The question asked is in the image attached below.
Answers with nice explanation and step wise order will be marked brainliest.
Thanks for your kind help.

The Question Asked Is In The Image Attached Below.Answers With Nice Explanation And Step Wise Order Will

Answers

Answer 1

Answer:

[tex]y' = \dfrac{1 + x \sin x - x \cos x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

Step-by-step explanation:

[tex] y = \dfrac{x + \sin x}{\cos x - x} [/tex]

Derivative of a quotient:

[tex] \dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{g'h - h'g}{h^2} [/tex]

Recall:

[tex] \dfrac{d}{dx} \sin x = \cos x [/tex]

[tex] \dfrac{d}{dx} \cos x = - \sin x [/tex]

[tex] y = \dfrac{x + \sin x}{\cos x - x} [/tex]

[tex] y' = \dfrac{dy}{dx} = \dfrac{(1 + \cos x)(\cos x - x) - [(- \sin x - 1)(x + \sin x)]}{(\cos x - x)^2} [/tex]

[tex]y' = \dfrac{\cos x - x + \cos^2 x - x \cos x - (-x \sin x - \sin^2 x - x - \sin x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{\cos x - x + \cos^2 x - x \cos x + x \sin x + \sin^2 x + x + \sin x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{\sin^2 x + \cos^2 x + x - x - x \cos x + x \sin x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{1 + x \sin x - x \cos x + \sin x + \cos x}{(\cos x - x)^2}[/tex]


Related Questions

can someone pls help me

Answers

Answer:

arc EFC = 237°

Step-by-step explanation:

arc DEF = 140°

arc EF = 140° - 83° = 57°

arc DC = arc FG

arc DC = (360° - 140° - 140°)/2 = 40°

arc EFC = arc CG + arc FG = arc EF = 140° + 40° + 57° = 237°

Howard invested $2,500 in a local bank at a rate of 1.25% for 5 years. How
much interest will Howard earn in 5 years?

Answers

Howard will make $156.25 in 5 years!

Ellie puts 35 quarter into stacks with the same number of quarter in each stack

Answers

Answer:

Ellie can make eight stacks of quarters with four quarters in each stack

Step-by-step explanation:

what is solution to 8x=2/3

Answers

there should be a cross multiplication

3(8x)=2

expanding bracket

24x=2

multiple both sides by 24

x=1/12

15) Suzanne bought 3 quarts of orange juice, 4 quarts of apple juice, and 5 quarts of
water at the store. How many gallons of liquid did she buy?

Answers

Answer:

3 liquid gallons

Step-by-step explanation:

3 + 4 + 5 = 12

12 ÷ 4 = 3 liquid gallons

NEED ANSWER ASAP,BRAINLIEST FOR CORRECT ANSWER. IM FAILING SCHOOL

Answers

Answer:

c is the anser

Step-by-step explanation:

Solve for f(2)

f(x)=2x-4

f(2)=?

Answers

Answer:

0

Step-by-step explanation:

Plug 2 in for x

[tex]2(2) -4[/tex]

Simplify

[tex]4-4[/tex]

[tex]=0[/tex]

42 - 5z + 3(x + y), when x=4, y=9, z=7

Answers

Answer:91

Step-by-step explanation: 42 - 5(7) (4+9)

5*7=35

42-35= 7

(4+9)=13

7(13)= 91

The value of expression,42 - 5z + 3(x + y) at x=4, y=9, z=7 will be 46.

What is a mathematical expression?

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression.

It is given that the expression is,42 - 5z + 3(x + y)

We have to find the value of the expression at x=4, y=9, and z=7.

The value of the expression is obtained by putting the values,

=42 - 5z + 3(x + y)

=42-5(7)+3(4+9)

=42-35+3(13)

=42-35+39

=46

Thus, the value of the expression will be 46.

Learn more about the expression here:

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A fundraiser was able to raise money to buy food for the food pantry.
They collected $34.99, $38, $12.30, and $45 last week.How much did they
collect in all?

Answers

Answer:

https://youtu.be/cqF6M25kqq4

Step-by-step explanation:

Find the perimeter of the polygon with the vertices G(2, 4), H(2,−3), J(−2,−3), and K(−2, 4).

Answers

Answer:

22 units

Step-by-step explanation:

Graphed to solve.

Width:

The distance between points K and G, and points J and H is both 4 units. So for both distances between the set of points will be 8 units total.

Length:

The distance between points G and H, and points J and K is both 7 units. So for both distances between the sets of points will be 14 units total.

14 + 8 = 22

Write 2.83 as a mixed number and as an improper fraction.
Do not try to simplify your answers.


