Can someone check my answers?
1. Convert 13pi/30 to degree measure.
78°
2. Find the distance between (4,4) and (8,7).
5
3. What is the vertex of the parabola y = (x + 8)^2 - 2?
(-8,-2)
4. The graph of y = 6(x - 8)^2 + 1 open downward.
False.
5. An angle that measures pi radians equals 360°.
False.
6. What is the center of the graph of 6(x + 9)^2 + 4(y - 2)^2 = 36?
(-9,2)
7. Find the four corners of the fundamental rectangle of the hyperbola: x^2/81 - y^2/36 = 1.
(±9,±6)
8. Find the exact solutions of x^2 - (y - 6)^2 = 36 and y = -x^2.
-x^4 - 11x^2 - 36?
9. If sin B = 5√2/5√3, find the value of csc B.
√6/2
10. Which value is greater: sin 60° or cos 30°?
They are equal.
1. A = (13pi/30)/(2pi) * 360o.
A = 13pi/30 * 1/2p1 * 360
A = 13/30 * 1/2 * 360 = 78o.
2. d^2 = (8-4)^2 + (7-4)^2 = 25.
d = 5.
3. Y = (x+8)^2 - 2.
Y = x^2 + 16x + 64 - 2 = x^2 + 16x + 62
(-8,-2).
4. Opens Upward.
5. pi radians = 180o.
9. csc B = 5sqrt(3)/5sqrt(2) = sqrt(3)/sqrt(2) = sqrt(3/2).
10. sin60 = cos30.
1. To convert radians to degrees, you can use the formula: Degree measure = (radian measure) × (180/π).
For 13π/30, the degree measure would be (13π/30) × (180/π) = 390/3 = 130°.
So, the correct answer is 130°.
2. To find the distance between two points (x1, y1) and (x2, y2), you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2).
In this case, the points are (4,4) and (8,7).
Using the formula, the distance would be:
Distance = √((8 - 4)^2 + (7 - 4)^2) = √(16 + 9) = √25 = 5.
So, the correct answer is 5.
3. The vertex of a parabola in the form y = (x - h)^2 + k is at the point (h, k).
In this case, the equation is y = (x + 8)^2 - 2.
So, the vertex would be (-8, -2).
So, the correct answer is (-8, -2).
4. The graph of y = 6(x - 8)^2 + 1 opens upward, not downward.
So, the statement "The graph of y = 6(x - 8)^2 + 1 opens downward" is False.
5. A full circle has an angle measure of 2π radians, which is equal to 360°.
Therefore, an angle that measures π radians is only half of a circle, which is equal to 180°.
So, the statement "An angle that measures π radians equals 360°" is False.
6. The equation of the given graph is in the form (x - h)^2/a^2 + (y - k)^2/b^2 = 1, where (h, k) represents the center.
In this case, the equation is 6(x + 9)^2 + 4(y - 2)^2 = 36.
Comparing it with the standard form, we see that the center is at the point (-9, 2).
So, the correct answer is (-9, 2).
7. The equation of the hyperbola is in the form x^2/a^2 - y^2/b^2 = 1.
Comparing it with the standard form, we can see that a = 9 and b = 6.
For a hyperbola, the four corners of the fundamental rectangle are (±a, ±b).
So, the correct answer is (±9, ±6).
8. The given equations are x^2 - (y - 6)^2 = 36 and y = -x^2.
By substituting the value of y from the second equation into the first equation, we get x^2 - (-x^2 - 6)^2 = 36.
Simplifying this equation would result in a polynomial of degree 4, not just a single value.
So, the answer needs to be in the form of a polynomial equation, not just a single value.
The equation you provided (-x^4 - 11x^2 - 36) seems to be one way of representing the exact solutions, but it would need to be verified.
9. The cosecant function (csc) is the reciprocal of the sine function (sin).
If sin B = 5√2/5√3, then csc B would be the reciprocal of sin B, which is √3/√2.
To rationalize the denominator, multiply both numerator and denominator by √2.
So, csc B = (√3/√2) × (√2/√2) = √6/2.
So, the correct answer is √6/2.
10. The sine function (sin) of 60° is equal to √3/2.
The cosine function (cos) of 30° is also equal to √3/2.
Since sin 60° and cos 30° have the same value, they are equal.
So, the statement "sin 60° is greater than cos 30°" is False.