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marysya [2.9K]
3 years ago
7

Integral of sec (3x) tan (3x) dx

Mathematics
1 answer:
zhannawk [14.2K]3 years ago
5 0
\int {sec (3x)tan(3x)} \, dx= \int { \frac{1}{cos(3x)}* \frac{sin(3x)}{cos(3x)}  } \, dxSubstitution:u=cos(3x), du=-3sin(3x)dx, sin(3x)dx= du/-3 Integral becomes:\frac{-1}{3} *\int { \frac{1}{ u^{2} } } \, du= \frac{-1}{3} \int {u^{-2} } \, du=\frac{ u^{-1} }{3}= \frac{1}{3u}= \frac{1}{3cos(3x)}+C 
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Mark has a piece of wood 4 1/4 feet long. Tony has a piece of wood 1 2/4 feet long. How much wood do the boys have altogether. p
Alona [7]
They have 5 3/4 ft

4+1=5
1/4+2/4=3/4


but hey, its not the length of your wood that matters, its how you use it XD
8 0
3 years ago
The linear inequality y<-2/3x+2 is graphed. Determine a solution for the inequality. A) (0,2) B) (3,0) C) (0,0) D) (0,3)
jenyasd209 [6]

Hello!

The graph y < -2/3x + 2 has a dotted line. That means that any points on the dotted line or not shaded, is not a solution to this inequality. Since we are given 4 choices, we can substitute those values into the given inequality to see if it is true.

A) (0, 2)

2 < -2/3(0) + 2

2 < 2, this is false.

B) (3, 0)

0 < -2/3(3) + 2

0 < -2 + 2

0 < 0, this is false.

C) (0, 0)

0 < -2/3(0) + 2

0 < 2, this is true.

D). (0, 3)

3 < -2/3(0) + 2

3 < 2, this is false.

To check if choice C) (0, 0) is true, we should look at the given graph.

Since (0, 0) is in the shaded area, and is not graphed on the dotted line, therefore, a solution to this linear inequality is C, (0, 0).

5 0
4 years ago
How do u make 3/4 in a mix number as a whole number or decimal?
KengaRu [80]
In decimal form it's .75 and that's all you can make it
7 0
3 years ago
Walter invests $100,000 in an account that compounds interest continuously and earns 12%. How long will it take for his money to
prohojiy [21]

Answer:

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

3 = e^{0.12 t}

Now we can apply natural logs on both sides;

ln(3) = 0.12 t

And then the value of t would be:

t = \frac{ln(3)}{0.12}= 9.16 years

And rounded to the nearest tenth would be 9.2 years.

Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

A =P e^{rt}

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means A= 300000 and we want to find the value for t.

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

3 = e^{0.12 t}

Now we can apply natural logs on both sides;

ln(3) = 0.12 t

And then the value of t would be:

t = \frac{ln(3)}{0.12}= 9.16 years

And rounded to the nearest tenth would be 9.2 years.

5 0
3 years ago
Dominic is building a bench with a seat in the shape of a trapezoid. One base is 5 feet. The other base is 4 feet. The perpendic
Vlad [161]
By definition, the formula for finding the area of a trapezoid is
 A = [(b1 + b2) x h] / 2
 Where,
 b1: Base 1
 b2: Base 2
 h: height, or distance between bases.
 Substituting we have:
 A = ((5 + 4) * (2.5)) / 2
 A = 11.25 feet ^ 2

 Answer: 
 the area of the seat is:
 A = 11.25 feet ^ 2
8 0
3 years ago
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