Answers

Answer:

Mixed number: [tex]2\frac{83}{100}[/tex]

Improper Fraction: [tex]\frac{283}{100}[/tex]

Answer:

[tex]\frac{238}{100}\\\\2\frac{38}{100}[/tex]

Step-by-step explanation:

2.83/1

To make this a normal fraction, the top has to be a whole number, so we can multiply the top and bottom by 100 to slide the decimal point twice.

238/100

This can be shown as a mixed number by removing the 200 which is divisible by 100

[tex]2 \frac{38}{100}[/tex]

Note: The reason the question says not to simplify is because 283 is a prime and cannot be simplified

At a furniture store, the employees earn a 2.5% commission on every sale they make. If Ginny made $8850 in sales one week, how much did she earn in commission?
help please :( 100 points

Answers

Answer:

She earned 221.25 in commission

Step-by-step explanation:

2.5% of 8850 is 221.25

need please solving for x​

Answers

Answer:

x = 15

Step-by-step explanation:

Corresponding sides of similar shapes are proportional to each other. Thus:

(10 + 2)/10 = (x + 3)/x

12/10 = (x + 3)/x

Cross multiply

12*x = (x + 3)*10

12x = 10x + 30

12x - 10x = 30

2x = 30

x = 30/2

x = 15

Please help me i will give you 50 points if you do

Answers

Answer:

6(4X-1) = 24X -6 , (2 . 12X ) - (2 . 3) .

24X+6 = (6 . 4X) + (6 . 1) , 6( 4X + 1 ) .

(4 . 6X) - (4 . 2) = 24X + 8 , 4(6X + 2) .

Step-by-step explanation:

Hope it was helpful dear , good luck ^^

Solve for x, show work!

Answers

Answer: x=3

Step-by-step explanation:

One of the properties of diagonals of a rectangle is that they bisect each other, meaning that four segments are equal.

For example, in this question, according to the property, AE, CE, DE, BE will be equal.

Solve:

AE=CE

AE+CE=AC

CE+CE=AC

DB=AC

DB=2CE

(18)=2(4x-3)

18=8x-6

18+6=8x-6+6

24=8x

24/8=8x/8

x=3

Hope this helps!! :)

Please let me know if you have any questions

HELP NEED SOON!! A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were
defective. A store clerk generates random numbers to simulate a random sample of this shipment. The
clerk lets the numbers 1 through 300 represent defective MP3 players, and the numbers 301 through
5,000 represent working MP3 players. The results are given.
4,942 368 110 4,758 4,452 610 773 171 460 2,699
Based on this sample, how many of the MP3 players might the clerk predict would be defective?
The manager would expect
defective players in the shipment.

Answers

Answer:

2?

Step-by-step explanation:

From my understanding, all numbers 300 and below represent defective mp3s, so there's two.

On a survey of students at CAMS, 75% of students said
they preferred Soda instead of Juice.
6. If 420 students preferred Soda, how many students
did they survey in total?

Answers

Answer:Total number of students surveyed =560

Step-by-step explanation:

Number of students who preferred soda =420

Percentage of students who preferred Soda =75%

Percentage of students who preferred juice =100-75%=25%

Using the formula,

Percentage of students who preferred Soda x total number of students surveyed =Number of students who preferred soda

Therefore we have that

total number of students surveyed  =Number of students who prefeerd juice/Percentage of students who preferred Soda

Total number of students surveyed =420/75%

=560

help please it needs to be don by 4:00​

Answers

1: x=1
2: (1,-4)
3: min
4: -3
5: -1 and 3
6: all real numbers
7: y>or equal to -4
8: x=2
9: (2,-1)
13: c=121

those are all i can do for now hope they help

Find the exact value of cos (11pi/8)

Thank you!! I will mark brainliest!!

Answers

The exact value of [tex]cos(\frac{11\pi }{8} )[/tex] is [tex]-\sqrt{\frac{2+\sqrt{2} }{4} }[/tex].

What is the exact value of trigonometric function?

The exact values of trigonometric functions are values of trigonometric functions of certain angles that can be expressed exactly using expressions containing real numbers and roots of real numbers. These values are also called analytic values of trigonometric functions or trigonometric values of special angles.

What is trigonometric function?

The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.

According to the given question.

We have a trigonometric function

[tex]cos(\frac{11\pi }{8} )[/tex]

We have to find the exact value of the above trigonometric function.

since,

[tex]\frac{11\pi }{8}[/tex] can be written as [tex](\pi +\frac{3}{8\pi } )[/tex]

[tex]\implies cos(\frac{11\pi }{8} ) = cos(\pi +\frac{3}{8}\pi )[/tex]

And we know that,

Cos(π + θ) = -cosθ

Because, π + θ lies in third quadrant and in third quadrat cos gives negative values.

