Chapter 10: Q 10.12 (page 1160)

Solve $3 t^{2} + 6 = 70$ .

Short Answer

Expert verified

The solutions are $t = \frac{8 \sqrt{3}}{3}, t = - \frac{8 \sqrt{3}}{3}$ .

Step by step solution

Given Information.

The Given equation is $3 t^{2} + 6 = 70$ .

Isolate the quadratic term and makes its coefficient one.

$3 t^{2} = 70 - 6 3 t^{2} = 64 t^{2} = \frac{64}{3}$

Use the square root property.

$t = \pm \sqrt{\frac{64}{3}}$

Factor the radical.

$t = \pm \sqrt{\frac{64}{3}} t = \pm \sqrt{\frac{8 \times 8}{3}} t = \pm \frac{8}{\sqrt{3}}$

Rationalize the denominator.

$t = \pm \frac{8}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} t = \pm \frac{8 \sqrt{3}}{3}$

Rewrite to show two solutions.

$t = \frac{8 \sqrt{3}}{3}, t = - \frac{8 \sqrt{3}}{3}$

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Solve $3 t^{2} + 6 = 70$ .

Short Answer

Step by step solution

Given Information.

Isolate the quadratic term and makes its coefficient one.

Use the square root property.

Rationalize the denominator.

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Solve 3t2+6=70.

Short Answer

Step by step solution

Given Information.

Isolate the quadratic term and makes its coefficient one.

Use the square root property.

Rationalize the denominator.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve $3 t^{2} + 6 = 70$ .