What is the value of x? ​

Answer:

[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}[/tex]

General Formulas and Concepts:
Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:
[tex]\displaystyle (uv)' = u'v + uv'[/tex]

Derivative Rule [Quotient Rule]:
[tex]\displaystyle \bigg( \frac{u}{v} \bigg)' = \frac{vu' - uv'}{v^2}[/tex]

Derivative Rule [Chain Rule]:
[tex]\displaystyle [u(v)]' = u'(v)v'[/tex]

Step-by-step explanation:

*Note:

Since the answering box is way too small for this problem, there will be limited explanation.

Step 1: Define

Identify.

[tex]\displaystyle y = \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \times \frac{\tan^2 x + 5x}{\csc^2 x + 3}[/tex]

Step 2: Differentiate

We can differentiate this function with the use of the given derivative rules and properties.

Applying Product Rule:

[tex]\displaystyle y' = \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) '[/tex]

Differentiating the first portion using Quotient Rule:

[tex]\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( \cos^2 x - 3\sqrt{x} + 6 \big)' \big( \sin^2 x + 6 \big) - \big( \sin^2 x + 6 \big)' \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}[/tex]

Apply Derivative Rules and Properties, namely the Chain Rule:

[tex]\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}[/tex]

Differentiating the second portion using Quotient Rule again:

[tex]\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( \tan^2 x + 5x \big)' \big( \csc^2 x + 3 \big) - \big( \csc^2 x + 3 \big)' \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]

Apply Derivative Rules and Properties, namely the Chain Rule again:
[tex]\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]

Substitute in derivatives:

[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2} \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}[/tex]

Simplify:

[tex]\displaystyle y' = \frac{\big( \tan^2 x + 5x \big) \bigg[ \big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - 2 \sin x \cos x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \bigg]}{\big( \sin^2 x + 6 \big)^2 \big( \csc^2 x + 3 \big)} + \frac{\big( \cos^2 x - 3\sqrt{x} +6 \big) \bigg[ \big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) + 2 \csc^2 x \cot x \big( \tan^2 x + 5x \big) \bigg] }{\big( \csc^2 x + 3 \big)^2 \big( \sin^2 x + 6 \big)}[/tex]

We can rewrite the differential by factoring and common mathematical properties to obtain our final answer:

[tex]\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}[/tex]

∴ we have found our derivative.

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Topic: Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

==============================================

Remember, prime numbers have only 2 factors: 1 & themselves.

For example, 5 is a prime number because it's only divisible by 1 and 5 (itself)

Now, write down some primes.

1) between 45 and 55

   - 47

   - it's only divisible by 1 and itself, so it IS prime

2) 62 and 72

67, because it is divisible by 1 and itself only.

====================================================

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

$4440 for all performances

Step-by-step explanation:

11 × ¢120 for short performances

12 × $260 for long performances

$1320 for short performances

$3120 for long performances

To get the totel you add them up

( $1320 + $3120)

The total is $4440

Answer:

there are 18 milk chocolates

Answer:

Step-by-step explanation:

convert it to fraction first: 2/5 are plain and 3/5 is milk

30÷5= 6

2x6=12

3x6=18

to check wheter or not it is correct add the amount. if it gets the total, it is correct.

Answer:

$750

Step-by-step explanation:

2500 divided by 100 = 25 and 25 x 30 = 750

Sorry if im wrong

The price for 2500 pencils is $750.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

A box of 100 personalized pencils costs $30.

So, cost of 1 pencil = $30 / 100 = 3/10

Now, the price to buy the 2500 pencils

= 2500 x 3/10

= 250 x 3

= $750

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#SPJ2

The length of the blade of the windmill will be equal to 7 feet.

We have the equation

[tex]\rm h=7 \ Sin(\dfrac{\pi}{21t})+28[/tex]

At the time 't' = 0, the end of the blade is pointing to the right parallel to the ground meaning it is at the same height as the other end. (Ф = 0°)

So, by calculating the maximum height of this end at  Ф = 90°. we can calculate the length of the blade.

