Plz , worth 20 pts.

determine the approximate value of t.

2.03

5.54

6.4

15.45

The approximate value for t is 5.54

Option B

Step-by-step explanation:

The law of cosines generalizes the Pythagorean formula to all triangles. It says that , the square of one side of the triangle, is equal to product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

According to the given triangle in figure, the values are

a = 5

b = 4

c = t

Substituting all the given values in the formula, we get

Taking square roots, we get the value for ‘t’ as below,

                             t = 5.536 (approximately 5.54)

B. 5.54

Step-by-step explanation:

To find out what t is, use the formula t=√[r² + s² - 2rs * cos(T)].

t = √[4² + 5² - 2(4(5)) * cos(75)]

t = √[16 + 25 - 8(5) * cos(75)]

t = √[41 - 40 * cos(75)] (For convenience, 40 * cos(75) has been approximated.

t = √[41 - 10]

t = √31

To approximate a square root subtract the lower square (25) from 31 and put that over the higher square (36) minus the lower square (25).

t ≈ 5 + (31 - 25)/(36 - 25)

t ≈ 5 + 6/11

t ≈ 5 6/11 ≈ 5.54, so B is the answer.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)