Mathematics College

Help with proving the following

Answers

Answer 1

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

First step

⇒ consider the fact cotθ = 1 / (tanθ)

[tex]\frac{1+tanx}{1+cotx} =\frac{1+tanx}{1+\frac{1}{tanx} }[/tex]

Second step

⇒ form a common denominator for the fraction in the 'denominator'

[tex]\frac{1+tanx}{1+\frac{1}{tanx} } =\frac{1+tanx}{\frac{tanx+1}{tanx} }[/tex]

Let's flip over the fraction on the denominator

[tex]\frac{1+tanx}{\frac{tanx+1}{tanx} } =(1+tanx) * \frac{tanx}{1+tanx} =tanx[/tex]

And there you go, you have proved the statement by following these steps!

*note, I used 'x' because the equation creator didn't have 'θ' symbol

Hope that helps!

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Related Questions

Martin has written the first 50 terms of the sequence with nth term 150 -4n. Work out which term is the first negative term.

what is the answer to this help

Answers

The first negative term of the sequence is -2

How to find the terms of a sequence?

The terms of the sequence which is the first negative term can be calculated as follows:

The sequence with nth term is 150 - 4n.

The first negative term will be the first term you will multiply by 4 that will be greater than 150.

Therefore,

nth term with first negative number = 150 - 4(38)

nth term with first negative number = 150 - 152

nth term with first negative number = -2

Therefore, the first negative term of the sequence is -2

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solve which 2 digit number is one more than a square and one less than cube?

Answers

The 2-digit number is 26:

26 - 1 = 25 is a square number.

26 + 1 = 27 is a cube number.

How to find the number?

Here we want to find a 2-digit number N, such that:

N + 1 is a cube number.N - 1 is a square number.

To do that, we can just create a list of cubic and square numbers of 2 digits, these are:

Square numbers:

4*4 = 16

5*5 = 25

6*6 = 36

etc...

Cube numbers:

3*3*3 = 27

4*4*4 = 64

etc...

Now, we can see that 25 is a square number and 27 is a cube number, then our 2-digit number can be 26.

Because:

26 - 1 = 25 is a square number.

26 + 1 = 27 is a cube number.

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1) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino. What would you expect to be true for all expected values for these seven games? In your discussion, also state whether the expected value is positive or negative. 1 ) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino . What would you expect to be true for all expected values for these seven games ? In your discussion , also state whether the expected value is positive or negative.

Answers

As per the question seems, the expected value can be positive, negative or zero.

The given question is of probability, which cannot be negative so don't get confused between expected values and probability, expected value and be negative, positive or zero.

What is probability?

Probability can be defined as the ration of favorable outcomes to the total number of events.

If person playing different games in casino , the probability of that person winning could be varying from 0/7 to 7/7 which implies that person can win from zero games to all games. If that person wins all the 7 games that mean he the gain in values, but if the loses 1 games or more games there than he supposed have gain or have loosen expected values so it can be positive, negative or zero. however the person loosen every game their is certain negative expected values.

Thus, The expected value can be positive, negative or zero.

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Solve the inequality −38<5x+7≤17

Answers

The answer to this inequality would be -9

66877383

Step-by-step explanation:

I made a single dad be single of ⅝

Suppose that $4000 is placed in a savings account at an annual rate of 6.4%, compounded quarterly. Assuming that no withdrawals are made, how long will it
take for the account to grow to $4916?
Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answers

Answer:

3.25 years (nearest hundredth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsed

Given:

A = $4916P = $4000r = 6.4% = 0.064n = 4 (quarterly)

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 4916=4000\left(1+\frac{0.064}{4}\right)^{4t}[/tex]

[tex]\implies \sf 4916=4000\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \dfrac{4916}{4000}=\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \dfrac{1229}{1000}=\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=\ln \left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=4t \ln \left(1.016\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln \left(\frac{1229}{1000}\right)}{4\ln \left(1.016\right)}[/tex]

[tex]\implies \sf t=3.247594892...[/tex]

Therefore, it will take 3.25 years (nearest hundredth) for the account to grow to $4916.

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x is increased by 50% and decreased by 30%. What is the result?

