Answer:
R = 4cm
Step-by-step explanation:
V = π(R)²h = 480π
Divide by π
(R)²h = 480
Substitute h with 30
30*(R)² = 480
Divide by 30
(R)² = 16
Square root
R = 4cm
We do not accept R= -4 because it's a length, so it must be positive.
Answer:
‹A = 141°
‹B = 28°
‹C = 11°
*These angles are rounded to the nearest whole*
Step-by-step explanation:
Because you are only given sides you can find an individual angle measures with the inverse law of cosines.
Remember the side opposite of the angle corresponds to that angle.
a² = b² + c² - 2bc cos(A) →
A = cos⁻¹ (a² - b² - c² / -2bc)
b² = a² + c² - 2ac cos(B) →
B = cos⁻¹ (b² - a² - c² / -2ac)
c² = a² + b² - 2ab cos(C) →
C = cos⁻¹ (c² - a² - b² / -2ab)
To answer this, set up a system of equations. What we know is that
5x + 2y = 100
And...
x+y=38
x represents the unknown number of 5 points questions
y represents the unknown number of 2 point questions
In my opinion the easiest way to solve this is to use substitution (that is when you find out the value of one variable, either x or y, and substitute that value as the variable).
So,
x+y=38
Subtract x from both sides
y=38-x
Now, plug (38-x) in as y in the other equation.
5x + 2(38-x) = 100
5x + 76-2x= 100
3x+76=100
3x=24
x=8
Now that you know that x=8, you can solve for y.
5x+2y=100
5(8)+2y=100
40+2y=100
2y=60
---- ------
2 2
y=30
X=8
Y=30
There are 8 five point questions on the test and 30 two point questions on the test
Reflection about the y-axis is according to the rule
(x,y)->(-x,y)
Therefore F(x,y) -> F'(-x,y)
The distance between F' and F is (-x,y)-(x,y)=-2x, or the positive distance is 2x.
