Answer:
$4000 was invested at 4%, 2500 was invested at 3%
Step-by-step explanation:
First and foremost the question has to be define.
Total amount raised is $6500
Savings account percentage simple interest =3%
Government Bond: 4% simple interest
Equation for amount invested at each rate:
(6500-x)0.03 + 0.04x = 235
195 - 0.03x + 0.04x = 235
0.01x = 40
x = 4000
$4000 was invested at 4%, 2500 was invested at 3%
Answer:
10
Step-by-step explanation:
if she runs 5 km in half an hour, she runs 10 in a whole hour.
Answer:
= -180
Step-by-step explanation:
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
Answer:
A = –3
B = 7
Step-by-step explanation:
[(10x³y⁵)(4x²y¯²)/20x¯⁴yᵇ]ᵃ = y¹²/8x²⁷
The value of a and b can be obtained as shown in the attached photo.