Now, we know that a general model equation of a circular simple harmonic motion is represented as

[tex]\rm y=A\ Sinwt+k[/tex]

Where A is the amplitude that is, maximum displacement from mean to maximum position.

ω is the angular frequency.

Comparing the above equations we can conclude that

A = 7

so the difference in blade's end height at Ф = 0° and Ф = 90° is 7 feet.

To know more about simple harmonic motion follow

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Answer:

7ft or option 1

Step-by-step explanation:

Answer:

Bottom left = 8

Top right = 15

Middle right = 25

Step-by-step explanation:

Total = 40

3 + 5 = 8

40 / 8 = 5

1 part = 5

5 x 3 = 15

5² = 25

She makes a minimum monthly payment of 62.52 dollars. Then the correct option is B.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

May currently has a balance of $1,817.43 on her credit card.

If she must make a minimum monthly payment of 3.44% of her total balance.

Then the minimum payment will be given as

Minimum payment = 0.0344 × 1817.43

Minimum payment = 62.519 ≅ 62.52

More about the percentage link is given below.

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Answer: WZ=10, YZ=15

Step-by-step explanation:

Steps to finding the line in the diagram with the format 'ax + by = c

1. Find the slope

                  [tex]Slope = \frac{y2-y1}{x2-x1} =\frac{4-0}{0-3} =-\frac{4}{3}[/tex]

2. Set up, with any one point on the line and the slope, in point-slope form

        [tex](y-y0)=m(x-x0)\\(y-4)=-\frac{4}{3} (x-0)\\y-4 = -\frac{4}{3} x\\\frac{4}{3}x+y = 4[/tex]

Answer: [tex]\frac{4}{3}x+y = 4[/tex]

Hope that helps!

Answer:

[tex]\sf 4x+3y=12[/tex]

Step-by-step explanation:

Choose two points on the line:

Let [tex]\sf (x_1,y_1)=(0,4)[/tex]

Let [tex]\sf (x_2,y_2)=(3,0)[/tex]

Use the slope formula to find the slope of the line:

[tex]\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-4}{3-0}=-\dfrac43[/tex]

Use the point-slope formula to find the equation of the line:

[tex]\sf y-y_1=m(x-x_1)[/tex]

Substitute values into the formula:

[tex]\sf y-4=-\dfrac43(x-0)[/tex]

Expand the brackets:

[tex]\sf y-4=-\dfrac43x[/tex]

Add 4 to both sides:

[tex]\sf y=-\dfrac43x+4[/tex]

Rearrange into the form [tex]ax+by=c[/tex]

Multiply both sides by 3

[tex]\sf 3y=-4x+12[/tex]

Add 4x to both sides:

[tex]\sf 4x+3y=12[/tex]

Divide money earned by hours worked to get the hourly rate of $11.00 per gour.

Answer: C. $11.00 per hour

Answer:

The answer should be B. 86.7

Answer:

1944 cubic cm

Step-by-step explanation:

Find the answer by figuring out the volumes independently for each figure.  After doing that, add both volumes together to get the full volume.

Bottom figure: 1440 cubic cm

Top figure: 504 cubic cm

Add those together: 1944 cubic cm

[tex]0.75x = 15[/tex]

[tex]x = \frac{15}{0.75} = 20[/tex]

[tex]0.15(20) = 3[/tex]

Answer: You can use the definition of percentage and the proportions to solve this question. 75% means 75/100, the you want to know which fraction of 15 equals 75/100, which is to solve this proportion: 75/100 = 15/x. Solving for x, x = 15 * 100 / 75 = 20. You can check that the 75% of 20 is equal to 15: 20 * 75% = 20*75/100 = 15. So, the answer is 20.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Okay, so we know that Base*Length=Area, so we just have to divide the area by the base, so the formula here is Area/Base=Length.

