Identify the area of the polygon with vertices t(6,5), a(8,−1), s(4,−2), and k(−1,4).

Answers

Answer 1

Answer:

  36.5 square units

Step-by-step explanation:

There are a number of ways to compute the area of a polygon from the coordinates of its vertices. There are algebraic formulas, geometric methods involving decomposing the figure, and an interesting method described by Pick's theorem.

__

Geometry

The figure can be enclosed by a rectangle that is 7 units high by 9 units wide. The actual figure is obtained by removing the triangular corners of this rectangle. The areas of those are given by the triangle area formula ...

  A = 1/2bh

Working clockwise from lower left, the triangle base (horizontal) and height (vertical) dimensions are 5×6, 7×1, 2×6, 4×1. That means the area of the triangles is ...

  A = 1/2(5×6 +7×1 +2×6 +4×1) = 1/2(30 +7 +12 +4) = 1/2(53) = 26.5

The area of the bounding rectangle is ...

  A = bh = 9×7 = 63

So, the area of the figure is the difference ...

  A = 63 -26.5 = 36.5 . . . square units

__

The other methods of finding the area have been added as attachments.

Identify The Area Of The Polygon With Vertices T(6,5), A(8,1), S(4,2), And K(1,4).
Identify The Area Of The Polygon With Vertices T(6,5), A(8,1), S(4,2), And K(1,4).
Identify The Area Of The Polygon With Vertices T(6,5), A(8,1), S(4,2), And K(1,4).

Related Questions

You are paid $1380 for working 80 hours in two weeks at your full-time job. At this rate of pay, how much would you be paid if ypu worked 100 hours in a month

Answers

Answer:

To answer this, we have to do the equation below:

[tex]1,380/80[/tex]

When we do this, we come up with the answer of 17.25

Now we know that we get paid $17.25 an hour.

Now, we must do the equation below:

[tex]100 X 17.25[/tex]

When we multiply, we get the answer of 1,725

So, we get paid $1,725 if we work for 100 hours.

Step-by-step explanation:

Hope this helps!

PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP

What are the new coordinates of Point R after a 90 degree clockwise rotation?

Answers

Step-by-step explanation:

P(-4,-1)======P'(-1,4)

Q(-4,-3)=====Q'(-3,4)

R(-2,3)======R'(3,2)

Henry found some pants on sale for 60% off. If the pants were originally $100, how much are they now?

Answers

If something is 60% off, that means it is now going to be 40% of its original price because

100 - 60 = 40

To find final price multiply the percentage as a decimal by the price.

40% is 40/100 which as a decimal is 0.4

0.4 x 100 = $40

The pants will be 40 dollars.

Answer:

$40

Step-by-step explanation:

Old Sale Price = $100

It was given 60% discount

 60% of 100 = 0.6 x 100 = 60

we remove the discount from  the original price( 100 -60 ) =  40.

So the new sale price for the pants are now $40

9x+3=14give your answer as an improper fraction in its simplest form

Answers

Answer:

11/9

Step-by-step explanation:

A rectangular prism has a length of 3 inches, a width of 5 inches, and a height of 7 inches.

What is the volume of the prism?

Enter your answer in the box as a simplified mixed number or a decimal.


in.³

Answers

Answer:

105³

Step-by-step explanation:

3x5=15

15x7=105

105 is your answer.

Problem 2
What is the probability of pulling a heart, replacing it, pulling a club, replacing it, pulling a diamond,
replacing it, then pulling a spade, all from a standard deck?.

Answers

Answer:

subtract one for heart drawn without replacement leaves 51 cards on which thirteen are clubs. probability of drawing club 13/51. After drawing a heart as first card there are 51 cards left and 13 of them are clubs. So the probability on drawing a club then equals 13/51

Please help! Its due today!

Answers

Answer:

don't know if this is the right way butttt i'm going to give it a shot

Step-by-step explanation:

Cost: I'm guessing this is for the rent for the shoes or is the total cost?

