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Grace [21]
3 years ago
10

Integral of cosecx dx =log|tanx/2| show that.​

Mathematics
1 answer:
Pie3 years ago
7 0

ANSWER:

Let t = logtan[x/2]

⇒dt = 1/ tan[x/2] * sec² x/2 × ½ dx

⇒dt = 1/2 cos² x/2 × cot x/2dx

⇒dt = 1/2 * 1/ cos² x/2 × cosx/2 / sin x/2 dx

⇒dt = 1/2 cosx/2 / sin x/2 dx

⇒dt = 1/sinxdx

⇒dt = cosecxdx

Putting it in the integration we get,

∫cosecx / log tan(x/2)dx

= ∫dt/t

= log∣t∣+c

= log∣logtan x/2∣+c where t = logtan x/2

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Diameter=10.5 in . Determine the area of each circle. Use 3.14 or 22/7 for pie . Round to the nearest tenth.
zloy xaker [14]

Answer:

86.5 square inches

Step-by-step explanation:

Area of circle: pi*r^2

  • first find the radius

10.5in /2= 5.25in

  • find the square

5.25^2=27.5625

  • multiply with pi

27.5625*3.14=86.54625

rounded 86.5 in

5 0
3 years ago
Rationalize the denominator √7x/75
Leokris [45]
Do what the problum ids telling you than apply it to the math and you will always get the right answer
7 0
3 years ago
Answer all parts of number 1 thank you.
Scorpion4ik [409]

Hi!

1.)

a:A u B=

(1.0. - 5. \frac{1}{2} .e)

(The same elements are written once.)

b:A u C

(1.0 - 5. \frac{1}{2} .2)

c:B u C

( - 5 .1.e.0.2)

Note:I used dots to mean commas .

Good work!

7 0
2 years ago
Plot a graph for the following data recorded for an object falling from rest
shusha [124]
  1. The kind of curve obtained is linear.
  2. The relationship between the variables is direct variation.
  3. After 4.5 seconds, I expect the velocity to be equal to 140 ft/s.
  4. The amount of time required for the object to attain a speed of 100 ft/s is 3.2 seconds.

<h3>What is a graph?</h3>

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to plot a graph for the data (velocity and time) recorded for an object that is falling from rest.

Based on the graph for the data (see attachment), we can logically deduce the following points:

  • The kind of curve obtained is linear.
  • The relationship between the variables is direct variation.
  • After 4.5 seconds, I expect the velocity to be equal to 140 ft/s.
  • The amount of time required for the object to attain a speed of 100 ft/s is 3.2 seconds.

Read more on graphs here: brainly.com/question/25875680

#SPJ1

Complete Question:

Plot a graph for the following data recorded for an object falling from rest

a. What kind of a curve did you obtain?

b. What is the relationship between the variables?

c. What do you expect the velocity to be after 4.5 s?

d. How much time is required for the object to attain a speed of 100 ft/s?

7 0
2 years ago
1) WET SURPRISE A water balloon is launched off of a patio. The path of the water
mart [117]

The function of the water balloon is an illustration of a quadratic function.

The balloon will splat on the ground after 2.5 seconds

The function is given as:

h(t) = -6t^2 + 13t + 5

When the balloon splats on the ground, the value of h(t) is 0.

So, we have:

-6t^2 + 13t + 5 = 0

Expand the expression

-6t^2 + 15t- 2t + 5 = 0

Factorize the above expression

-3t(2t - 5)- 1(2t - 5 )= 0

Factor out 2t - 5 in the 2t - 5

(-3t - 1)(2t - 5 )= 0

Split the equation into 2

-3t - 1 = 0\ or\ 2t - 5= 0

Rewrite as:

-3t = 1\ or\ 2t = 5

Solve for t

t = -\frac 13\ or\ t = \frac 52

The value of t cannot be less than 0 i.e. negative.

So, we have

t = \frac 52

Divide 5 by 2

t = 2.5

Hence, the balloon will splat on the ground after 2.5 seconds

Read more about quadratic functions at:

brainly.com/question/11631534

6 0
3 years ago
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