1. Add 9
2. Add 1/3
3. Add 15
Answer:
A. &. D
Step-by-step explanation:
Open and to the right.
105° can be expressed as 60°+45°. What we have then is sin(60°+45°). The sum pattern for sin is sin(a)cos(b)+cos(a)sin(b). We will fill in as follows: sin(60)c0s(45)+cos(60)sin(45). Now draw those special right triangles in the first quadrant to get the exact values for each. The sin of 60 is
, the cos of 45 is
, the cos of 60 is 1/2, and the sin of 45 is
. When we put all that together we get
. Simplifying all of that we have
. We can put that over the common denominator that is already there and get
. Not sure if that's simplified enough; you may be at the point in class where you are rationalizing your denominator, but I'm not sure, and if you're not, I don't want to confuse you.
If you would like to know what is the following expression in the simplest form, you can calculate it like this:
If you 24v / 3v divide by v, you will get 24 / 3. Now, if you divide 24 by 3, you will get 8.
The simplest form of 24v / 3v would be 8.
Question:
What is the following product?
(√14 - √3) (√12 + √7)
Answer:
2√42 + 7√2 - 6 - √21
Step-by-step explanation:
Given.
(√14 - √3) (√12 + √7)
Required
Product
(√14 - √3) (√12 + √7)
We start by opening the brackets
√14(√12 + √7) -√3(√12 + √7)
√(14*12) + √(14*7) - √(3*12) - √(3*7)
Expand individual brackets
√(2*7*2*6) + √(2*7*7) - √(3*3*4) - √(3*7)
= √(2*2*7*6) + √(2*7*7) - √(3*3*4) - √(3*7)
= √(4*42) + √(2*49) - √(9*4) - √(3*7)
Split Roots as follows
= √4 * √42 + √2 * √49 - √9 * √4 - √21
Take square root of perfect squares
= 2 * √42 + √2 * 7 - 3 * 2 - √21
= 2√42 + 7√2 - 6 - √21
Hence, the result of the product (√14 - √3) (√12 + √7) is 2√42 + 7√2 - 6 - √21
