The graph of a quadratic equation opens down when the value of a,b or c Is negative
1 answer:
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Consider inequality This inequality is equivalent to inequality
This means that
The greatest integer number n, such that when dividing by 7 gives the remainder 4 is 39. Then subtract 7, you get 32, then 25 and so on.
When n=-39, -32, -25, -18, -11, -4, 4, 11, 18, 25, 32, 39 then dividing by 7 the remainder is 4.
Answer: 12 integers.
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.
Answer:
A = 12000(1.0002466)²⁹²⁰
Step-by-step explanation:
The formula for the amount after compound interest is:
"A" is the amount, or balance.
"P" is the principal, or starting amount/investment.
"i" is the interest rate for each compounding period.
"n" is the number of compounding periods.
The interest rate each compounding period, "i", is calculated with i=r/c
"r" is the annual interest rate in decimal form.
"c" is the compounding frequency. (If compounded annually, c=1. If monthly, c=12.)
The number of compounding periods, "n", is calculated with n=tc.
"t" is the time in years.
"c" is the compounding frequency.
In this problem:
t = 8
P = 12,000
r = 9%, or r = 0.09 for decimal form.
c = 365
Calculate "i" and "n".
i = r/c
i = 0.09/365
i = 0.00024657534
i ≈ 0.0002466
n = tc
n = 8(365)
n = 2920
Substitute these back into the formula:
A = P(1 + i)ⁿ
A = 12000(1+0.0002466)²⁹²⁰
A = 12000(1.0002466)²⁹²⁰