Mathematics College

Please solve this for me

Answers

Answer 1

[tex]6 sin² x + 4 cos²x = Stanx[/tex]

[tex]Correct option is B)

Given, 4cos2x+6sin2x=5

[/tex]

[tex]⇒4cos2x+4sin2x+2sin2x=5

⇒2sin2x=1⇒sin2x=21=(21)2

⇒x=nπ±4π

[/tex]

Solve any question of Trigonometric Functions with:-

Answer 2

[tex]~~~~~~6 \sin^2 x + 4 \cos^2 x = 5 \tan x \\\\\implies 3 \cdot 2\sin^2 x + 2 \cdot 2 \cos^2 x = 5 \tan x\\ \\\implies 3(1- \cos 2x ) + 2( 1 + \cos 2x) = 5 \tan x\\\\\implies 3 - 3 \cos 2x +2 +2 \cos 2x = 5 \tan x\\\\\implies 5- \cos 2x = 5 \tan x\\ \\\implies 5 - \left(\dfrac{1- \tan^2 x}{ 1+ \tan^2 x} \right)=5 \tan x\\\\\implies \dfrac{5+5 \tan^2x -1 + \tan^2 x}{1+ \tan^2 x} = 5 \tan x\\\\\implies 4 + 6\tan^2 x = 5( \tan x)(1+ \tan^2 x)\\\\\implies 4 +6\tan^2 x = 5 \tan x + 5 \tan^3 x[/tex]

[tex]\implies 5\tan^3 x -6 \tan^2 x+5 \tan x-4=0\\\\\implies 5 \tan^3 x - 5 \tan^2 x - \tan^2x + \tan x+ 4\tan x -4=0 \\\\\implies 5\tan^2 x(\tan x-1) -\tan x(\tan x-1) +4(\tan x-1)=0\\\\\implies ( \tan x - 1)( 5 \tan^2 x- \tan x +4) =0\\\\\implies \tan x =1\\\\\implies x = n \pi+ \dfrac{\pi}4[/tex]

Related Questions

Which is the greatest?

5/100 5/10 24/1000

Answers

Answer:

5/10

Step-by-step explanation:

To solve this problem we find equivalent fractions with the same denominator:

The LCM of 10,100 and 1000 is 1000. So we make all the denominators 1000:

5/100 = 50/1000

5/10 = 500/1000

24/1000 = 24/1000

Now we compare the numerators and see which is the largest number.

24 < 50 < 500

So 5/10 must be the greatest.

Hope this helped and brainliest please

Find the first four terms of:
a) An arithmetic series with first term of 3 and sum to five terms is 75

Answers

[tex]\textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\[-0.5em] \hrulefill\\ a_1=3\\ n=5\\ S_5=75 \end{cases} \implies \begin{array}{llll} S_5=\cfrac{5(a_1+a_5)}{2} \\\\\\ 75=\cfrac{5(3+a_5)}{2} \end{array} \\\\\\ 150=5(3+a_5)\implies \cfrac{150}{5}=3+a_5\implies 30=3+a_5\implies \boxed{27=a_5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ n=5\\ a_5=27\\ a_1=3 \end{cases}\implies 27=3+(5-1)d \\\\\\ 24=(5-1)d\implies 24=4d\implies \cfrac{24}{4}=d\implies \boxed{6=d} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\LARGE Terms}}{3~~,~~\stackrel{3+6}{9}~~,~~\stackrel{9+6}{15}~~,~~\stackrel{15+6}{21}}~\hfill[/tex]

A total of 840 people ate at lunch.Which statement is true

Answers

what kinda question is this

3. If I give you £90 because I want to give you
90% of my prize, what did I win?

Answers

Answer:

Step-by-step explanation:

Multiply 90/100 with 90 = (90/100)*90 = (90*90)/100 = 81.

i got 100. not sure how the other guy got 81, but what i did is compare it to a test score or a discount. if you have a total of 100 possible points on the test with every question worth 10 points and i got 9 questions right, i got a 90 percent.

let's say a shopping discount. If you got a 90% discount for a item with original price of $100, it costs $10 with "90" being the amount you took off

if 100 isn't right, i honestly have no clue lol. good luck though

The lengths of the 2 legs of right triangle AABC shown
below are given in inches. The midpoint of AB is how
many inches from A?

