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Reil [10]
3 years ago
15

We must use substitution to do this second integral. We can use the substitution t = 7x, which will give dx = Correct: Your answ

er is correct. dt. Ignoring the constant of integration, we have sin(7x) dx =
Mathematics
1 answer:
tankabanditka [31]3 years ago
6 0

Answer:

Therefore, the solution is:

\boxed{\int \sin 7x\, dx=-\frac{\cos 7x}{7}}

Step-by-step explanation:

We calculate the given integral.  We use the substitution t = 7x.

\int \sin 7x\, dx=\begin{vmatrix} 7x=t\\ 7\, dx=dt\\ dx=\frac{dt}{7} \end{vmatrix}\\\\=\int \sin t \cdot \frac{1}{7}\, dt\\\\=\frac{1}{7}\cdot (-\cos t)\\\\=-\frac{\cos 7x}{7}

Therefore, the solution is:

\boxed{\int \sin 7x\, dx=-\frac{\cos 7x}{7}}

You might be interested in
If Jake buys 3 new shirts, how many of them would you expect to be t-shirts, and how many would you expect to be collared?
Sophie [7]

Answer:

2 t-shirts ; 1 collar shirt

Step-by-step explanation:

We need to first obtain the ratio of T - shirts to collar shirts :

T - shirts = 10

Collar shirts = 5

Ratio = T - shirts / Collar shirts = 10 / 5 = 2 /1 = 2:1

Hence, using the ratio obtained ; if Jake buys 3 new shirts :

Number of T-shirts :

(Ratio of t-shirts / total ratio) * new t-shirts

2/3 * 3 = 2 t-shirts

Collar shirts :

1/3 * 3 = 1

2 t-shirts ; 1 collar shirt

4 0
2 years ago
The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppos
xenn [34]

Answer:

(a) P(X > $57,000) = 0.0643

(b) P(X < $46,000) = 0.1423

(c) P(X > $40,000) = 0.0066

(d) P($45,000 < X < $54,000) = 0.6959

Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

<em>Let X = annual salaries in the metropolitan Boston area</em>

SO, X ~ Normal(\mu=$50,542,\sigma^{2} = $4,246^{2})

The z-score probability distribution for normal distribution is given by;

                      Z  =  \frac{X-\mu}{\sigma }  ~ N(0,1)

where, \mu = average annual salary in the Boston area = $50,542

            \sigma = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

    P(X > $57,000) = P( \frac{X-\mu}{\sigma } > \frac{57,000-50,542}{4,246 } ) = P(Z > 1.52) = 1 - P(Z \leq 1.52)

                                                                     = 1 - 0.93574 = <u>0.0643</u>

<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

    P(X < $46,000) = P( \frac{X-\mu}{\sigma } < \frac{46,000-50,542}{4,246 } ) = P(Z < -1.07) = 1 - P(Z \leq 1.07)

                                                                     = 1 - 0.85769 = <u>0.1423</u>

<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

    P(X > $40,000) = P( \frac{X-\mu}{\sigma } > \frac{40,000-50,542}{4,246 } ) = P(Z > -2.48) = P(Z < 2.48)

                                                                     = 1 - 0.99343 = <u>0.0066</u>

<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.

(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)

    P($45,000 < X < $54,000) = P(X < $54,000) - P(X \leq $45,000)

    P(X < $54,000) = P( \frac{X-\mu}{\sigma } < \frac{54,000-50,542}{4,246 } ) = P(Z < 0.81) = 0.79103

    P(X \leq $45,000) = P( \frac{X-\mu}{\sigma } \leq \frac{45,000-50,542}{4,246 } ) = P(Z \leq -1.31) = 1 - P(Z < 1.31)

                                                                      = 1 - 0.90490 = 0.0951

<em>The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively</em>.

Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = <u>0.6959</u>

3 0
2 years ago
Complete the square to factor X^2 +10X=-8
ella [17]

Answer: x=\sqrt{17}-5 and x = -\sqrt{17}-5

Step-by-step explanation:

Alright, lets get started.

The given equation is :

x^{2} +10x = -8

Adding 8 in both sides, it will become

x^{2} +10x + 8 = -8 +8

x^{2} +10x + 8 = 0

To make it perfect square, we need to add 25 and subtract 25

x^{2} +10x + 8 +25-25= 0

x^2+10x+25+8-25=0

(x+5)^2+8-25=0

(x+5)^2-17=0

Adding 17 in both sides  

(x+5)^2=17  

taking square root

x+5=\sqrt{17}

So,

x=\sqrt{17}-5 and x = -\sqrt{17}-5  .. Answer

Hope it will help :)

7 0
3 years ago
Read 2 more answers
PLZ HELP I NEED TO SUMMIT THIS
weeeeeb [17]
Help with what, unless there is a picture, my phone is glitchy and i cant see pics for sum reason
4 0
2 years ago
I will mark them as brainliest who solve it
konstantin123 [22]

Answer:

now the answer sorry for that i am in 5th grade so i dont know sorry

Step-by-step explanation:

8 0
3 years ago
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