Answer:
1) ∠A=84°
2) ∠C=20°
Step-by-step explanation:
1)
First, find ∠C:
<em>(I'm assuming the exterior angle of 126° makes a straight line with ∠C)</em>
The angles on a straight line always add up to 180. Therefore:
∠C+126=180
∠C=180-126
∠C=54
Then find ∠B:
We also know that all the angles in a triangle add up to 180. Therefore:
∠A+∠B+∠C=180
∠A+∠B+54=180
∠A+∠B=126
<em>(we know ∠A=2(∠B))</em>
2(∠B)+∠B=126
3(∠B)=126
∠B=42
Now, find ∠A:
∠A=2(∠B)
∠A=2(42)
∠A=84°
2)
First, find ∠B:
<em>(Again, I'm assuming the exterior angle of 100° makes a straight line with ∠B)</em>
The angles on a straight line always add up to 180. Therefore:
∠B+100=180
∠B=180-100
∠B=80
Then find ∠A:
We also know that all the angles in a triangle add up to 180. Therefore:
∠A+∠B+∠C=180
∠A+80+∠C=180
∠A+∠C=100
<em>(we know ∠A=4(∠C))</em>
4(∠C)+∠C=100
5(∠C)=100
∠C=20°
1.
Use this rule: √ab = √a√b
√12√x^2
Simplify √12 to 2√3
2√3√x^2
Simplify √x^2 to x
2√3x^2
3.
Multiply the numerator and denominator by the conjugate.
2√x/x
Point L is the midpoint
The midpoint is halfway between the two points. In this case, Point F and Point B are 10 units away from each other. The midpoint is the distance between the points (10) divided by 2.
Answer:
<em>The domain of f is (-∞,4)</em>
Step-by-step explanation:
<u>Domain of a Function</u>
The domain of a function f is the set of all the values that the input variable can take so the function exists.
We are given the function
It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:
4 - x > 0
Subtracting 4:
- x > -4
Multiplying by -1 and swapping the inequality sign:
x < 4
Thus the domain of f is (-∞,4)
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
