Mathematics High School


[tex] \sf \large \: If \: y = Sin x \: * Cos \: 2x \: Find \frac{dy}{dx} [/tex]








Thanku!​

Answers

Answer 1

Answer:

cos (x) cos (2x) - 2sin(x) sin(2x)

Solution:

(See the solution in the photo)

[tex] \sf \large \: If \: Y = Sin X \: * Cos \: 2x \: Find \frac{dy}{dx} [/tex]Thanku!
[tex] \sf \large \: If \: Y = Sin X \: * Cos \: 2x \: Find \frac{dy}{dx} [/tex]Thanku!
Answer 2

Answer:

[tex]\sf -5\cos \left(x\right)+6\cos ^3\left(x\right)[/tex]

explanation:

[tex]\sf y = sin(x) * cos(2x)[/tex]

[tex]\rightarrow \sf \frac{d}{dx}\left(sin\left(x\right)\ * \:\:cos\left(2x\right)\right)[/tex]

[tex]\sf \bold {Apply\:the\:Product\:Rule}:\quad \left(f\cdot g\right)'=f\:'\cdot g+f\cdot g'[/tex]

[tex]\rightarrow \sf \frac{d}{dx}\left(\sin \left(x\right)\right)\cos \left(2x\right)+\frac{d}{dx}\left(\cos \left(2x\right)\right)\sin \left(x\right)[/tex]

[tex]\sf \bold{ Apply \ differentiation \ rule \ \ \ : } \ \ \ sin(x) = cos(x) \ \ and \ \ cos(x) = -sin(x)[/tex]

[tex]\rightarrow \sf \cos \left(x\right)\cos \left(2x\right)+\left(-\sin \left(2x\right)\ * \:2\right)\sin \left(x\right)[/tex]

[tex]\rightarrow \sf \cos \left(x\right)\cos \left(2x\right)\left-2\sin \left(2x\right)\sin \left(x\right)[/tex]

[tex]\sf \bold {use \ the \ formulae \ : \ cos(2x) = 2cos^2(x) - 1} \ {and} \ \ \sf \bold{sin(x) = 2 sin x cos x}[/tex]

[tex]\rightarrow \sf cos(x) (2cos^2 (x) -1) -2(2sin(x)cos(x)sin(x))[/tex]

[tex]\rightarrow \sf 2cos^3 (x) - cos(x) - 4sin^2(x) cos(x)[/tex]

[tex]\rightarrow \sf -5\cos \left(x\right)+6\cos ^3\left(x\right)[/tex]

Related Questions

A cabinet is the shape of a triangular prism. The triangular base has a base length of 14 inches and a base height of 22 inches. The cabinet is 67.5 inches tall. What is the volume of the cabinet?

Answers

Answer:

As Per Provided Information

We have been asked to determine the volume of triangular Prism . Volume of Triangular Prism is calculated by using the following formula

[tex] \bf \: Volume_{(Triangular~Prism)} = \cfrac{1}{2} \times b \: \times h \times l [/tex]

Substitute the given value and let's calculate the volume of cabinet .

[tex] \sf \: \longrightarrow Volume_{(Triangular~Prism)} \: = \cfrac{1}{2} \times 14 \times 22 \times 67.5 \: \: \\ \\ \sf \: \longrightarrow Volume_{(Triangular~Prism)} \: = \frac{1}{ \cancel2} \times \cancel14 \times 22 \times 67.5 \: \: \\ \\ \\ \sf \: \longrightarrow Volume_{(Triangular~Prism)} \: = 7 \times 22 \times 67.5 \: \: \\ \\ \\ \sf \: \longrightarrow Volume_{(Triangular~Prism)} \: = \: 154 \times 67.5 \: \: \\ \\ \\ \sf \: \longrightarrow Volume_{(Triangular~Prism)} \: = 10395 {cm}^{3} [/tex]

Therefore,

Volume of the Triangular Prism Cabinet is 10395 cm³.

PLEASE HELP!!!
Only answer if you know the answer
​

Answers

Answer:

132

Step-by-step explanation:

A sample contains 16.75 g of the radioisotope u-236 and 50.25 g of its daughter isotope, th-232. how long did it take for decay to take place if one half-life of u-236 is 23 million years? 46 million years 69 million years 92 million years 115 million years

Answers

If one half-life of U-236 is 23 million years then it will take 45.5 or approximately 46 million years to decay. Then the correct option is A.

What is half-life?

Half-life is the time interval that is needed to decay the atomic nuclei of a radioactive sample.

A sample contains 16.75 g of the radioisotope U-236 and 50.25 g of its daughter isotope, Th-232.

