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Solnce55 [7]
2 years ago
6

Solve for x. Leave your answer in the simplest form.

Mathematics
2 answers:
zavuch27 [327]2 years ago
5 0

Apply Pythagorean theorem

  • H²=9²+5²
  • H²=81+25
  • H²=106

So

  • x²=106+4²
  • x²=106+16
  • x²=122
  • x=√122
  • x=11.04≈11
Murrr4er [49]2 years ago
5 0

Answer:

√(122)

Step-by-step explanation:

Pythagoras Theorem:  a² + b² = c²

(where a and be are the legs, and c is the hypotenuse, of a right triangle)

First, find the length of the hypotenuse of the triangle with legs of 9 and 5 units:

⇒ 5² + 9² = c²

⇒ 25 + 81 = c²

⇒ c² = 106

⇒ c = √(106)

Therefore √(106) is the longest leg of the other triangle.

So we can now use this measurement to find x (the hypotenuse) of the other triangle:

⇒ 4² + √(106)² = c²

⇒ 16+ 106 = c²

⇒ c² = 122

⇒ c = √(122)

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Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
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Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

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Number of t-shirts to make maximum profit = 2790 shirts

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Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

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x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

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At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

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