to find u, which we assume is an angle of course, we can take arctan of both sides. so arctan(-7.721) = -1.4420. this angle is in quadrant 4, but it is not in the range. In this instance you just go around the circle again, or add 2pi, which gets us 4.8412. You can check and you get the same answer if you take the tangent of either.

So now we have a number in the appropriate range in the appropriate quadrant. That means we have the correct angle. The question asks what is sine of that angle cut in half. so sin(4.8412/2), which gets you your answer. let em know if something didn't make sense.

7 0

3 years ago

Two fractions have denominators of x^2+ 6x + 9 and x^2. What is the Least Common Denominator?

Gala2k [10]

SOLUTION

Write out the denominator of the fraction, we have

$\begin{gathered} x^2+6x+9 \\ \text{And } \\ x^2-9 \end{gathered}$

We want to obtain the least common denominator.

To do this, we need to factorize each of the expression given

$\begin{gathered} x^2+6x+9 \\ =x^2+3x+3x+9 \\ =x(x+3)+3(x+3) \\ =(x+3)(x+3) \end{gathered}$

Then we factorise the other fraction using difference of two square

$\begin{gathered} a^2-b^2=(a-b)(a+) \\ \text{Then} \\ x^2-9=x^2-3^2 \\ =(x-3)(x+3) \end{gathered}$

The the factorise expression becomes

$(x+3)(x+3)\text{ and (x-3)(x+3)}$

To obtain the least common denominator, we select the common factor and the product of the other factor,

Hence

$\begin{gathered} \text{common factor=(x+3)} \\ \text{The other factors are (x-3)(x+3)} \\ \text{Then } \\ \text{Least co}mmon\text{ denominator becomes } \\ (x+3)(x-3)(x+3) \end{gathered}$

Thus

The Least Common Denominator is (x +3)(x+3)(x-3) (Last Option )

5 0

1 year ago

William cycles at a speed of 15 miles per hour. he cycles for 12 miles from home to school. if he increases his cycling speed by

Alja [10]

12/15=4/5 original speed
12/20=3/5 increase by 5mph
He will reach 12 minutes earlier than he goes 15 miles per hour.
Correct me if I am wrong.

3 0

3 years ago