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ratelena [41]
3 years ago
10

10 points

Mathematics
1 answer:
Masteriza [31]3 years ago
4 0

Answer:

The narrator uses the word they and tells us each person's thoughts.

Step-by-step explanation:

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Answer:

16 cents

Step-by-step explanation:

The answer is 16 cents because 207 cents divided by 12.5 oz equals 16 cents.

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It took a car 5 days to travel 1459 miles. What was the car's average speed, in miles per hour?
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The ratio of boys to girls at a movie is 4:7. If there are 21​ girls, how many boys are at the​ movie?
GaryK [48]

Answer:

12 boys

Step-by-step explanation:

7 x 3 = 21

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12 boys

3 0
3 years ago
If the integral of the product of x squared and e raised to the negative 4 times x power, dx equals the product of negative 1 ov
Nataly_w [17]

Answer:

A + B + E = 32

Step-by-step explanation:

Given

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C

Required

Find A +B + E

We have:

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C

Using integration by parts

\int {u} \, dv = uv - \int vdu

Where

u = x^2 and dv = e^{-4x}dx

Solve for du (differentiate u)

du = 2x\ dx

Solve for v (integrate dv)

v = -\frac{1}{4}e^{-4x}

So, we have:

\int {u} \, dv = uv - \int vdu

\int\limits {x^2\cdot e^{-4x}} \, dx  = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx

-----------------------------------------------------------------------

Solving

\int xe^{-4x} dx

Integration by parts

u = x ---- du = dx

dv = e^{-4x}dx ---------- v = -\frac{1}{4}e^{-4x}

So:

\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx

\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx

\int xe^{-4x} dx = -\frac{x}{4}e^{-4x}  -\frac{1}{4}e^{-4x}

So, we have:

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x}  -\frac{1}{4}e^{-4x}]

Open bracket

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x}  -\frac{1}{8}e^{-4x}

Factor out e^{-4x}

\int\limits {x^2\cdot e^{-4x}} \, dx  = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}

Rewrite as:

\int\limits {x^2\cdot e^{-4x}} \, dx  = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}

Recall that:

\int\limits {x^2\cdot e^{-4x}} \, dx  = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C

\int\limits {x^2\cdot e^{-4x}} \, dx  = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}

By comparison:

-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2

-\frac{1}{8}x = -\frac{1}{64}Bx

-\frac{1}{8} = -\frac{1}{64}E

Solve A, B and C

-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2

Divide by -x^2

\frac{1}{4} = \frac{1}{64}A

Multiply by 64

64 * \frac{1}{4} = A

A =16

-\frac{1}{8}x = -\frac{1}{64}Bx

Divide by -x

\frac{1}{8} = \frac{1}{64}B

Multiply by 64

64 * \frac{1}{8} = \frac{1}{64}B*64

B = 8

-\frac{1}{8} = -\frac{1}{64}E

Multiply by -64

-64 * -\frac{1}{8} = -\frac{1}{64}E * -64

E = 8

So:

A + B + E = 16 +8+8

A + B + E = 32

4 0
3 years ago
One acute angle of a right triangle measures 28°. To the nearest tenth, what is the length of the side opposite that angle if th
vitfil [10]
C because it is the answer
3 0
3 years ago
Read 2 more answers
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