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2 years ago

Triangle FGH is similar to JKM.

Mathematics

1 answer:

mario62 [17]2 years ago

8 0

Answer: J = 14.4 cm

Step-by-step explanation:

<em>K is similar to G</em>

So we can find the scale that FHG was dilated by dividing the side length of G by the side length of K

16.56/9.2 = 1.8

So the sides of the triangle KMJ were multiplied by a factor of 1.8

to find m :

25.92/1.8 = 14.4

J = 14.4

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Lubov Fominskaja [6]

Answer:

48 dollars.

Step-by-step explanation:

If Mr. George starts with 42, and adds 6, his new balance should equal 48 because you add the two numbers.

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2 years ago

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3 years ago

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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.

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

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8 0

1 year ago

A semicircular archway is built in front of a garden using 8 congruent granite tiles, as shown in the diagram. Find the area of

crimeas [40]

So there's 8 tiles.
Radius from archway to the outer edge would be : 7 +1 = 8ft

You can use this formula to count the area of semi circle : π r^2/2

A = 3.14 x 8ft^2 = 100.48 ft ^2
A = 3.14 x 7ft^2= 76.92 ft^2

100.48 - 76.92 = 23.55 ft^2

Then you have to divide it with the total tiles
23.55/8 = 2.94 ft^2 per tile >> (rounded to nearest tenth)

hope this helps

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2 years ago