Please help me do this mathematics question experts

Please Help Me Do This Mathematics Question Experts

Answers

Answer 1

[tex]\textbf{(i)}\\\\~~~~~~~y= e^{3x} \sin 2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( e^{3x} \sin 2x \right)\\\\\\~~~~~~~~~~~~=e^{3x} \dfrac{d}{dx} \sin 2x + \sin 2x \dfrac{d}{dx} e^{3x}\\\\\\~~~~~~~~~~~~=2e^{3x} \cos 2x + 3e^{3x}\sin 2x \\\\\\[/tex]

[tex]\textbf{(ii)}\\\\~~~~~~~~y = \dfrac{e^{3x}}{\cos 2x}\\\\\\\implies \dfrac{dy}{dx} = \dfrac d{dx} \left(\dfrac{e^{3x}}{\cos 2x} \right)\\\\\\~~~~~~~~~~~=\dfrac{\cos 2x \dfrac{d}{dx}\left(e^{3x} \right) -e^{3x} \dfrac{d}{dx}( \cos 2x) }{\cos^2 (2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x+2e^{3x}\sin2x }{\cos^2(2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x}{ \cos^2(2x)} + \dfrac{2e^{3x} \sin 2x}{\cos^2(2x)}\\\\\\~~~~~~~~~~~=3e^{3x}\sec (2x) + 2e^{3x}\sec (2x) \tan (2x)[/tex]

[tex]\textbf{(iii)}\\\\~~~~~~~~~y=( 3x+2)^3\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}(3x+2)^3\\\\\\~~~~~~~~~~~=3(3x+2)^2 \dfrac{d}{dx} (3x+2)\\\\\\~~~~~~~~~~~=3(3x+2)^2 \cdot 3\\\\\\~~~~~~~~~~~=9(3x+2)^2[/tex]

[tex]\textbf{(iv)}\\\\~~~~~~~~~x^2 +y^2 = 5xy\\\\\\\implies \dfrac{d}{dx}(x^2 +y^2) = 5\dfrac{d}{dx} (xy)\\\\\\\implies 2x + 2y \dfrac{dy}{dx} = 5\left(x \dfrac{dy}{dx} +y\right)\\ \\\\\implies 2x +2y \dfrac{dy}{dx} = 5x \dfrac{dy}{dx} +5y\\\\\\\implies 2y \dfrac{dy}{dx} - 5x \dfrac{dy}{dx} = 5y-2x\\\\\\\implies (2y-5x) \dfrac{dy}{dx} = 5y-2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{5y-2x}{2y-5x}[/tex]


Related Questions

At the school track meet, Dita ran 100 meters at a rate of 6.25 meters per second.

Time = StartFraction distance Over rate EndFraction

How long did it take Dita to finish the race?
16 seconds
93.75 seconds
106.25 seconds
625 seconds

Answers

original equation

[tex]v=\frac{d}{t}[/tex]

solve for t

[tex]t=\frac{d}{v}\\\\t=\frac{100}{6.25} \\\\t=16[/tex]

It took Dita 16 seconds to finish the race

Answer:

a

Step-by-step explanation:

aaaaaaa

its a

16 seconds

if the circle passing through the point (-1,0) touches the y- axis at (0,2) then what's the equation of the circle?​

Answers

Answer:

  (x +2.5)² +(y -2)² = 6.25

Step-by-step explanation:

A radius of a circle is perpendicular to the tangent line at the point of tangency. This means the center of the circle lies on the horizontal line through the point (0, 2), which is on the vertical tangent x=0 (the y-axis).

The center of a circle lies on the perpendicular bisector of any chord, so the perpendicular bisector of the given two points will pass through the circle center.

__

equation of the chord bisector

The slope of the chord between the given points is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (2 -0)/(0 -(-1)) = 2   ⇒   perpendicular has slope -1/2

The midpoint of the chord is ...

  M = (A +B)/2 = ((0, 2) +(-1, 0))/2 = (-1, 2)/2 = (-1/2, 1)

The point-slope form of the perpendicular through the midpoint of the chord is ...

  y -1 = -1/2(x -(-1/2))

__

center of the circle

For y = 2, the x-value is ...

  2 -1 = -1/2(x +1/2)

  -2 = x +1/2 . . . . . . multiply by -2

  -2.5 = x . . . . . . . subtract 1/2

The circle center is (-2.5, 2), and the radius is 2.5 (distance from center to y-axis).

__

equation of the circle

The equation can be written as ...