Also,

[tex]cos\frac{\alpha }{2} = \pm\sqrt{\frac{1+cos\alpha }{2} }[/tex]        ....(i)

Therefore,

[tex]cos(\pi +\frac{3}{8} \pi )[/tex]

[tex]= -cos(\frac{3}{8} \pi )[/tex]

[tex]= -cos(\frac{3}{2(4)} \pi )[/tex]

[tex]= -\sqrt{\frac{1+cos\frac{\pi }{4} }{2} }[/tex]

[tex]= -\sqrt{\frac{1+\frac{1}{\sqrt{2} } }{2} }[/tex]

[tex]= -\sqrt{\frac{1+\frac{\sqrt{2} }{2} }{2} }[/tex]

[tex]= -\sqrt{\frac{2+\sqrt{2} }{4} }[/tex]

Hence, the exact value of [tex]cos(\frac{11\pi }{8} )[/tex] is [tex]-\sqrt{\frac{2+\sqrt{2} }{4} }[/tex].

Thus, option A is correct.

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What is the slope-intercept equation of the line going through (3, -6) and
(1,2)?
A. y=-4x+ 2
B. y = -4x + 1
O c. y-2 = -4(x - 1)
O D. y=-4x + 6

Answers

Hi there!

[tex]\large\boxed{D. \text{ }y = -4x + 6}[/tex]

To derive an equation given the points, we can use the slope formula:

[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]

Plug in the corresponding coordinates:

[tex]slope = \frac{-6-2}{3-1}[/tex]

Simplify:

[tex]slope = \frac{-8}{2} = -4[/tex]

Therefore, we have:

y = -4x + b

Plug in the x and y values for a coordinate to solve for b:

2 = -4(1) + b

2 = -4 + b

b = 6

The equation is:

y = -4x + 6. The correct answer is D.

Determine if the triangle is a right triangle.

Answers

Answer:

Yes, this is a right triangle

Step-by-step explanation:

a² + b² = c²

65² + 72² = 97²

4225 + 5184 = 9409

9409 = 9409

Since the hypotenuse equals the 2 legs, it's a right triangle

can someone help me pls?

Answers

Okay so basically the 12 yd is your diameter for the circle,
Since you want the whole perimeter of the circle, which is the shaded area, you will find the circumference (perimeter) of the circle.
Using the equation of:
pi x diameter
and you will find your answer
in this case your answer is 37.699

Which of the numbers given
are rational?
Select all that apply:

8.634092...

6.28232

7144

1.465359...

32.71481

Answers

Answer:

7144

Step-by-step explanation:

Which choice includes all of the solutions to 2x2 + x – 3 = 0 by factoring

A. 1
B. 3, –1/2
C. –1, 3/2
D. 1, –3/2

Answers

Answer:either c or b

Step-by-step explanation: to be honest I searched up

The solution of Equation 2x² + x -3 =0 by factoring is 1 and -3/2.

What is Factorization?

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

We have the equation 2x² + x -3 =0

Now, factorizing the above equation using splitting the middle term we get

2x² + x -3 =0

2x² + 3x - 2x -3 =0

x( 2x + 3) - (2x+ 3)= 0

(2x + 3)(x - 1)= 0

x = -3/2 or 1.

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what is the slope of the line shown?​

Answers

answer: i believe it is 1/2

Find the lateral area, surface area and volume of the cube

Answers

Answer:

Lateral Area = 13 x 13 x 4 = 676 ft²

Surface area = 13 x 13 x 6 = 1014 ft²

Volume = 13 x 13 x 13 = 2197 ft³


Giving brainly to the correct answer!

Answers

Answer: A

Step-by-step explanation:

Well four weels in every car so it’s 4 times cars (a)

4 times A=W

Step-by-step explanation: im smart also if u do multiply it by a by 4 it equals  W

Find the surface area of the prism. 3m, 4m, 8m,5m

Answers

Step-by-step explanation:

480 is the answer // provide picture for better answer

PLEASEEE HELP PLS ASAPPP GIVING BRAINLIEST!!!!

Answers

Answer:

50 is the answer brainliest?

Step-by-step explanation:

The rabbit population at the city park increases by 14% per year. If there are intially 481 rabbits in the city park.

Write a model for the population (y) in terms of years (t).
y =

Find the population in 17 years.

Answers

Answer:

y = 0.14t + 481

Population in 17 years: 483.38

Step-by-step explanation:

y = (m) (x) + b

y = (slope) (x) + starting value

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