Answer:
0.2 coulombs is the answer
For each parabola, you have to do a system of equation with the line y = x - 5 and find which of them has one real solution.
For that you can solve the systems and find the roots, but you can also use the rule that to have one real solution the discriminant of the quadratiic equation (b^2 - 4ac) has to be zero.
1)
y = x - 5
y = x^2 + x - 4
=> x - 5 = x^2 + x - 4
=> x^2 + 1 = 0
It is easy to tell, by simple inspection, that this equation has not real solutions.
2)
y = x -5
y = x^2 + 2x - 1
=> x - 5 = x^2 + 2x - 1
=> x^2 + x + 4 = 0
discriminant = b^2 - 4ac = 1^2 - 4(1)(4) = 1 - 16 = - 15
A negative discriminant means that there are not real solutions.
3)
y = x - 5
y = x^2 + 6x + 9
x - 5 = x^2 + 6x + 9
=> x^2 + 5x + 14 = 0
=> b^2 - 4ac = 5^2 - 4(1)(14) = 25 - 56 = - 31 => no real solutions
4)
y = x - 5
y = x^2 + 7x + 4
x - 5 = x^2 + 7x + 4
=> x^2 + 6x + 9 = 0
=> b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0 => the system has one real solution.
By the way, that solution is easy to find because you can factor the equation as: (x + 3)^2 = 0 => x = - 3
Answer:
C
Step-by-step explanation:
Answer:
$120.1355
Step-by-step explanation:
We can model this as an exponencial function:
P = Po * (1+r)^t
Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.
For this case, we have that Po = 900, r = -25% = -0.25 and t = 7, so we can find the value of P
P = 900 * (1 - 0.25)^7 = $120.1355
The price after 7 years will be $120.1355.
Answer:
38.25 cm²
Step-by-step explanation:
We use the formula for the length of an arc to find the central angle of the sector of the circle.
Then we use the formula for the area of a sector of a circle to find the area.
Length of arc of circle of radius r:
s = arc length
n = measure of the central angle of the sector
Area of sector of circle of radius r:
A = area of sector of circle
n = measure of the central angle of the sector