Initially, the whole sample is consisting the radioisotope. Then the initial total mass will be

m₀ = 16.75 + 50.25

m₀ = 67 g

Now we also know that the half-life is 23 million years. Then we have

[tex]m = m_oe^{- \lambda t}[/tex]

Then put the value

[tex]\begin{aligned} 16.75 &= 67 e^{- \lambda t}\\\\0.254 &= e^{- \lambda t}\\\\\lambda t &= 1.37\\\\\dfrac{ln2}{23 \rm \ million \ years } \times t &= 1.37\\\\t &= 45.5 \ \rm million\ years \end{aligned}[/tex]

If one half-life of U-236 is 23 million years then it will take 45.5 or approximately 46 million years to decay. Then the correct option is A.

More about the half-life link is given below.

https://brainly.com/question/24710827

Answer:

a. 46 million years

Step-by-step explanation:

HELP ASAP A function is defined by fx) = 6x+1.5. What is f(2.5)?

Answers

Answer:

f(2.5) = 16.5

Step-by-step explanation:

To evaluate f(2.5), substitute x = 2.5 into f(x) , that is

f(2.5) = 6(2.5) + 1.5 = 15 + 1.5 = 16.5

Complete two expressions that have the same product as 3 x 5 . 12

__________ x

1

12 __________ x

3

12 hurry up please

Answers

Answer:
Hope this helped :)

You have one coupon for x dollars off and another coupon for x% off.

Write a rule that helps you decide when you should use one instead the other.

Answers

Answer:

if you want an item that is 100 dollars of then you would like the precent of because 1-100 percent is 1-100 so the larger the number the more you would want the percent but if it is 10% or 5 dollars of on an item of 10 dollars then the dollars of would be better so the higher the number the more you want percentage.

Please help me answer this question please?

Part c

Answers

Answer:

ok 12 is 12 1 is 1 2 is 2 and three is treee

Evaluate a + 6 for a = 10
16
6
60

Answers

I think the correct answer is 4 but if you have to pick from the options you were given to with 16

Help guys asap this is due today. Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double the height.

The volume of the cylinder in^3?

The volume of with the same radius and double the height is ?

Answers

Answer:

226.2 in³ and 452.4 in³

Step-by-step explanation:

Volume of original shape:

Volume = base area x height
Volume = πr² x 2
Volume = π(6)² x 2
Volume = 113.10 x 2
Volume = 226.2 in³

Volume with same radius but double the height:

Volume = base area x height
Volume =  πr² x 2(2) ----------> multiplied by 2 because height is being doubled
Volume = 113.10 x 4
Volume = 452.4 in³

if two angles 2x+10°and 3x+20°are supplementary find x ​

Answers

Answer:

x = 30

Step-by-step explanation:

Supplementary angles sum to 180° , then

2x + 10 + 3x + 20 = 180 , that is

5x + 30 = 180 ( subtract 30 from both sides )

5x = 150 ( divide both sides by 5 )

x = 30

The area of a rectangle is given by x2 - 12x + 35. Determine the length and breadth in
terms of x. Hence, determine the length and breadth if x = 20.
(3)

Answers

Answer:

[tex]x+7; x+5; 27; 25[/tex]

Step-by-step explanation:

First of all, we need to write [tex]x^2+12x+35[/tex] as a product. The easiest way is to find a pair of numbers whose product is 35 and sum is 12. Looking at the product, you notice it's 7 and 5, which added together indeed give 12.

The two side length are thus [tex]x+7[/tex] and [tex]x+5[/tex].

In the specific case, when [tex]x=20[/tex] the two sides measures 27 and 25.

40 points!
create one equation with a fraction and show the work to solve it.

Answers

Answer: 3x/6=4

Step-by-step explanation:

3x/6 = 4

multiply 6 on both sides to remove fraction.

3x=24

x=8

Rachel took out a personal loan for $4,500 with a monthly payment of $173.06 for 36 months. determine the finance charge on rachel's loan if she takes all 36 months to pay it off. a. $48.06 b. $1,730.16 c. $4,500.00 d. $6,230.16

Answers

The finance charge on Rachel's loan if she takes all 36 months to pay it off is $1730.16.

The amount of personal loan = $4500

Monthly payment =$173

Loan tenure = 36 months

The total amount that Rachel will pay for 36 months = 36*173.06

The total amount that Rachel will pay for 36 months = $6230.16

What is the finance charge?

A finance charge refers to any cost related to borrowing money, obtaining credit, or paying off loan obligations.

The finance charge on Rachel's loan if she takes all 36 months to pay it off  = The total amount that Rachel will pay till 36 months - Amount of personal loan

The finance charge on Rachel's loan = 6230.16-4500 = $1730.16

Therefore, The finance charge on Rachel's loan if she takes all 36 months to pay it off is $1730.16.

To get more about monthly payments visit:

https://brainly.com/question/2151013

What is four hundred seventy five and nineteen thousandths in standard form

Answers

Answer:

475.019

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

Điền số nguyên để
-3/5<...<-1

Answers

I don't know to this problem sorry

Ms. Caswell deposits $450 into an account earning 8% simple interest per year. How
much simple interest is earned after 4 years?

