3

marin [14]

Answer:

$\sec x + c$

Step-by-step explanation:

$\int \frac{ \sin \: x}{ { \cos}^{2}x } \: dx \\ \\ = \int \frac{ \sin \: x}{ { \cos}x } . \frac{ 1}{ { \cos}x } \: dx \\ \\ = \int \tan x . \sec x \: dx \\ \\ = \sec x + c$

7 0

3 years ago

Find the annual interest rate

patriot [66]

The annual interest rate is 6.2%.

Solution:

Given data:

Interest = $310

Principle = $1000

Time = 5 years

To find the annual interest rate:

Simple Interest formula:

$$S.I=\frac{PRT}{100}$

Substitute the given values in the formula, we get

$$310=\frac{1000\times R \times5}{100}$

Do cross multiplication.

$$310 \times 100=1000\times R \times5$

Divide both sides of the equation by 1000, we get

$$\frac{310 \times 100}{1000}=\frac{1000\times R \times5}{1000}$

$31=R\times 5$

Divide by 5 on both sides of the equation, we get

$$\frac{31}{5}=\frac{R\times 5}{5}$

$6.2=R$

R = 6.2%

Hence the annual interest rate is 6.2%.

8 0

3 years ago

Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2.

azamat

First one is 5x-2 Second one is 8-3x and Third is -5x*4

3 0

3 years ago

Yesterday 160 guest at a hotel called for room service, and 240 guest did not called for room service. What is the percentage of

Dmitry [639]

160/400
80/200
40/100
C

8 0

3 years ago

Find the number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4. Hint consider the

Verdich [7]

Answer:

1364 is the number of possibilities for positive integers less than 1,00,000.

Step-by-step explanation:

1. 5 digit numbers:

We have 5 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 5 digit numbers:

$4 \times 4 \times 4 \times 4 \times 4\\ \Rightarrow 1024$

2. 4 digit numbers:

We have 4 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 4 digit numbers:

$4 \times 4 \times 4 \times 4 \\ \Rightarrow 256$

3. 3 digit numbers:

We have 3 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 3 digit numbers:

$4 \times 4 \times 4 \\ \Rightarrow 64$

4. 2 digit numbers:

We have 2 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 2 digit numbers:

$4 \times 4 \\ \Rightarrow 16$

5. 1 digit numbers:

We have 1 place here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 1 digit numbers:

$4$

We can add all the above possibilities to find the total.

So, number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4 = 1024 + 256 + 64 + 16 + 4 = 1364

3 0

3 years ago