Answer:
16.2 feet
Step-by-step explanation:
Reference angle = 62°
Opposite = x
Adjacent = 8.6
Apply trigonometric function, TOA:
Tan 62 = Opp/Adj
Tan 62 = x/8.6
8.6 × Tan 62 = x
16.1742476 = x
x = 16.2 ft (nearest tenth)
Answer:
We conclude that a function is defined as having only one corresponding y-value for each x-value.
Hence, option (C) is true.
Step-by-step explanation:
We know that A function is a certain relationship is defined as having only one corresponding y-value for each x-value.
Considering the function
Here,
- x is the input and f(x) or y is the output.
- 'x' is often called an independent value and y is called the 'dependent' value.
Considering the table
x y
1 2
2 3
3 4
4 5
The values in the table satisfy the function y = x+1.
It is clear from the table that the function has only one corresponding y-value for each x-value. In other words, there is no repetition of 'x' value.
Therefore, we conclude that a function is defined as having only one corresponding y-value for each x-value.
Hence, option (C) is true.
Answer:
The interval of convergence is -1<x<1
Step-by-step explanation:
To find the interval of convergence of the series, we will use the condition for convergence of a series according to Ratio test.
The solution is as shown in the attachment.
Answer:
The negative solution
-2
Step-by-step explanation:
Let the number be
Then 5 times the number is 5x.
14 less than the square of the number is
So our equation becomes
This implies that
We factor to get:
Answer:
we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
Step-by-step explanation:
let the 20% solution = x liters
let the 50% solution = y liters
total solution of the mixture of the two solutions in % = 28%
total solution of the mixture of the two solutions in liters = 75 liters
considering the total solutions given, we will have the following equations if we mix the solutions in equal proportion;
20x + 50y = 28 (75)
0.2x + 0.5y = 0.28(75)
0.2x + 0.5y = 21 -------equation 1
Also,
x + y = 75 ------equation 2
y = 75 - x
(substitute this into equation 1)
0.2x + 0.5(75 - x) = 21
0.2x + 37.5 - 0.5x = 21
0.2x - 0.5x = 21 - 37.5
-0.3x = -16.5
x = -16.5 / -0.3
x = 55 liters
Recall, y = 75 - x
y = 75 -55
y = 20 Liters
Thus, we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
