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cupoosta [38]
3 years ago
12

Solve.

="TexFormula1" title=" \sqrt{3 x - 11} - \sqrt{x} + 5 = 6" alt=" \sqrt{3 x - 11} - \sqrt{x} + 5 = 6" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
5 0
Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6

Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1

(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1

Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x

Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2

Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2

Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144

Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0

The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0

Divide both sides by -4:
(x - 9) (x - 4) = 0

Split into two equations:
x - 9 = 0 or x - 4 = 0

Add 9 to both sides:
x = 9 or x - 4 = 0

Add 4 to both sides:
x = 9 or x = 4

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct

The solution is:
Answer:  x = 9
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e-lub [12.9K]
<h3>Answer:  33.75 feet</h3>

In fraction form, this value is equal to 135/4

33.75 ft is equivalent to 33 ft, 9 inches.

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Explanation:

Refer to the diagram below.

The key point to start with is point H, which is the vertex of the parabola.

Recall that vertex form is

y = a(x-h)^2 + k

What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.

So,

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45 = a(-60)^2 + 30

45 = a(3600) + 30

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a = 1/240

This then means:

y = a(x-h)^2 + k

y = (1/240)(x-60)^2 + 30

This is the equation of our parabola. Plug in x = 30 to determine the height of point K

y = (1/240)(x-60)^2 + 30

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Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches

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