A. 16
B. 20
C. 21
D. 28
E. 40

Answers

Answer:

E. 40

Step-by-step explanation:

First, we can start out by stating that this is a right triangle, since it has a right angle, shown by the marker square in the corner of the triangle. The x part, is called the hypotenuse. When finding the value of the hypotenuse, we use a thing called the Pythagorean Theorem. This theorem is :

a^2 + b^2 = c^2

a is one side length, and b is the other. c is the hypotenuse. To find x, the hypotenuse, we simply plug in the values, and solve.

24^2+32^2 = c^2

576 + 1024 = c^2

1600 = c^2

40 = c

The answer is E. 40.

Need help with this problem, doesn't make sense to me.

Answers

Answer:

A = x² - 5x - 8

Step-by-step explanation:

Finding x

Area (deck) = Area (Rectangle) - [Area (bench) + Area (planter)]A = x(x - 4) - [ 2(6) + 1/2(2)(x - 4) ]A = x(x - 4) - [12 + x - 4]A = x² - 4x - 8 - xA = x² - 5x - 8

PLEASE HELP WILL MAEK YOU THE BRAINLIEST

Answers

Answer:

Step-by-step explanation:

[tex]F =\cos 0^{\circ} = 1[/tex]

does the formula matter in area?

Answers

Answer:

Yes

Step-by-step explanation:

You need the formula to solve area.

You must plug in / subsitute numbers in order to find the area.

Yes you need the formula

2.48 times 3.25 equals

Answers

The answer is 8.06.

Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=3x+5
s(x)=4x
Write the expressions for (r-s)(x) and (r*s)(x) and evaluate (r+s)(-2).

Answers

A function assigns the values. The value of (r+s)(-2) is equal to 9.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the function r(x)=3x+5, while s(x)=4x, therefore, the expressions can be written as,

(r-s)(x) =r(x)-s(x) = 3x+5 - 4x = -x+5

(r*s)(x) = r(x)·s(x) = (3x+5)·(4x) = 12x² + 20x

The expression for (r+s)(x) can be written as,

(r+s)(x) = r(x)+s(x) = 3x+5+4x = 7x+5

(r+s)(-2) = 7(-2)+5 = -14+5 = 9

Hence, the value of (r+s)(-2) is equal to 9.

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Examine the system of equations.

t = 5c + 35,

t = 10c

How many solutions will the system have?

What is the reason you determined that number of solutions?

Answers

Answer:

One solution

Step-by-step explanation:

Analyzing both equations

Simplify both to simplest formy = 5c + 35 = c + 7y = 10c

Slope is different

As the slopes are different, then it can be concluded that the system has only one solution.

Answer:

How many solutions will the system have?

✔ one solution

What is the reason you determined that number of solutions?

✔ The equations graph intersecting lines.

Solve for x in the inequality 11|x + 1| < 44

Answers

[tex]~~~~~~11|x+1| < 44\\\\\implies |x+1| < \dfrac{44}{11}\\\\\implies |x+1| < 4\\\\\implies x +1 > -4~~~ \text{and}~~~ x+1 < 4\\\\\implies x > -4-1~~~ \text{and}~~~~ x < 4-1\\\\\implies x > -5~~~~~~~~ \text{and}~~~~~ x < 3\\\\\text{Hence,}~~ -5 < x < 3[/tex]

PLEASE HELP!

Correct answers will be mark as BRAINLIEST and get 50 points

If wrong answers will be reported

Answers

Mean=Sum of data/No of data

17,19,25

Mean

17+19+25/361/3

38,36,34,32

Mean:-

38+36+34+32/4140/435

8.3,2.6,7.4,1.8,9.5

Mean

8.3+2.6+7.4+1.8+9.5/529.6/55.92

-5,-2,-1,0,-9,4

Mean

-5+2-1+0-9+4/6-9/6

Answer:

See below ~

Step-by-step explanation:

Mean = 17 + 19 + 25 / 3Mean = 61/3Mean = 20.3

Mean = 38 + 36 + 34 + 32 / 4Mean = 140/4Mean = 35

Mean = 8.3 + 2.6 + 7.4 + 1.8 + 9.5 / 5Mean = 29.6/5Mean = 5.92

Mean = -5 + 2 - 1 + 0 - 9 + 4 / 6Mean = -9/6Mean = -1.5

1. The constant of variation for the table below is -8. true or false X 8 16 24 y 1 2 3

Answers

Answer:

False

Step-by-step explanation:

The formula for direct variation is ...

y = kx

where k is the constant of variation.

