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Lelu [443]
3 years ago
14

How do you do these two questions?

Mathematics
1 answer:
nignag [31]3 years ago
5 0

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

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dlinn [17]

Answer:

d=101.4\ \text{pounds}/\text{feet}^3

Step-by-step explanation:

Given that,

Mass of material, m = 6900 grams

Volume of the material, V = 4.5 quarts

We need to find the density in pounds per cubic foot

We know that,

1 pound = 453.59 grams

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Also, 1 cubic foot = 29.92 quarts

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Or

d=\dfrac{15.21\ \text{pounds}}{0.15\ \text{feet}^3}\\\\d=101.4\ \text{pounds}/\text{feet}^3

Hence, the density of the material is 101.4\ \text{pounds}/\text{feet}^3

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3 years ago
Please answer the following questions: <br><br> 1. 1/2*8=<br> 2. 1/4*4=<br> 3. 1/3*6=
yan [13]
Hey there!

When we multiply fractions and whole numbers, we simply take that whole number and put it over them, and just multiply across. That gives us:

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Notice how it's four, because when we have a fraction, we divide. 8 divided by 2 equals four. Next:

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4/4 is equal to 1 because 4 divided by 4 is one. 4 goes into 4 once. Next, we have:

\frac{1}{3}*6 = \frac{6}{3} = 2

That's because 6/3 = 2.

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7 0
3 years ago
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3 years ago
How do you solve this (5/6)(5/6)
Vikentia [17]

Answer:

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Step-by-step explanation:

Use the top top, bottom bottom method.

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