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If
(1)/(6)sqrtk-3=1-sqrtk, approximately what is the value of
k ?
Choose 1 answer:
(A) 1.9
(B) 2.9
(C) 3.4
(D) 11.8

If $\frac{1}{6} \sqrt{k}-3=1-\sqrt{k}$ , approximately what is the value of $k$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ . $9$ $\newline$ (B) $2$ . $9$ $\newline$ (C) $3$ . $4$ $\newline$ (D) $11$ . $8$

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Full solution

Q. If

\frac{1}{6} \sqrt{k}-3=1-\sqrt{k}

, approximately what is the value of

k

?

\newline

Choose

1

answer:

\newline

(A)

1

.

9

\newline

(B)

2

.

9

\newline

(C)

3

.

4

\newline

(D)

11

.

8

Rewrite Equation: Rewrite the equation to isolate the square root terms on one side: $\newline$ (\frac{\(1\)}{\(6\)})\sqrt{k} - \(3 + \sqrt{k} = $1$
Combine Like Terms: Combine like terms: $\frac{1}{6}\sqrt{k} + \sqrt{k} = 1 + 3$
Find Common Denominator: Find a common denominator for the square root terms: $\newline$ $\frac{1}{6}\sqrt{k} + \frac{6}{6}\sqrt{k} = 4$
Add Fractions: Add the fractions: $(1+6)/(6)\sqrt{k} = 4$
$\newline$ $\newline$
Multiply Both Sides: Multiply both sides by $\frac{6}{7}$ to isolate $\sqrt{k}$ : $\sqrt{k} = \frac{4 \times 6}{7}$
Calculate Right Side: Calculate the right side: $\sqrt{k} = \frac{24}{7}$
Square Both Sides: Square both sides to solve for $k$ : $k = \left(\frac{24}{7}\right)^2$
Calculate Square: Calculate the square: $\newline$ $k = \frac{24^2}{7^2}$ $\newline$ $k = \frac{576}{49}$
Simplify Fraction: Simplify the fraction to find the approximate value of $k$ : $k \approx 11.755$
Round Value: Round the value of $k$ to one decimal place to match the answer choices: $k \approx 11.8$

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