If -8 is the constant of variation, we should have ...

1 = -8×8 . . . . false

1 ≠ -64

The constant of variation is not -8.

Additional comment

The constant of variation is 1/8.

The following number line contains the points A, B, C, D, and E.

Complete each of the following prompts with a numerical answer only.
Enter answers in their most simplified form.
The probability that a point chosen at random on AE is on AB is...

1/2
4/5
1/5
7/10

Answers

The probability that a point chosen at random on AE is on AB is; 1/5.

What is the probability that a point chosen at random on AE is on AB?

The total distance over AE is given as; |-5 -5| = 10.

And the total distance covered over AB is; |-5 -(-3)| = 2.

On this note, the required probability is; 2/10 = 1/5.

Answers

Answer:

y = 4√x

Step-by-step explanation:

Finding the constant of proportionality, k

y = k√x24 = k√36k = 24/6 = 4

Equation

y = k√xy = 4√x

Answer:

Y will equal

4√x as the answer

Use Euler’s Formula to find the missing number.
Edges: 37
Faces: 25
Vertices: ?

Answers

Answer:

Step-by-step explanation:

Comment

The formula that relates edges faces and vertices is F + V = E + 2

Givens

Edges (E): 37

Faces (F) = 25

Vertices: x

Solution

25 + x = 37 + 2 Subtract 25 from both sides.

25-25 +x= 37 - 25 + 2 Combine

x = 12 + 2

x = 14

Answer: The vertices = 14

How to calculate minimization of cost when given the marginal revenue

Answers

Answer: Cost is minimized at the levels of capital and labor such that the marginal product of labor divided by the wage (w) is equal to the marginal product of capital divided by the rental price of capital (r)

Step-by-step explanation:

A case of 24 cans of soup costs $38.16. What is the cost of 7 cans of soup?

Answers

Answer:

$11.13

Step-by-step explanation:

24 cans = $38.16

divide both sides by 24 to find the cost per can, as this leaves us with 1 can on one side

24 cans / 24 = $38.16 / 24

1 can = $1.59

multiply both sides by 7 to get 7 cans of soup on one side, which is what we want

1 can * 7 = $1.59 * 7

7 cans = $11.13

A particular fruit's weights are normally distributed, with a mean of 615 grams and a standard deviation of 10 grams.

The heaviest 10% of fruits weigh more than how many grams?

Give your answer to the nearest 0.1 gram.

Answers

The heaviest 10% of fruits weigh more than 814.79 grams.

The problem setup implies that the weight of this fruit is a random variable when it says a particular fruit's weights are normally distributed.

What are the formula weights are normally distributed?

Define X = Random Variable of the fruit's weight

[tex]X \sim N(mean = 760, standard deviation = 39)[/tex]

We want to find the specific gram value for which 8% of the fruits are heavier

The 92nd percentile of X's normal distribution

[tex]Solve for x: Pr( X < x ) = Normal( 760, 39 ) CDF = .92[/tex]

Standardizing we obtain

[tex]Pr( [X - 760]/39 < [x - 760]/39 ) = Pr( Z < [x - 760]/39 ) = .92,[/tex]

where Z is a standard normal random variable

[tex]Pr( Z < [x - 760]/39 ) = Standard \ Normal \ CDF( [x - 760]/39 )[/tex]

==> Set this equal to .92:

[tex]Standard \ Normal \ CDF( [x - 760]/39 ) = .92[/tex]

Then, from the standard normal table:

[tex][x - 760]/39 = Inverse Standard Normal[/tex]

[tex]CDF( .92 ) = 1.405[/tex]

Use algebra to solve for x:

[tex]x = 39 * 1.405 + 760 = 814.795[/tex]

Therefore the heaviest 10% of fruits weigh more than 814.79 grams.

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14÷2+3²×(7-2) pemdas order

Answers

Answer:

Step-by-step explanation:

14÷2+3²×(7-2) pemdas order

14 : 2 + 3^2 * (7 - 2) =

14 : 2 + 3^2 * 5 =

14 : 2 + 9 * 5 =

7 + 9 * 5 =

7 + 45 =

Find the distance (A) for the bend of electrical conduit that is passing under the girder shown in the figure.?