Bowler World: 5 + 1.1g = c | c + 1.1g = t {(this is the other option) probs not correct}

Lucky Spares: 3 + 1.5g = c | c + 1.5g = t

K so personally you should choose option 1 (for example: 5 + 1.1g = c), i have no idea how the proper format is supposed to be

either i hope this helps :)

How has the polygon RQTS been translated to produce a polygon with Q’ at (-3, -3)?


shift down 5 units
shift down 6 units
shift down 2 units
shift down 3 units

Answers

Answer: Shift down 3 units

Step-by-step explanation:

From the figure its clear that the existing coordinate of the polygon RQTS are : (−3,0)

Since we have to translate the polygon to (−3,−3)

So:

−3−(−3)=0

−3−(0)=−3

Therefore shift down 3 units is the correct answer

Answer:

shift down 5 units

Step-by-step explanation:

i took the quiz

Four beakers contain water as shown below.



Which two beakers of water can be combined to fill one beaker to exactly 1,000 mL?


beaker B and beaker C

beaker B and beaker C

beaker A and beaker C

beaker A and beaker C

beaker A and beaker B

beaker A and beaker B

beaker A and beaker D

beaker A and beaker D

Answers

Answer:

A&C

Step-by-step explanation:

It would be A because it has 750 mL and C because it has 250mL and 750+250=1000

Also can you mark brainlyist you dont have to

if f(x)=2x^2-3x+4, find f(x+3)

Answers

Step-by-step explanation:

well, the approach is totally simple : we use (x+3) everywhere where we have "x" in the function expression.

so,

f(x+3) = 2(x+3)² - 3(x+3) + 4 =

= 2(x² + 6x + 9) - 3x - 9 + 4 =

= 2x² + 12x + 18 - 3x - 9 + 4 =

= 2x² + 9x + 13

I need help

Imagine that you designed a firework. When the firework first explodes, it splits into eight sparkles. Each of those sparkles then explodes and splits into eight new sparkles.

How many sparkles would the second explosion produce? Explain how you determined your answer.

Answers

Answer:

8 x 8 = 64

Step-by-step explanation:

Just including the second explosion, each of the 8 sparks bursts into 8, that means 8 sparks were produced 8 times, or 8x8

Answer:

1 sparkle Burst it produces 8 sparkles so you say 8×8×8×8×8×8×8×8

A box has a square base with side x cm , height 4 cm and volume 289 cm^3. Find x

Answers

Answer:

8.5 cm

Step-by-step explanation:

volume = height × area of base

since this a square, area of base = x²

so 289 = 4 × x²

x² = 289 ÷ 4

x² = 72.25

so x = √72.25

x = 8.5cm

hope this helps

A company has an opportunity to bid on three contracts. determine which would be the best investment given the information in the table below. probability of profit and loss by contract contract profit, probability of profit probability to break even loss, probability of loss southeast $45,000, 50% 30% $6,000, 20% southwest $60,000, 35% 40% $10,000, 25% california $112,000, 20% 40% $40,000, 40% southeast southwest california all contracts include a probability for loss.

Answers

The best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.

What is probability?

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A company has an opportunity to bid on three contracts. Probability of profit and loss by all three contract is listed in the table below.

Contract profit,   (P)* of profit, (P)* to break even loss, (P)* of loss

Southeast $45,000, 50% 30% $6,000, 20% Southwest $60,000, 35% 40% $10,000, 25% California $112,000, 20% 40% $40,000, 40%

The company which will give the maximum profit probability and minimum loss probability will be the best investment.

In the above table, the southeast contract has the maximum probability of profit, which is 50% among all the contracts. Similarly, it has the lowest probability of loss, which is 20%.

Thus, the best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.

Learn more about the probability here;

https://brainly.com/question/24756209

Answer:

It's A. Southeast

Step-by-step explanation:

and Intervention
1. The library is 5 miles from the post office. How many yards is the library
from the post office?
yards

Answers

8800 yards. I think, not sure.

HI!! Please answer this!