That would get us 120/8=Length,

and if we just divide 120 by 8 we get 15, so the length is 15

Answer:

Step-by-step explanation:

Radius = circumference / 2π

= 43.96 / 2π

= 7.00 yards to the nearest hundredth.

Answer:

X ~ B(n, p)

Given: X ~ B(2, 5/17)

⇒  n = 2

⇒  p = 5/17

Binomial distribution formula:

[tex]\sf P(X = x) = nC_x (1-p)^{(n-x)}p^x[/tex]

As n = 2, calculate P(X = 0), P(X = 1) and P(X = 2):

[tex]\sf P(X = 0) = 2C0 (\frac{12}{17})^{(2-0)}(\frac{5}{17})^0=\dfrac{144}{289}}[/tex]

[tex]\sf P(X = 1) = 2C1 (\frac{12}{17})^{(2-1)}(\frac{5}{17})^1=\dfrac{120}{289}}[/tex]

[tex]\sf P(X = 2) = 2C2 (\frac{12}{17})^{(2-2)}(\frac{5}{17})^2=\dfrac{25}{289}}[/tex]

**Probability Distribution Table attached**

Answer:

-1

Step-by-step explanation:

angle 0: 7pie/4

=7*180/4

=1260/4

=315

hence reference angle(0)= 315

now, tan 0 = tan315

= tan(360-45)

= -tan45

= -1

The place values in 5.6 and 1.78 are the positions of the digits in the numbers

In a number, the non-zero digit at the left-most position is the greatest place value

This means that:

The greatest place value in 5.6 is 5 (i.e. ones place)

The greatest place value in 1.78 is 1 (i.e. ones place)

So, we can conclude that the largest place value common in 5.6 and 1.78 is the ones place

Hence, Nichole is correct

Read more about place values at:

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Answer:

1

Step-by-step explanation:

5 + 4 - (8 x 3 – 22)* x 4

5 + 4 - (24 - 22) x 4

5 + 4 - 2 x 4

5 + 4 - 8

1

Answer:

16

Step-by-step explanation:

5+4- (8x3-22) ↑4 x4

         16

5+4 - (24-22) ↑4 x4

5+4- (2) ↑4 x4

2x2x2x2=16

hope that helps:)

Answer:

1/6

Step-by-step explanation:

Given;

Luis is going to roll a six-sided die. What is the probability that the die lands on the number 4?

Solve:

Six-sided die = 6

There are only one 4 in the six-sided die.

Hence, fraction = [tex]\frac{1}{6}[/tex]

~Lenvy~

Answer:

y = x - 5

Step-by-step explanation:

Line A

Equation

Answer:

Step-by-step explanation:

Job B has a larger starting bonus than Job A: true,
Job B pays 400, A pays 300.

Job A pays more per hour than Job B: true,
Job A pays 12.50 per hour, Job B pays 10 per hour.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \frac{1}{2} (5 + 13) - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{1}{2} (18) - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: 9 - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \:4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \:(5 + 11) - (24 - 15) \times 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:16 - (9 \times 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:16 - 27[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: {6}^{2} + (3 \times 7) - (9 \div 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:36 + 21 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:57 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:54[/tex]

Answer:

70 dolls

Step-by-step explanation:

Hello!

The ratio is 5:2, which are division of  a whole. They can be represented as 5x and 2x.

Jacky has 5x dolls, and Peter has 2x dolls. They were equal after subtracting 15 dolls from 5x and adding them to 2x.

Equation:

Solve:

So Jacky has 5(10) dolls, or 50 dolls, and Peter has 2(10) or 20 dolls.

The total sum is 70 dolls.

Answer:

50

Step-by-step explanation:

If we divide the shape we can get 3 x 10 with equals 30. Then take the remaining which is 2 x 10 and we get 20. Add the two to get 50. The area is 50sq miles.

Hope this helps. pls mark brainliest