Answers

Answer:

15 1/8"

Step-by-step explanation:

Adding the values

⇒ 9 3/4" + 2 1/8" + 3 1/4"

⇒ 13 + 2 1/8"

⇒ 15 1/8"

Jeremy wants to visit the Duck Pond. Which is a correct description of how to find the ordered pair for the Duck Pond?

Answers

Answer: 2,4

Step-by-step explanation:

Rewrite 5 2/3 using radical notation.

Answers

The radical form of [tex]5^{\frac{2}{3}}[/tex] is [tex]\sqrt[3]{25}[/tex].

What is Radical Notation?

If n is a positive integer that is greater than 1 and a is a real number then, n√a = [tex]a^{1/n}[/tex]. where n is called the index, a is called the radicand, and the symbol √ is called the radical.

Here, given value = [tex]5^{\frac{2}{3}}[/tex]

= [tex](5^2)^{1/3}[/tex]

= [tex](25)^{1/3}[/tex]

= [tex]\sqrt[3]{25}[/tex]

Thus, the radical form of [tex]5^{\frac{2}{3}}[/tex] is [tex]\sqrt[3]{25}[/tex].

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The population of a small town was 10,800 in 2002. Since then the population has decreased at a rate of 2.5% each year. Write an exponential function to model the situation then find the population of 2020

Answers

Answer:

See below

Step-by-step explanation:

A 2.5 % decrease means 97.5 % remains (.975)

population = 10800 ( .975) ^n where n = years past 2002

in 2020 n = 18

10800 (.975)^18 = 6847 people

Which statement is true?

7.11>−7.1

7.11≤−7.1

7.11<−7.1

Answers

Step-by-step explanation:

I think 1 is correct..

all positive numbers are greater than negative. 7.11 is greater that -7.1

Answer:

7.11 > -7.1

Step-by-step explanation:

» Concept

Negative numbers will always be less than positive numbers. Negative numbers will always have the (-) sign to indicate its value.

» Solution

The only correct inequality is A. 7.11 > -7.1 because it displays that the positive number, 7.11, is greater than the negative number, -7.1.

What is the formula for standard error of the mean?

Answers

Write the formula σM =σ/√N to determine the standard error of the mean.

What is the volumen , in cube centimeters, if a cube with a side length, s, of 0.2cm?

Answers

Answer:

[tex]\frac{1}{125}[/tex]cm³

Step-by-step explanation:

volume of cube= (side)³

0.2³ = [tex]\frac{1}{125}[/tex]

There are 12 turkey sandwiches and 8 ham sandwiches. There are 6 bags of chips and 10 bags of pretzels. What is the probability of selecting a turkey sandwich and a bag of pretzels?
a) 1/5
b) 3/8
c) 3/5
d) 5/8

Answers

The probability of selecting a turkey sandwich and a bag of pretzels is 3/8.

What is the probability?

Probability determines the likelihood that an event would happen. The odds the event occurs is 1 and the odds that the event does not occur is 0.

The probability of selecting a turkey sandwich and a bag of pretzels = number of turkey sandwiches / total number of sandwiches x number of pretziel bags / total number of bags

12/20 x 10/16 = 3/8

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a small flash driver has a storage capacity of 200gb, a medium 350gb, and a large 600gb. the small flash driver is 1/4 inch long, the medium is 1/2 inch long, and the large 1 inch long. Javier owns the same number of flash drives of all three sizes, giving him a total of 11,500gb of storage capacity. what is the combined length of all his flash drives?

Answers

The small flash driver is 1/4 inch long, the medium is 1/2 inch long, and

the large 1 inch long. The combined length of all his flash drives is 11/8 inch.

How many megabytes in 1 gigabyte?

1 gigabyte = 1000000000 bytes

1 megabyte = 1000000 bytes

1 gigabyte = 1000 megabytes

A small flash driver has a storage capacity of 200Gb, a medium 350GB, and a large 600Gb.

The small flash driver is 1/4 inch long, the medium is 1/2 inch long, and

the large 1 inch long.

Javier owns the same number of flash drives of all three sizes, giving him a total of 11,500Gb of storage capacity.

The combined length of all his flash drives

= 1/4 + 1/2 + 1

= 11/ 8

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