Answer:
Step-by-step explanation:
13p⁵ + 6p - 12p² -(-9p - p² - 13p⁵) = 13p⁵ + 6p - 12p² + 9p + p² + 13p⁵
{Distribute (-1) to the second expression}
= <u>13p⁵ + 13p⁵</u> <u>-12p² + p²</u> <u>+ 6p + 9p</u>
{Combine like terms}
= 26p⁵ - 11p² + 15p
The answer is 5 cents because if the bat is a dollar more, then it the bat would be $1.05, and 0.05 + 1.05 = $1.10
you could also use the equation x + (x + 1) = 1.10 where x is the cost if the ball and x + 1 is the cost of the bat. x + x + 1 is the same as 2x + 1 = 1.10, and when solved x = 0.05.
Answer:
y = -3
Step-by-step explanation:
As per the condition given
8 + y = 5
y = 5 - 8 = -3
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