Answers

Answer:

its the same as increasing x by 5 percent

Answer:

1.05x is the answer

Step-by-step explanation:

Find the surface of the cube with length of a side

Answers

Answer: 319.74 square mm

Step-by-step explanation:

[tex]6(7.3)^2=319.74[/tex]

Select all of the equations that represent linear relationships. 5 + 2y = 13 y = 7 y – 5 = 2(x – 1) = x + 7 x = –4

Answers

The equations that represent linear relationship is y – 5 = 2(x – 1)

What are linear functions

Linear functions are functions that has a leading degree of 1. According to the question, we need to determine the function that represents linear equation.

The required equation must have a degree of 1 and must contain both dependent and independent variables.

The equations that represent linear relationship is y – 5 = 2(x – 1)

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Answer:

The anser is:

Step-by-step explanation:

I hope this helps, have a blessed day :)

Evaluate the following.

Answers

Step-by-step explanation:

1) 3 + 4 = 7

2) 6 - 6 = 0

3) 1 + 3 = 4

4) 6 + 9 = 15

5) 10 - 14 + 2 = -2

6) 2 + 3 - 5 = 0

Which of the expressions below cannot be rewritten using the associative
property?
.
OA. 15 (410)
OB. (5+14) + 10
OC. 12 (17 ÷ 2)
OD. (12.9) •10
SUBMIT

Answers

Answer:

Step-by-step explanation:

Help please quueens i need help

Answers

Answer:

x = 3

Step-by-step explanation:

We can use the following equation to solve for x:

[tex]315=9x-27+8x+24+5x-17+2x+23\\315=(9x+8x+5x+2x)+(-27+24-17+23)\\315=24x+3\\312=24x\\13=x[/tex]

Giving brainliest :)

Answers

The system of equation that will represent her purchase is as follows:

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

How to represent system of equation?

At store A she will pay a total sum of $50.73 for bread and milk.

At store B she will pay a total sum of $51.63 for bread and milk.

Therefore, the system of equation that will represent her purchase is as follows:

where

b = number of bread

m = number of milk

Therefore,

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

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Write "six times x minus 3" as an expression.

Answers

Answer:

6x-18

Step-by-step explanation:

6*(x-3)

multiply 6 with x and 3

Solve for x. Enter the solutions from least to greatest.
Round to two decimal places.
(x + 8)^2 - 7 = 0

asap will give brainliest

Answers

The value of x according to the equation in the task content is; -5.35 or -10.65.

What is the value of x in the equation?

The equation given in the task content is; (x + 8)² -7 = 0.

Hence, the equation can be solved as follows;

(x + 8)² - 7 = 0

x² + 16x +64 -7 = 0

x²+ 16x +57 = 0

By solving by means of the quadratic formula, we have;

x = -5.35

x = -10.65

Answers

The amount Barbara earned this month is $1512.

How much did Barbara earn?

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

Barbara's earnings = percentage commission x worth of goods sold

7% x 21,600

0.07 x 21,600 = $1512

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2011?
7. Maria, a sales representative for a large consumer goods company, is paid 3% of the total profits earned by her company.
Her company averages 10% profit on sales. If Maria's total income for the year was $60,000, what total sales did her
company realize?

Answers

Step-by-step explanation:

60000÷ 10 = 600 and 600 ÷ 3 =20

The total sales realized by the company was $20,000,000.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Let x be the total sales realized by the company.

Maria's pay is 3% of the total profits, which is 3% of 10% of total sales

0.03(0.1x) = 0.003x.

Her total income is given as $60,000, so we have:

0.003x = 60000

Solving for x:

x = 60000/0.003 = 20,000,000

Therefore, the total sales realized by the company was $20,000,000.

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For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .

The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!

Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

Part b: Find two values of x that will create a profit of $50 .

The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).

Answers

The equation for the profit from selling the items is P = 40x-0.5x²-300. The values of x are 10 and 70.

