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dedylja [7]
3 years ago
14

How do I find the volume of this right triangular prism?

Mathematics
1 answer:
frozen [14]3 years ago
8 0
I’ll try to make a step by step demonstration! Feel free to skip to step 5 for the answer, though
1. The formula for a right triangular prism is (1/2)*base*height*length, and we know what the base (4 cm) and length (8 cm) are, but not the height
2. To find the height we must divide the side triangle into two, which then gives us two right triangles
3. Focusing on just one of the right triangles, its base will be 2 cm rather than 4 (as it has been divided by two) and its hypotenuse will be 4 cm; using Pythagorean’s theorem (a^2 + b^2 = c^2), solve for the missing side (the height), which should end up being √12
4. Multiply! (1/2)4*√12*8 ≈ 55.425
5. Round to the nearest tenth —> 55.4
I hope this helped somewhat! Comment if clarification is needed
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Do the points lie on the line of the given equation. Y = -0.25 X. Show your work.
meriva
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2 years ago
Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to neg
Mars2501 [29]
The function is f(x)= x^{5} -9x ^{3}

1. let's factorize the expression x^{5} -9x ^{3}:

f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )


2.  
The end behavior of f(x), whose term of largest degree is x^{5}, is the same as the end behavior of  x^{3}, which has a well known graph. Check the picture attached. 

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of x^{2})

so, like the graph of x^{3}, the graph of f(x)= x^{5} -9x ^{3} :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

7 0
3 years ago
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Elan Coil [88]

Answer:

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Step-by-step explanation:

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3 0
2 years ago
Z varies directly as x^3 and inversely as y^3. If z=167 when x = 3 and y=10, find z if X=4 and y=6
Liula [17]

Answer is 1832.7

step by step

z=kx^3 / y^3

167=27k/1000

k=16700/27

k=6185.2, then

z=6185.2×4^3/6^3

z=6185.2×64/216

z=1832.7

8 0
2 years ago
System of equations <br> 3x-2y=8<br> -2x+5y=-9<br> x=<br> y=
natka813 [3]

Answer:

2y = 3x - 8

y = 3/2x - 4

Work

-2x + 5(3/2x - 4) = -9

-2x + 15/2x - 20 (+20) = -9 (+20)

-4/2x + 15/2x = 11

11/2x * (2/11) = 11 (2/11)

x = 2

3(2) - 2y = 8

6 (-6) - 2y = 8 (-6)

-2y = 2

y = - 1

final answer:

x = 2

y = -1

7 0
3 years ago
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