Find the remainder when f(x) = x3 + 14x2 − 7x − 10 is divided by x − 3
2 answers:
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Answer:
see explanation
Step-by-step explanation:
(a)
The zeros are x = 1 and x = 5, thus the factors are (x - 1) and (x - 5)
f(x) = a(x - 1)(x - 5)
To find a substitute (0, 15), the coordinates of the y- intercept into the equation.
15 = a(0 - 1)(0 - 5) = a(- 1)(- 5) = 5a ( divide both sides by 5)
a = 3
Thus h = 1, k = 5, a = 3 and
f(x) = 3(x - 1)(x - 5)
(b)
The axis of symmetry is a vertical line with equation x = c ( c is a constant )
The axis of symmetry passes through the midpoint of the zeros
x = =
= 3
Equation of axis of symmetry is x = 3
(c)
The axis of symmetry passes through P, with x- coordinate x = 3
Substitute x = 3 into the function for corresponding value of y
f(3) = 3(3 - 1)(3 - 5) = 3(2)(- 2) = - 12
Coordinates of P = (3, - 12 )
Answer:
- September
Step-by-step explanation:
The temperature in Beijing, in m months after January, is given by the following equation:
In which m is the number of months after January.
During which month in the year would the temperature reach 55°F?
We have to find m for which: T(m) = 55. So
Now, we apply the inverse cosine, on both sides of the equation, to find the value of m.
Now, with the help of a calculator, in radians:
8.27 months after January, since 8.27 + 1 = 9.28, it happens during the month of September.