Mathematics High School

Hi. I need help with these questions (see image)
Please show workings.
​

Hi. I Need Help With These Questions (see Image)Please Show Workings.

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the chain rule

Given

y = f(g(x)), then

[tex]\frac{dy}{dx}[/tex] = f'(g(x))  × g'(x) ← chain rule

and the standard derivatives

[tex]\frac{d}{dx}[/tex] ([tex]log_{a}[/tex] x ) = [tex]\frac{1}{xlna}[/tex] , [tex]\frac{d}{dx}[/tex](lnx) = [tex]\frac{1}{x}[/tex]

(a)

Given

y = [tex]log_{a}[/tex][tex]\sqrt{(1+x)}[/tex]

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{lna\sqrt{(1+x)} }[/tex] × [tex]\frac{d}{dx}[/tex] ([tex](1+x)^{\frac{1}{2} }[/tex]

   = [tex]\frac{1}{lna\sqrt{(1+x)} }[/tex] × [tex]\frac{1}{2}[/tex] [tex](1+x)^{-\frac{1}{2} }[/tex] × [tex]\frac{d}{dx}[/tex] (1 + x)

   = [tex]\frac{1}{lna\sqrt{(1+x)} }[/tex] × [tex]\frac{1}{2\sqrt{(1+x)} }[/tex] × 1

   = [tex]\frac{1}{2lna(1+x)}[/tex]

   = [tex]\frac{1}{(1+x)lna^2}[/tex]

(b)

Given

y = ln sinx

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{sinx}[/tex] × [tex]\frac{d}{dx}[/tex](sinx)

   = [tex]\frac{1}{sinx}[/tex] × cosx

   = [tex]\frac{cosx}{sinx}[/tex]

   = cotx

Related Questions

What does x equal in the equation 5x-5=7+2x

Answers

Answer: x= 4 (simplify the terms)

Answer:

[tex] \fbox{x = 4} [/tex]

Step-by-step explanation:

Simplify the expressions in the equation by applying the properties of equality.

1) [tex] 5x-5=7+2x [/tex]

2)

What do I do I don’t get it

Answers

Answer:

3*sqrt3=sqrt3=3by the power of 1/2

i’m pretty sure its V3

PLS HELP NOOOOOOOOWWWWWWWWWWW

Answers

OMGGMGMFKF WHAT IS THATTTYY HAHA IS THAT MATH BRO? HOW U FEELING CAUSE ION KNOW HOW TO HELP

Sydney says the slope of this line is 6/4
.

Deja says, "No, the slope of this line is 1.5"

Who is correct?
Sydney
Deja
Both
Neither

Answers

Answer:

Both

Step-by-step explanation:

Bc, 6/4 is equal to 1.5

Answer:

Both

Step-by-step explanation:

If you think about it, 6/4 is the same thing as 1.5, 6/4 is in the fraction form and 1.5 is in the decimal form. So, Deja and Sydney are both correct.

Hope this helps :D

Help Please Quickly I need help now​

Answers

Answer:

C) Mrs. Benjamin

C) 9 mrs. Benjamin

​Together, teammates Pedro and Ricky got 2674 base hits last season. Pedro had 284 more hits than Ricky. How many hits did each player​ have?

Answers

Pedro- 2674 hits
Ricky- 2390 hits
Explanation: Pedro has 2674 hits it says “Pedro had 284 more hits than Ricky” 2674 - 284 = 2390. Pedro has 2674 hits and Ricky has 2390 hits

solve this 1/5×=25. ​

Answers

Answer:

x=125

Step-by-step explanation:

Answer:

×=0.008

Step-by-step explanation:

I hope this help

What is the volume of the composite figure.Please Help

Answers

Answer:

2,304 Inches

(づ￣ ³￣)づhave A nice day

solve for c
c/6=12


A.2
B.6
C.18
D.72

Answers

Its A becuase 12/6=2

What was the balance before the debit card payment on June 14?

A sample check register.


$236.84


$550.20


$694.26


$931.10

Answers

Answer:

931.10

Step-by-step explanation:

I had to take this same question on a quiz...

Answer: 931.10

Step-by-step explanation: I took the test and got it right

Part 1
Washington, DC, was warmer in February (4.3°F)than in December (44°F). Write an inequality for this relationship.

Answers

Because December is really cold

Answer:

Step-by-step explanation:

4.3 °F > 4 1/4 °F

im very confused with how to solve and would like help please​

Answers

Answer:

(x+1 )- (x-2) ≠ -1

Step-by-step explanation:

Find the area and perimeter. Stuck on this one need help

Answers

9514 1404 393

Answer:

area: 114 square unitsperimeter: 44 units

Step-by-step explanation:

The figure is a trapezoid with bases 12 and 7, and a height of 12. The area formula is ...

  A = (1/2)(b1 +b2)h

  A = (1/2)(12 +7)(12) = 114 . . . square units area

__

The length of side AB can be found using the distance formula:

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((6 -(-6))^2 +(1 -6)^2) = √(144 +25) = 13

The sum of the side lengths is then ...

  13 +7 +12 +12 = 44 . . . units perimeter

Please Help!!! A bicycle has wheels 28 inches in diameter. tachometer determines that the wheels are rotating at 180 RPM (revolutions per minute). Find the speed the bicycle is traveling down the road.