How to solve for the expression

We have the cost function in this question to be

Cx = 60x+300

Revenue = 100x−0.5x²

A. The revenue function is stated as the revenue - cost

= (100x−0.5x²)-60x+300

We have to open the equation

40x-0.5x²-300

B. when profit is 50 dollars

50 = 40x-0.5x²-300

We have to multiply both sides by 10

500 = 400x - 5x² - 3000

We have to collect like terms and form a quadratic equation

5x² - 400x - 3500 = 0

We have to solve the quadratic equation above using a quadratic calculator.

Hence

x = 10, 70

So the two values that would create a profit of 50 dollars is 10 and 70.

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Which of the following best represents the altitude, h, of the triangle shown? (5 pts.) A. tan 75° B. 11.5 sin 75° C. D. 23 cos 75° 23 sin 75° M21 R 23* 759

Answers

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio shows the relationship between the sides and angles of a right angle triangle.

Let us assume that the right triangle has a altitude h, hypotenuse of 23 and angle between base and hypotenuse is 75°, hence:

sin(75) = h/23

h= 23sin(75)

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

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You are playing an online game with your friend and they are on level 4. You are on level 6 and can beat, on average, 4 levels per hour. If your friend can beat 5 levels per hour, how many hours will it take for you and your friend to be on the same level? Think about how you would solve this question. Write at least two sentences about how you would attempt this problem. You can think about a new method of solving or use methods that you already have learned.

Answers

It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it would take to be on the same level with your friends. I am at level 6 and my friend is on level 4, hence:

5t = 4t + 2

t = 2 hours

It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.

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A garden table and a bench cost $700 combined. The garden table costs $50 less than the bench. What is the cost of the bench?

Answers

The bench costs $325

Cost of bench = x

Cost of garden table = x - 50

x - 50 + x = 700

2x - 50 = 700

2x = 750

x = 325

Cost of bench=x. Cost of garden table=x-50 X-50+x=700 2x-50=700 2x=750 X=375

11.
An IV of D5W 1000 mL was ordered to infuse over 8 hr at a rate of 42 gtt/min (42 macrogtt/min). Drop
factor: 20 gtt/mL. After 4 hr, you notice that only 400 mL has infused.
Recalculate the rate in gtt/min for the remaining solution

Answers

The rate is 50gtt per minutes.

How to calculate the growth rate?

From the information, out of the total hours of 8 hours, four hours were used.

The volume will be:

= 1000 - 400

= 600ml

Time = 4 × 60 = 240 minutes

Drop factor = 20

Therefore, the growth rate will be:

= 600/240 × 20

= 50gtt/min

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Which ordered pairs make both inequalities true? Check all that apply.

Answers

We can actually deduce here that the ordered pairs that make both inequalities true are:

(1,1)(2, 2)

What is inequality?

An inequality is known to be an expression that shows that certain variables or values are not equal to each other. It is usually seen in an inequality expression as:

> (greater than)< (less than)≥ (greater than or equal to) ≤ (less than or equal to).

We see the attached image that shows the graph of inequality and which completes the question.

The options that complete the question are:

A. –2, 2

B. (0, 0)

C. (1,1)

D. (1, 3)

E. (2, 2)

When we insert the values of each axes into the inequality expressions given, we will discover that the ordered pairs that the inequalities true is (1,1) and (2, 2).

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5 pts Which side would create a right triangle if the first two sides have lengths 7 and 123 5 pts Which side would create a right triangle if the first two sides have lengths 7 and sq rt 123

Answers

Answer:

sqrt(172) = hypotenuse

Step-by-step explanation:

IF those are the leg lengths (sides) and not the hypotenuse, then use Pythagorean theorem

c^2 = 7^2 + sqrt (123) ^2

c = sqrt (172)

If sqrt 172 is the hypotenuse :

(sqrt123)^2 = 7^2 + x^2

then x = sqrt (74 )

You enter a room. 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.

How many legs are on the ground?

Answers

Answer:

Step-by-step explanation:

I think it’s a trick question because “legs” can also mean like chair legs that hold it up. Therefore:

2 dogs = 8 legs

4 horses = 16 legs

1 giraffe = 4 legs

And a bed: 4 legs(things that hold it up)

And a chair: 4 legs (things that hold it up)

This is assuming that the bed is a normal bed with stools holding it up

And the chair has 4 piles aswell as no missing legs in the animals… lol

8 sin x cos3 x + 8 sin3 x cos x = ?