You install a mailbox by buriyng a post as shown. According to postal service guidelines, the bottom of the box must be at least 41 inches, but no more than 45 inches, above the road. Write two inequalities that describe the possible length x, in inches, of the post.

Answers

Answer:

41 ≤ x

x ≤ 45

Step-by-step explanation:

Which shapes have two pairs of parallel sides

Answers

Answer:

a rhombus would have 2 pairs of parallel sides, or a parallelogram. (First image is parallelogram and second is rhombus)

Find the geometric mean of 3 and 13. Show work

Answers

Answer:

b

Step-by-step explanation:

a/b=c/d

ad=bc

3/x=x/13

3*13=x*x

√39=√x2

6.244997998398=x

what fraction gives you an answer of 11/12

Answers

Hi there! The fraction that gives you 11/12 is 44/ 48.

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Hope this helps you!

Convert the following fraction to a decimal -11/16

Answers

Answer:

-0.6875

Step-by-step explanation:

[tex]Convert\ -11/16\ to\ decimal\\ \downarrow\\ -0.6875[/tex]

I hope this helps you

:)

Answer: -0.6875.

Step-by-step explanation: -1/16 is -0.0625, and if you add -1/16 eleven times, you get -0.6875.  Therefore, -11/16 as a decimal is -0.6875.

Have a great day! :)

Calculate the average daily balance, finance charge, and new balance using the average daily balance method. Round all dollar amounts to the nearest cent. If applicable, include a thousands comma. Monthly rate: 1.75% Date Payments Purchases Balance Number of Days Product 9/1-9/5 $387.525 1,937.60 976 $50.00 $337.521 337.52 977 - 9/18 A В С 9/19 $62.66 $400.181 400.18 9/20-9/30 D E F Total 30 G A= $ BE C= $ D=$ E= F=$ G=$ Average daily balance : 30 = $ Finance charge = monthly rate x average daily balance = $ New balance = previous balance payment/credits + finance charge + new purchases = $​

Answers

Answer:

Step-by-step explanation:

Credit should go to the previous helper here:

https://brainly.com/question/21285117

I have not cross-checked but the previous answers were:

"

For average daily balance:

Form date 9/1 to date 9/5 :

Balance x number of the days = $ 387.52 x 5 days = $ 1937.6

As on date 9/6 :

($ 387.52 - $ 50.00) x 1 day = $ 337.52

From date 9/7 to date 9/18 :

Balance = $ 337.50

Number of days = 12 days

Therefore, product = 12 days x $ 337.52

= $ 4050.24

As on 9/19 :

($ 337.52  + $ 62.66) x 1 day = $ 400.18

From date 9/20 to date 9/30

Balance :$ 400.18

Number of days = 11 days

Therefore, product = 11 days x $ 400.18

= $ 4401.98

Average daily balance

=  ($ 1937.6 +  $ 337.50 + $ 4050.24 + $ 400.18 + $ 4401.98) / 30

= $ 370.91

Finance charge = $ 370.91 x 1.75 %

= $ 6.49

New balance = $ 370.91 + $ 6.49

= $ 377.4

"

what is the equation of the line that passes through each pair of points for (-2,3) (3,-2)

Answers

Answer:

y = -x + 1

example:

(-2, 3)

y = -(-2) + 1

y = 2 + 1

y = 3

Answer:

y = -x + 1

Step-by-step explanation:

slope = (y2-y1)/(x2-x1) = (-2-3)/(3-(-2)) = -5/5 = -1

y-int: y=mx+b --> plug in a point --> 3 = (-1)(-2)+b --> b=1

y = -x + 1

Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town. He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below. According to this information, what would be the best estimate for Sam to quote as expected profits in the next year in his new business plan? Business Year Net Profit 1 $43,502. 25 2 $47,417. 45 3 $51,685. 02 4 $56,336. 68 5 $61,406. 98 a. $66,477. 28 b. $66,933. 60 c. $72,003. 91 d. $72,957. 63.