Answers

Answer:

402.336 meters per minutes

Step-by-step explanation:

revolutions per minute = speed in meters per minute / circumference in meters.

Diameter = 28 inches

Circumference of the wheel = 2πr

r = Diameter/2 = 28/2 = 14

Circumference = 2 × π × 14

= 87.964594301 inches

Approximately = 88 inches

Note that:

1 inch = 0.0254 metre

88 inches = x

x = 88 × 0.0254 meters

x = 2.2352 meters

Hence:

Revolutions per minute = Speed in meters per minute / circumference in meters.

Speed = Revolutions per minute × circumference in meters.

Speed = 180 RPM × 2.2352 meters

Speed = 402.336 meters per minutes

Speed of the bicycle traveling down the road = 84π.

It is given that

Diameter of the wheel (2r) = 28 inches, where 'r' is the radius

Speed N(in revolutions per minute) = 180rpm

What is the formula for angular speed?

Angular speed ω = [tex]\frac{2\pi N}{60}[/tex]radian per second.

[tex]w= \frac{2*\pi*180 }{60 } = 6\pi[/tex] radian per second

Speed of bicycle V = r*ω

Where,

r= radius of the wheel

[tex]V = 14*6*\pi = 84\pi inches/second[/tex]

Therefore,

speed of the bicycle traveling down the road = 84π.

To get more about circular motion problems refer to:

https://brainly.com/question/106339

Fast please correct the problems

Answers

I don’t really know:(

Need Help with this please!!

Answers

Answer:

A is 85 degrees

can someone please help me i dont even know

Answers

Answer:

just know so please give me a good rating

Which of these is an example of an overdraft?
A.having $378.12 in your checking account and writing a check for $349.02.
B.having $450.22 in your checking account and writing a check for $462.05.
C.having $183.19 in your checking account and writing a check for $144.43
D.having $556.29 in your checking account and writing a check for $490.77

Answers

Answer: B.having $450.22 in your checking account and writing a check for $462.05.

Step-by-step explanation: took the quiz.

solve for “x”.

2x = 5

thanks to whoever helps!! :)

Answers

Answer is 2.5 bc u have to divide 5 by 2 then u get ur answer

Answer:

2.5

Step-by-step explanation:

In this equation x is equal to 2.5. I got this answer by dividing both sides of the equation by 2, since we do the opposite operation of how the equation is set up. Have a great day! :)

A circle has a diameter of 6ft What is the area of the circle? ​

Answers

Answer:

28

Step-by-step explanation:

1/2(6x - 10)-x+=? plz

Answers

Answer:

x=2.5

Step-by-step explanation:

1/2(6x-10)-x=0 Replace the ? with a 0 so you can solve for x.

So your going to want to distribute everything in parentheses by 1/2 first to get 3x-10-x=0 Next your going to simply the equation by combining like terms to get 2x-5=0. Next add five to both sides so that 2x=5. Finally divide both sides by 2 and the answer is x=2.5.

Hope this helped!

the sum of four times a number and seventeen 65. find the the number

Answers

Answer:

13 divided by 7

Step-by-step explanation:

Slope rise over run (must be expressed as a fraction) send help plssssssSSS

Answers

Answer:

-1/2

Step-by-step explanation:

if you pick any two points on the line, you count how many units up and how many units across. you also have to put your answer in simplest form. the slope is a negative slope since its going downwards from left to right. your answer is -1/2

You have $25.00. You want to buy chocolate for Valentines Day. Each box costs $6.99?Do you have enough money to buy three boxes? Do you have any amount of money leftover? If so, how much?

(Can someone help?)

Answers

Answer:

yes and u will have and u will have 0.28 left over

Step-by-step explanation:

25/7=0.28

can someone help me with this

Answers

Answer:

1. 40 members

2. 4 cheerleaders

3. 40 marbles

4. 2 marbles

5. 8

6. 24

Step-by-step explanation:

1. cross multiply 12/x=30/100

2. cross multiply 12/x=10/100

3. 18/x=45/100

4. x/40=5/100

5. we know 5% is 2 marbles. multiply by 4 to get 8 marbles.

6. 20%=8 marbles. 60/20= 3. 3 x 8= 24 marbles.

Find the product. Write your answer as a decimal 0.01(4.6)(-200) =

Answers

Answer:

I believe the answer is -9.2

Step-by-step explanation:

2(x+1) please do full steps and answer thank you i will give brainlist

Answers

Distribute the parentheses:

2(x + 1)

2 · x = 2x

2 · 1 = 2

2(x + 1) = 2x + 2

The cost of in-state tuition at the University of Florida is $6,380 and is increasing at a rate of 3.1% per year. Write and use an exponential function to find the tuition cost after 8 years. Round your answer to the nearest whole dollar. Help pls will give brainliest.

Answers

Answer:

loser

Step-by-step explanation:

PLEASE HELP ME WITH THESE TWO QUESTIONS ILL GIVE BRAINLIEST AND EVERYTHING ELSE

Answers

First question is 3rd box
Second question is 1st box

do anyone know about this ?

Answers

nope what class is that
Yes jerhhdbdvddh Hannah
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