Answers

Answer:

Step-by-step explanation:

We use the known identity:

sin (A + B) sin A cos B + cos A sin B.

8 sin x cos 3x + 8 sin 3x cos x

= 8 (sin x cos 3x + sin 3x cos x)

= 8sin (x + 3x)

= 8 sin 4x

Identity :

sin (A + B) sin A cos B + cos A sin B

= 8 sin x cos 3x + 8 sin 3x cos x

= 8 (sin x cos 3x + sin 3x cos x)

= 8sin (x + 3x)

= 8 sin 4x

DEF and RST are complementary angles. If DEF is (3(-5 + 2x)) and RST is (x - 7), what is the measure of DEF?

Answers

From the given information, the measure of DEF is 81°

Calculating the measure of angles

From the question, we are to determine the measure of DEF

From the given information,

DEF and RST are complementary angles. This means they sum up to 90°

Thus,

(3(-5 + 2x)) + (x - 7) = 90

(-15 + 6x) + (x - 7 ) = 90

-15 + 6x + x - 7 = 90

6x + x = 90 + 15 + 7

7x = 112

x = 112/7

x = 16

Then, substitute the value of x to determine the measure of DEF

(3(-5 + 2x))

= (3(-5 + 2(16)))

= (3(-5 + 32))

= (3(27))

= 81°

Hence, the measure of DEF is 81°

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let A and B sets. when do we say set A is equal to set B

Answers

Step-by-step explanation:

It is said A=B I have drawn the Venn diagram of A=B

Can i get a solution for this?

Answers

the effects of the given transactions on the accounting equation are:

increase in assets and increase in equity.increase in assets and increase in liabilities.no change increase in assets and increase in equity.decrease in assets and decrease in liabilities. decrease in assets and decrease in equity. decrease in assets and decrease in equity. decrease in assets and decrease in equity. no change increase in assets and increase in liabilities.

how is the accounting equation affected?

an investment would increase assets (cash) and also increase equity. every expense such as salaries would decrease assets and equity.

incurring debt would increase assets and liabilties while paying off debt would decrease both asset (cash) and liabilities.

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A bacteria culture starts with 1000 bacteria and the number doubles every 40 minutes. (a) find a formula for the number of bacteria at time (b) find the number of bacteria after one hour (c) after how many minutes will there be 50000 bacteria?

Answers

The formula for the number of bacteria at time t is 1000 x (2^t).

The number of bacteria after one hour is 2828

The number of minutes for there to be 50,000 bacteria is 324 minutes.

What is the number of bacteria after 1 hour?

The exponential function that can be used to determine the number of bacteria with the passage of time is:

initial population x (rate of increase)^t

1000 x (2^t).

Population after 1 hour : 1000 x 2^(60/40) = 2828

Time when there would be 50,000 bacteria : In(FV / PV) / r

Where:

FV = future bacteria population = 50,000PV = present bacteria population = 1000r = rate of increase = 100%

In (50,000 / 1000)

In 50 / 1 = 3.91 hours x 60 = 324 minutes

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A rectangle with base b and height h has an area of 235 square-inches. Express the perimeter of the rectangle as a function of its base

Answers

The perimeter of the rectangle as a function of its base is P = 2(b + 235/b)

What are perimeters?

The perimeter of a shape is the sum of the side lengths of the shape For all regular quadrilaterals, you add up the side lengths to determine the area

How to express the perimeter of the rectangle as a function of its base?

The given parameters are

Area = 235 sqare inches

The area of a rectangle is calculated using

Area = Base * Height

Note that the area of a shape is the amount of space on the shape

Recall that the area of a rectangle is calculated using

Area = Base * Height

Rewrite the above equation as

A = bh

So, we have

bh = 235

Make h the subject of the formula

h = 235/b

The perimeter of the rectangle is

P = 2(b + h)

So, we have

P = 2(b + 235/b)

Hence, the perimeter of the rectangle as a function of its base is P = 2(b + 235/b)