Does this triangle have a hypotenuse of 39 feet long?

9514 1404 393

  no — the hypotenuse is about 33.5 ft long

Step-by-step explanation:

The hypotenuse (h) is given by the Pythagorean theorem.

  h² = 15² +30² = 225 +900 = 1125

  h = √1125 ≈ 33.54

The hypotenuse of this triangle is not 39 feet long.

Additional comment

You can estimate the hypotenuse based on the relative side lengths. Here the short side is 1/2 the length of the long side. This means the hypotenuse will be longer than the long side by an amount between ...

  0.4(1/2)² = 0.1

and

  0.5(1/2)² = 0.125

times the length of the long side. That is, the additional length will be between 3 and 3.75 feet, so the hypotenuse will be shorter than 33.75 feet.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204