Answers

Answer:

$144

Step-by-step explanation:

Use the simple interest formula, I = prt, where I is the interest money created, p is the starting amount, r is the interest rate as a decimal, and t is the amount of time.

Plug in the original amount, interest amount, and amount of time:

I = prt

I = 450(0.08)(4)

I = 144

So, $144 in simple interest is made in 4 years

Carpenters refer to the slope of a roof as the pitch on the roof

Answers

Answer:

Step-by-step explanation:

pitch=4/12=1/3

Is 13 quarts greater than, less than, or equal to 4 gallons?

Answers

Answer:

Less than

Step-by-step explanation:

One quart is .25 of a gallon

less than
4 quarts per 1 gallon

Questions 3, 4, and 5.

Answers

Answers:

Reason 2) Given. Specifically, the diagram shows that the two angles are adjacent and supplementary, which is why the two angles are a linear pair.Reason 3) Definition of Linear Pair. As stated above, a linear pair of angles add to 180 degrees (they are supplementary).Statement 4) [tex]m \angle WZX = 90 \text{ and } m \angle WZV = 90[/tex] since the term "right angle" is another way of saying "90 degree angle"Statement 5) [tex]\overset{\leftarrow -\rightarrow}{WY} \perp \overset{\leftarrow -\rightarrow}{XV}[/tex] The upside down "T" symbol means "perpendicular". Perpendicular lines form 90 degree angles at the intersection.

Side note: The double arrow over WY and XV in statement 5 is supposed to be an unbroken line.

Jenna runs 6km per hour, how long would it take her to run 3km

Answers

It would take Jenna half an hour, or 30 minutes, to run 3 km.

Hope this helps!

A banner measures 5.4 feet long.

How long does the banner measure in inches and in yards?

Enter your answers in the boxes.

Answers

Answer:

64.8 inches, 1.8 feet

Step-by-step explanation:

5.4*12=64.8

5.4/3=1.8

Answer:

Inches: 64.8, Yards: 1.8

Step-by-step explanation:

To get inches you multiply 5.4 by 12 and you get 64.8. To get yards you divide 5.4 by 3 and you get 1.8.

what is the angle measure of 8?

Answers

Answer:

2x+8

Step-by-step explanation:

Since the two lines are crossing each other, angles on one side should be equal to the angle directly opposite them.

-2x8y=12 slope - intercept form

Answers

X equal 3 y equal 17

Answer:

you mean

2x-8y=12

8y=2x-12

y=(1/4)x-(3/2)

so intercept is-3/2

The first occurrence of the highest temperature in the
cycle is day with a temperature of °C.
The first occurrence of the lowest temperature in the
cycle is day with a temperature of °C.

Answers

Answer: 9,28

4,22

Step-by-step explanation:

Answer:

Step-by-step explanation:

Marcy is putting a wallpaper border at the top of the walls of her baby's rectangular room. The width of the room is 2 feet less than the length. If she needs 52 feet of border, what are the dimensions of the room?​

Answers

Answer:

The baby's rectangular room is 14 feet long and 12 feet wide

Step-by-step explanation:

Assume we set:

x=width of the room

y=length of the room

The width of the room is 2 feet less than the length:

[tex]x=y-2\qquad\qquad [1][/tex]

The total length of the wallpaper needed is the perimeter of the room. The formula for the perimeter of a rectangle is:

P=2x+2y

And the perimeter is equal to 52 feet:

2x+2y=52

Dividing by 2:

[tex]x+y=26\qquad\qquad [2][/tex]

Substituting x from [1]:

y-2+y=26

Simplifying:

2y-2=26

Adding 2:

2y=28

Solving:

y=28/2=14

y=14

Find x:

x=y-2=14-2=12

The baby's rectangular room is 14 feet long and 12 feet wide

In a 180-kilogram sample of ore, there was 3.2% metal. How many kilograms of metal were in the sample?

Answers

5.76 KG as 180 x 0.032 (3.2 percent) = 5.76

Which composite figure is made up of a cone and a cylinder?

Answers

Answer:

Your answer is B, the second one.

Step-by-step explanation:

a/b = (a+b)/a

What is the value of a/b? Please show all steps.

Answers

Answer:

1+b/a

Step-by-step explanation:

To find the amount of a/b we have to solve the equation

(a+b)/a

a/a+b/a

a/a is one so

1+b/a

what is the missing factor in x2−x−42=()(x−7)

Answers

Answer:

Step-by-step explanation:

The missing factor has the form (x - a).  The given factor is (x - 7).  The product (a)(-7) must be -42, and therefore the missing factor is (x + 6)

Plzz help this assignment is due tomorrow!!

Answers

Answer:

Rip dude XD Ur gonna die

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