\\
----------\\
h=4b\leftarrow 
\begin{array}{llll}
\textit{height is 4}\\
\textit{times the base}
\end{array}\\
A=288
\end{cases}\implies 288=\cfrac{1}{2}\cdot b\cdot 2b

solve for "b", to see what the base is

what about the height?  well, h = 4b
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3 years ago
Find the perimeter and volume of the shed.
Anni [7]

Answer:

Perimeter=48.497

Volume=997.661

Step-by-step explanation:

Perimeter:

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8 0
3 years ago
Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.
hram777 [196]

The center of mass is mathematically given as

\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}

<h3>What is the center of mass.?</h3>

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \  \ \  x \in(0,1)$ \\\end

We calculate the total mass of the system.

\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}

Step 03: Calculate the moment of the system.

\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}

we calculate the center of mass.

\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}

Read more about the center of mass.

brainly.com/question/27549055

#SPJ1

8 0
2 years ago
Find the indicated side of the<br> right triangle.
Advocard [28]

Answer:

?=9

Step-by-step explanation:

We have a special right triangle, the 45-45-90 triangle.

In a 45-45-90 triangle, the side lengths are x, and the hypotenuse is x√2.

Since we know that the side length is 9, this means that:

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The ? is 9.

8 0
3 years ago
Help me and I give you
Murljashka [212]
Im pretty sure its b im soo sorry if im wrong.
7 0
3 years ago
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