The answer could be 72 but i am not sure
The domain is the input of the function or n in this case. So, in the boxes, you would put [1, 2, 3, 4, 5, 6, ...]
The range is the output of the function or f(n) in this case. So, in the boxes, you would put [4, 6, 8, 10, 12, 14, ...]
We immediately find that
are possible choices, which makes
, respectively.
If
, we can eliminate the factor of
to get
Note that if
, we have equality, but this goes against our assumption that
. Note that
for all
, which means
is a monotonically increasing function, and is bounded between -1 and 1. On the other hand,
is a monotonically decreasing function that is unbounded. From this you can gather that the two functions never intersect for
(since
is always negative while
is always positive), which means
is the only solution to the equation above. However, this solution is actually extraneous, since the original equation contains a factor of
. So, in fact, the equation above has no solution for
.
That leaves us with
,
, and
.
Answer:
All answers are to 2 decimal places for accuracy.
1. Width is 27.71"
2. TV Size is 69.84"
3. Width is 51.96"
4. TV Size is 40.13"
5. Height is 26.06"
6.
Part 1: Diagonal is 61.91"
Part 2: Diagonal is 60.21"
Step-by-step explanation:
THe pythagorean theorem tells us that the sum of two legs of a triangle squared equal the hypotenuse squared.
<u>Note: </u>This applies for right triangles and the side opposite of the right angle is the hypotenuse
Also, to solve the first 5 problems, we can say:
#1 32” TV height: 16” width: _____
Let width be w
Width is 27.71"
#2 _____ TV height: 34” width: 61”
Let tv size be t
TV Size is 69.84"
#3 60” TV height: 30” width: _____
Let width be w
Width is 51.96"
#4 _____ TV height: 20” width: 35”
Let tv size be t
TV Size is 40.13"
#5 52” TV height: _____ width: 45”
Let height be h
Height is 26.06"
#6
<u>Part1:</u>
New dimensions would be
48+5 = 53" Width
27+3 = 30" Height
Let diagonal be d, so
Diagonal is 61.91"
<u>Part 2:</u>
New dimensions are:
48+3 = 51" Width
27 + 5 = 32" Height
Let diagonal be d, so
Diagonal is 60.21"
Answer:
Option (2)
Step-by-step explanation:
Step 1.
Step 2.
(cosA - cosB)² + (sinA - sinB)² = [cos(A - B) - 1]² + [sin(A - B) - 0]²
Step 3.
cos²A + cos²B - 2cosAcosB + sin²A + sin²B - 2sinAsinB = cos²(A - B) + 1 - 2cos(A - B) + sin²(A - B)
Step 4.
2 - 2cosAcosB - 2sinAsinB = 1 - 2cos(A - B) + 1
Step 5.
cosAcosB + sinAsinB = cos(A - B)
Therefore, Option (2) will be the answer.