  (x -h)² +(y -k)² = r² . . . . . . circle with center (h, k) and radius r

  (x -(-2.5))² +(y -2)² = 2.5²

  (x +2.5)² +(y -2)² = 6.25

What is the probability that a registered voter voted in the​ election?

Answers

Answer:

0.4714, a simplified 47%

Step-by-step explanation:

:)

The question is attached.

Answers

Answer:

A

Step-by-step explanation:

Please see attached, I have colour coded for your convenience

Translate into an equation.
The sum of seven and a number, x, is five.

Answers

Answer:

x + 7 = 5

Step-by-step explanation:

I think this should be an equation I’m in 7th and I am learning these again so it should be an equation.

Figure out this equation I already attempted to do it multiple times

Answers

Here's the link to the answer:

https://riverside.rocks/index.php

It’s a squared plus b squared

let y= -11sin(4x-8)
what is the amplitude?
what is the period?
what is the phase shift?

Answers

If the equation is y = - 11sin(4x - 8). Then amplitude will be 11, the time period is 4, and the phase difference is 8.

What is a sinusoidal Function?

It is a function that repeats itself in a particular time interval.

The sinusoidal function is given as

y= |A| sin(ωx - Φ) ...1

Where A is amplitude, ω is the time period, and Φ is the phase difference.

The equation is given below.

y =  -11 sin(4x - 8) ...2

Comparing the equations 1 and 2, then we have

Amplitude will be 11, the time period is 4, and the phase difference is 8.

More about the sine function link is given below.

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help me pleaseeeeeeeeeeeeeeeeee

Answers

Answer:

Step-by-step explanation:

Volume

V = w h l

V = 2*15*13

V = 390 ft^3

-------------------------

Surface area

SA = b*h

SA = 15*13

SA = 195

-------------------------

b) Surface area

C) Volume

anyone understands this?

Answers

Answer:

[tex]144^{90}[/tex]

Step-by-step explanation:

sqrt (144^180)   =    (144^180 )^1/2  = 144^90

Mr. Sanchez is pulling his luggage across the airport floor. He applies a 22-newton force to the handle of the bag when the bag makes a 72-degree angle with the floor. Find the magnitudes of the horizontal and vertical components of the force. Round your answers to the nearest tenth.

Answers

Magnitude equals 560 psi

Select all the correct measures of center and variation for the following data set.

10, 20, 31, 17, 18, 5, 22, 25, 14, 43



First quartile = 12



IQR = 11



Median = 19



Third quartile = 25



MAD = 7

Answers

Answer:

Median = 19

IQR = 11

Third quartile = 25

Step-by-step explanation:

Just caculate it...

A line passes through the point (-2, -9) and has a slope of 8

Answers

Step-by-step explanation:

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

[tex]y - ( - 9) = 8.(x - ( - 2))[/tex]

[tex]y = 8x + 16 - 9[/tex]

[tex]y = 8x + 7[/tex]

Answer:

y = 8x + 7

Step-by-step explanation:

We are given that a line contains the point (-2, -9), and a slope of 8

We want to write the equation of this line

There are multiple ways to write the equation of the line:

Slope-intercept form, written as y=mx+b where m is the slope and b is the y interceptStandard form, written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero and a cannot be negativePoint-slope form, written as [tex]y-y_1=m(x-x_1)[/tex], where m is a slope and [tex](x_1, y_1)[/tex] is a point

The most common of these 3 methods is slope-intercept form, so let's write our equation this way

As we are already given the slope, we can immediately plug that into our formula for m

Replace m with 8:

y=8x+b

Now we need to find b

As the equation passes through (-2, -9), we can use its values to help solve for b

Substitute -2 as x and -9 as y:

-9 = 8(-2) + b

Multiply

-9 = -16 + b

Add 16 to both sides

7 = b

Substitute 7 as b.

y = 8x + 7

Topic: finding the equation of the line

See more here: https://brainly.com/question/7358459

CAN ANYONE PLEASE HELP!’

Answers

Answer:

130 cm³

Step-by-step explanation:

Volume of the pyramid = 1/3 × base area × height

Calculating base area;

Area = length × width

= 8 × 7

= 56 cm²

Now, Volume = ⅓ × 56 × 7

= ⅓ × 392

= 130.6 cm³.

