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Natalija [7]
3 years ago
14

Pythagorean theorem in 3D

Mathematics
1 answer:
kiruha [24]3 years ago
5 0

Answer:

d = 6.997 or 7

Step-by-step explanation:

Use Pythagorean Theorem to find the diagonal of the end of the prism

2^2 + 3^2 = C^2     Simplify

4 + 9 = C^2             Add

13 = C^2                  Take the square root of both sides

3.6 = C

Now plug this into the Pythagorean Theorem equation for the diagonal of the whole prism.

3.6^2 + 6^2 = d^2     Simplify

12.96 + 36 = d^2       Add

48.96 = d^2               Take the square root of both sides

6.997 = d                   This can be rounded up to 7, if needed

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kvasek [131]

Hi there!

\large\boxed{36 \text{ feet}}

v = √2gh

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Simplify:

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Tai designed a staircase with a height-to- base ratio of 3 : 5. The height of the staircase is 9 feet. What should the base of T
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3 years ago
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Solve for x:<br> 3*4+-9-x=10
irina1246 [14]

Answer:

-7

Step-by-step explanation:

first multiply 3 and 4 because PEMDAS

so it now looks like

12 - 9 - x = 10

now minus 12 and 9

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move x to the other side by adding x to both sides

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and move 10 to the other side by subtracting  10 to both sides

3 - 10 = x

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now check

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2 years ago
Complete the steps for deriving the quadratic formula using the following equation.
Andrew [12]
Having obtained:

x^2+ \frac{b}{a}x+( \frac{b}{2a} )^2+ \frac{c}{a}-( \frac{b}{2a} )^2=0

the next thing to do is collect the first three terms and write them as the square of a binomial, and also collect the last two terms, writing each of them with a denominator equal to 4a^2

We have:

(x+\frac{b}{2a} )^2+( \frac{4ac}{4a^2}-\frac{b^2}{4a^2} )=0.

Then, we take ( \frac{4ac}{4a^2}-\frac{b^2}{4a^2} ) to the right side and write these two terms as one:


(x+\frac{b}{2a} )^2=\frac{b^2-4ac}{4a^2}.


Next, we take the square root of both sides, which has been shown in the solution.


Next, we have to take b/2a to the right hand side as -(b/2a), and removing the square in the denominator of the right hand side expression:

x=-\frac{b}{2a}\pm \frac{\sqrt{b^2-4ac}}{2a}}.



Answer: the steps to complete in the boxes are :

 
(x+\frac{b}{2a} )^2+( \frac{4ac}{4a^2}-\frac{b^2}{4a^2} )=0.

(x+\frac{b}{2a} )^2=\frac{b^2-4ac}{4a^2}.

x=-\frac{b}{2a}\pm \frac{\sqrt{b^2-4ac}}{2a}}.

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