The ratio of incorrect to correct answers on Marco's math test was 4 to 6. If Marco missed 39 problems, how many did he get corr
1 answer:
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Answer:
The functions given are:
f(x) = x²
g(x) = f(-4x-3) + 1
First, find f(-4x-3):
f(x) = x²
f(-4x-3) = (-4x-3)²
Find g(x):
g(x) = f(-4x-3) + 1
g(x) = (-4x-3)² + 1
g(x) = (-1)² (4x+3)² + 1
g(x) = (4x+3)² + 1
First take
y = (x)²
Compress the graph along x axis by multiplying x with 4
y = (4x)²
Shift the graph left by 0.75 units, by adding 3 to x term.
y = (4x+3)²
Shift the graph up by 1 unit by adding 1 to the total terms.
y = (4x+3)² +1
Givens
y = 2
x = 1
z(the hypotenuse) = √(2^2 + 1^2) = √5
Cos(u) = x value / hypotenuse = 1/√5
Sin(u) = y value / hypotenuse = 2/√5
Solve for sin2u
Sin(2u) = 2*sin(u)*cos(u)
Sin(2u) = 2() = 4/5
Solve for cos(2u)
cos(2u) = - sqrt(1 - sin^2(2u))
Cos(2u) = - sqrt(1 - (4/5)^2 )
Cos(2u) = -sqrt(1 - 16/25)
cos(2u) = -sqrt(9/25)
cos(2u) = -3/5
Solve for Tan(2u)
tan(2u) = sin(2u) / cos(2u) = 4/5// - 3/5 = - 0.8/0.6 = - 1.3333 = - 4/3
Notes
One: Notice that you would normally rationalize the denominator, but you don't have to in this case. The formulas are such that they perform the rationalizations themselves.
Two: Notice the sign on the cos(2u). The sin is plus even though the angle (2u) is in the second quadrant. The cos is different. It is about 126 degrees which would make it a negative root (9/25)
Three: If you are uncomfortable with the tan, you could do fractions.