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2 years ago

Select the lengths in centimeters that would form a right triangle

Mathematics

1 answer:

Ivenika [448]2 years ago

4 0

Answer:

9, 40 and 41

Step-by-step explanation:

All right triangle have lengths that follow the Pythagorean Theorem (a²+b² = c²). Right triangles have one angle equal to 90°. The two shorter sides form the right angle and the side opposite the right angle is called the hypotenuse.

Using the lengths given, we can use guess and check to see what sum of two sides squared would equal a third side, or just plug them into the equation: a²+b² = c² and see what lengths fit this equation.

I recommend starting with squares you are familiar with:

9² + 40²= 81 + 1600 = 1681

Now, take the √1681 to find the length of 'c', or the hypotenuse:

√1681 = 41

Since these three lengths fit the Pythagorean Theoreom, the would form a right triangle.

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1 year ago

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2 years ago

The maximum value of 12 sin 0-9 sin²0 is: -

jeka57 [31]

Answer:

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be $\theta$ rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

$f(\theta) = 12sin(\theta) - 9 sin^2(\theta)$

Taking the first derivative of this with respect to $\theta$ and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of $f(\theta)$ w.r.t $\theta$ is

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)$

And setting this = 0 gives

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0$

Eliminating $cos(\theta)$ on both sides and solving for $sin(\theta)$ gives us

$sin(\theta) = \frac{12}{18} = \frac{2}{3}$

Plugging this value of $sin(\theta)$ into the original equation gives us

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1 year ago

Estimate the square root of 50 to the hundredths place

Anarel [89]

We have the following expression:
root (50)
Rewriting we have:
root (50) = root (2 * 25)
root (2 * 25) = 5 * root (2)
5 * root (2) = 7.071067812
Round to the hundredths place:
root (50) = 7.07
Answer:
the square root of 50 to the hundredths place is:
7.07

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2 years ago

Read 2 more answers