Answers

Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.

What is net profit?

Net profit is the amount of a business earn after deducting all the expenditure over it.

Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town.

He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below.

Business Year      Net Profit 1                          $43,502.25 2                         $47,417.45 3                         $51,685.02 4                         $56,336.68 5                         $61,406.98

Using the regression graph, the quadratic equation we get for this data as,

[tex]y=192.4493x^2+3318.1733x+39998.214[/tex]

For the 6 year value,

[tex]y=192.4493(6)^2+3318.1733(6)+39998.214\\y\approx 66835.43[/tex]

This value is much near to the option b which is $66,933.60.

Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.

Learn more about the Net profit here;

https://brainly.com/question/4177260

need help with this one its "Find the slope of the line y = 7x + 9/16" please help

Answers

Answer:

slope = 7

Step-by-step explanation:

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope, and b is the y-intercept)

Therefore, for the equation: y = 7x + 9/16

Slope = 7y-intercept = 9/16

What is the total area of the three triangles? 12.5 square units 13 square units 13.5 square units 14 square units

Answers

The area of the considered 3 triangles is given by: Option B: 13 sq. units.

How to find the area of a triangle whose vertices' coordinates are given?

Suppose the vertices of the considered triangle ABC are on [tex]A(A_x,A_y), B(B_x,B_y), C(C_x,C_y)[/tex], then, the area of the triangle is given by:

[tex]Area = \dfrac{|A_x(B_y-C_y) + B_x(C_y-A_y) + C_x(A_y-B_y)|}{2}[/tex]

For this case, the missing image is attached below.

The second and third triangle are easy as their base and height are parallel to x or y axis.

We will find area of third triangle by coordinates of its vertices.

Getting area of first triangle:

Coordinates of A : (4,10)Coordinates of B : (5,7)Coordinates of C : (7,8)

Thus, we get:

[tex]Area_{ABC} = \dfrac{|4(7-8) + 5(8-10) + 7(10-7)|}{2} = \dfrac{7}{2} = 3.5 \: \rm unit^2[/tex]

Area of second triangle = [tex]\dfrac{|RS| \times h}{2}[/tex]base, and h is the perpendicular line connecting from line RS and the vertex T

From figure we see:

|RS| = 3 units, h = 3 units

Thus, area of second triangle = [tex]3 \times 3 /2 = 4.5 \: \rm unit^2[/tex]

Area of third triangle = [tex]\dfrac{|XY| \times h}{2}[/tex] where XY is base, and h is the perpendicular line connecting from line XY and the vertex Z

From figure we see:

|XY| = 5 units, h = 2 units

Thus, Area of third triangle = [tex]5 \times 2 /2 = 5 \: \rm unit^2[/tex]

Total area = 3.5 + 4.5 + 5  = 13 sq. units

Thus, the area of the considered 3 triangles is given by: Option B: 13 sq. units.

Learn more about area of a triangle from its vertices' coordinates here:

https://brainly.com/question/2532574

Answer:

13

Step-by-step explanation:

Maura is jogging on her treadmill. She runs 2.25 miles in
1
2
of an hour. At that speed, how many miles could Maura run in 1
1
2
hours?

Answers

Answer:

6.75 miles

Step-by-step explanation:

Since it is 2.25 per 1/2 hour to get to 1 1/2 hour you multiply by 3. Then you do 2.25 times 3 and it gives you 6.75 miles.

hope that helps

Answer:

6.75 miles

Step-by-step explanation:

How many 1/2 hours in 1 1/2 hour? 1.5 ÷ 0.5 = 3

2.25 x 3 = 6.75

OR

Find the unit rate = 2.25 x 2 = 4.50 (we multiply it by 2 because there 2 half hours in an hour)
4.50 x 1.50 = 6.75

IDENTIFY THE PROPERTY WHICH JUSTIFIES THE FOLLOWING CONCLUSION

A. REFLECTIVE PROPERTY
B. ADDITION PROPERTY OF EQUALITY
C. SYMMETRIC PROPERTY
D. MULTIPLICATION PROPERTY OF EQUALITY

1. If ×=4, then × + 2=7
....__.....__
2.AB = AB

3. If × = y, Then 2× = 2y

4. If 9 = 6+3, then 6+3 =9

Please answer correctly do not concentrate wrong and rely only on the pontos:)​

Answers

Answer:

Step-by-step explanation:

17) B. They are adding 2 to both sides.