Brainly for the one who help me

Answers

Answer:

prior to

Step-by-step explanation:

The scale of a model house to the actual house is 1:150. If the actual house size is 40 feet high, how many feet tall is the model? (round your answer to the nearest tenth​

Answers

Answer:  0.3 feet

Work Shown:

(1 ft)/(150 ft) = (x ft)/(40 ft)

1/150 = x/40

1*40 = 150*x

40 = 150x

x = 40/150

x = 4/15

x = 0.2667 approximately

x = 0.3

Note: 0.3 ft = 0.3*12 = 3.6 inches

if x:16::35:40 then x is ............ ans pls ​

Answers

Answer:

here is your answer

Step-by-step explanation:

cross multiplication

divide

Can someone answer theese 3 questions

Answers

Answer:

Which three questions?

Step-by-step explanation:

I've answered this first question, I guess I need two more...

There's no questions shown? Lol

The diagram shows the locations of Cody and Reese after running different directions from a tree. How far did Cody run?

Answers

Answer:

very very far indead he ran and ran without stopping

Which of the following does NOT contribute to global warming?
A. Oil
B. Gas
C. Nuclear power
D. Coal

Answers

Answer:

D. Coal.

Step-by-step explanation:

Doesn’t really affect the earth in any way.

what set of data corresponds to the dot plot​

Answers

The bottom answer matches. please give brainlest

find the domain and range

Answers

Answer:

Domain: all real numbers (all reals)

Range: y> OR EQUAL TO -2

Step-by-step explanation:

Hope this helps! ;-)

...........................................................

Answers

Answer:

55

Step-by-step explanation:

When you have your final draft, you are ready to_________your essay using the work processor.
A. Peer edit
B. Publish
C. Revise
D. Prewrite

Answers

Answer:

C) Revise

Step-by-step explanation:

A final draft needs to be revised before it can be published

Whats the difference between 16x + 5 and 4x + 5

Answers

Difference = -

Difference Between 16x+5 and 4x+5

16x+5-4x+5

C.L.T (Collect Like Terms)

16x-4x+5+5

12x+10

The volume of a right cone is 168π units^3. If its diameter measures 12 units, find its height

Answers

Answer:

14 units

Step-by-step explanation:

In the question, it is given that a right cone has a diameter of 12 units and volume of 168π units³ and we have to find the height of the cone.

[tex] \: [/tex]

To Find the height of the cone, we must know this formula :

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi r^2h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]

Where,

r refers to the radius of the cone. Here, the diameter is 12, Therefore the radius will be 6 units.

h refers to the height of the cone.

Now, we will substitute the values in the formula :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times (6)^2 \times h = 168 \pi}}}}}}} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times 36 \times h = 168 \cancel\pi}}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \ \times 36 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{36}{3} \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = \frac{168}{12} }}}}}}} \\ \\[/tex]

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\[/tex]

Therefore,

The height of the cone is 14 units .

john decides to buy a new laptop computer. it is on sale for 20% off and he has a coupon for 15% off the sale price. if sales tax is 6%, how much will john pay

Answers

The price that John would pay for the new laptop after accounting for the sales, price coupon and the sales tax is  0.72p.

What is the price John would pay?

After the sales price and coupon is applied, the price of the laptop would reduce.

Price after the sales price = (1 - 0.2) x p = 0.8p

Price after the coupon = (1 - 0.15) x 0.8p

0.85 x 0.8p = 0.68p

A tax increases the price of the laptop.

Price after the tax = (1 + 0.06) x 0.68p = 1.06 x 0.68p = 0.72p

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Can someone help me with this please?

Answers

The final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

What are matrices?

A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns in mathematics.

The calculation of the given matrix is as follows:-

[tex]\rm D-C= \left[\begin{array}{ccc}13&2&-5\\6&-4&0\\\end{array}\right] - \left[\begin{array}{ccc}1&4&-8\\3&-5&2\\\end{array}\right] \\[/tex]

[tex]\rm D-C= \left[\begin{array}{ccc}(13-1)&(2-4)&(-5+8)\\(6-3)&(-4+5)&(0-2)\\\end{array}\right][/tex]

[tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

Hence the final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

To know more about matrix follow

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given that (3x+2) is a factor of 3x^3+bx^2-3x-2. find the value of b?

Answers

Answer:

[tex]b = 2[/tex].

Step-by-step explanation:

By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].

Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:

[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].

Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:

[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].

Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:

[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].

[tex]b = 2[/tex].

5 STARS FOR A CORRECT ANSWER IMAGE ATTACHED can anyone please answer this or how i find the weighted mean?

Answers

So, basically this is the formula to calculate weight mean.

Thank you.

What is the range of the following relation?

Answers

Y is less than or equal to 0

Answer:

Y less than or equal to zero

Step-by-step explanation:

The graph shows that its moving downwards, therefore the Y value is decreasing..

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