18) A. A segment is equal to itself.

19) D. They are multiplying both sides by 2.

20) C. They are simply swapping the left and right hand sides of the equation

Find the area of the regular polygon. Give the answer to the nearest tenth.
Square with a radius of 13 m.

Answers

Answer:

338 m^2

Hope this helps!

If this helps please show your thanks by marking brainliest ;)

Alex constructs a circle that passes through all three vertices of the triangle shown.
E
Where will the center of the circle be located?

Answers

Answer: A, TRUST ME!

Step-by-step explanation:

Two sides of a parallelogram are 110 feet and 850 feet. The measure of the angle between these sides is 157 Find the area of the parallelogram to the nearest square foot.

Answers

Answer: 36533

Step-by-step explanation:

differentiate the following with respect to x

irrelevant answers will be reported​

Answers

Answer:

[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}[/tex]

Step 2: Differentiate

Apply Derivative Rule [Product Rule]:
[tex]\displaystyle y' = \big[ e^{x^2 + 7} \big]' \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = e^{x^2 + 7} (x^2 + 7)' \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Addition/Subtraction]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \big[ \sin (3x + 4) \big]' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Trigonometric Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \cos (3x + 4) (3x + 4)' \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Addition/Subtraction]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \big[ \sqrt{\csc (5x)} \big]'[/tex]Apply Derivative Rules [Basic Power Rule + Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{\big[ \csc (5x) \big] '}{2\sqrt{\csc (5x)}}[/tex]Apply Trigonometric Differentiation [Derivative Rule - Chain Rule]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{- \csc (5x) \cot (5x) (5x)'}{2\sqrt{\csc (5x)}}[/tex]Apply Derivative Rules and Properties [Basic Power Rule + Multiplied Constant]:
[tex]\displaystyle y' = 2xe^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)} + 3e^{x^2 + 7} \cos (3x + 4) \sqrt{\csc (5x)} + e^{x^2 + 7} \sin (3x + 4) \frac{-5 \csc (5x) \cot (5x)}{2\sqrt{\csc (5x)}}[/tex]Rewrite:
[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]

∴ we have found the derivative of the function.

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Learn more about differentiation: https://brainly.com/question/26836290
Learn more about calculus: https://brainly.com/question/23558817

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

Unit: Differentiation

To find the derivative of the function [tex]\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}[/tex] with respect to [tex]\displaystyle\sf x[/tex], we'll use the chain rule and product rule.

Let's break down the function into its individual parts:

[tex]\displaystyle\sf u= e^{x^{2}+7}[/tex]

[tex]\displaystyle\sf v= \sin(3x+4)[/tex]

[tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex]

Now, let's differentiate each part separately:

Using the chain rule, the derivative of [tex]\displaystyle\sf u= e^{x^{2}+7}[/tex] is:

[tex]\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}[/tex]

Using the chain rule, the derivative of [tex]\displaystyle\sf v= \sin(3x+4)[/tex] is:

[tex]\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)[/tex]

To differentiate [tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex], we can rewrite it as [tex]\displaystyle\sf w= (\csc(5x))^{1/2}[/tex]. Using the chain rule, the derivative of [tex]\displaystyle\sf w[/tex] is:

[tex]\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)[/tex]

Simplifying the derivative [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Now, using the product rule, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] can be calculated as follows:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}[/tex]

Substituting the values of [tex]\displaystyle\sf \dfrac{du}{dx}[/tex], [tex]\displaystyle\sf \dfrac{dv}{dx}[/tex], and [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further, we have:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

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