9/4 is between what two numbers

Answers

Answer 1

Answer: 9/4 is between 2 and 3

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Ex 2.11
20) A curve y''=12x-24 and a stationary point at (1,4). evaluate y when x=2.

Answers

So, dy/dx=0 at the point (1, 4) - that is where x=1 and y=4.

$\int { 12x-24dx } \n \n =\frac { 12{ x }^( 2 ) }{ 2 } -24x+C\n \n =6{ x }^( 2 )-24x+C$

$\n \n \therefore \quad { f }^( ' )\left( x \right) =6{ x }^( 2 )-24x+C$

But when x=1, f'(x)=0, therefore:

$0=6-24+C\n \n 0=-18+C\n \n \therefore \quad C=18$

$\n \n \therefore \quad { f }^( ' )\left( x \right) =6{ x }^( 2 )-24x+18$

Now:

$\int { 6{ x }^( 2 ) } -24x+18dx\n \n =\frac { 6{ x }^( 3 ) }{ 3 } -\frac { 24{ x }^( 2 ) }{ 2 } +18x+C$

$=2{ x }^( 3 )-12{ x }^( 2 )+18x+C\n \n \therefore \quad f\left( x \right) =2{ x }^( 3 )-12{ x }^( 2 )+18x+C$

Now when x=1, y=4:

$4=2-12+18+C\n \n 4=8+C\n \n C=4-8\n \n C=-4$

$\n \n \therefore \quad f\left( x \right) =2{ x }^( 3 )-12{ x }^( 2 )+18x-4$

Now when x=2,

$f\left( x \right) =2\cdot { 2 }^( 3 )-12\cdot { 2 }^( 2 )+18\cdot 2-4\n \n =16-48+36-4\n \n =0$

So when x=2, y=0.

$y''=12x-24\ny'=\int 12x-24\, dx\ny'=6x^2-24x+C\n\n0=6\cdot1^2-24\cdot1+C\n0=6-24+C\nC=18\ny'=6x^2-24x+18\n\ny=\int 6x^2-24x+18\, dx\ny=2x^3-12x^2+18x+C\n\n4=2\cdot1^3-12\cdot1^2+18\cdot1+C\n4=2-12+18+C\nC=-4\n\n 2x^3-12x^2+18x-4$

$y(2)=2\cdot2^3-12\cdot2^2+18\cdot2-4\ny(2)=16-48+36-4\n\boxed{y(2)=0}$

A ship drops its anchor into the water and creates a circular ripple. The radius of the ripple increases ata rate of 50 cm/s. If the origin is used as the location where the anchor was dropped into the water.

Find the equation for the circle 12 seconds after the anchor is dropped

Please write all the steps it’s for my summer school test and I need it done quick as possible thanks.

Answers

Answer:

The equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Step-by-step explanation:

To find the equation for the circle 12 seconds when the radius of the ripple increases at a rate of 50 cm/s, the circle radius will be;

50 * 12 = 600 cm

Then place the equation inform of Pythagoras equation which is;

x^2 + y^2 = r^2

Where r is the radius

x^2 + y^2 = 600^2

x^2 + y^2 = 360,000

Then, the equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Isabel reads 24 chapters of a book in 8 hours. what is the rate in chapters per hour?can someone please show me the steps to help me find the answer

Answers

GiveN:

Isabel reads 24 chapters of a book in 8 hours.

ToFind:

What is the rate in chapters per hour?

Step-wise-StepExplanation:

Considering that Isabel reads the book at a constant rate or we can say that no. of books she read is same for all the 8 hours.

⇒ In 8 hours = 24 chapters

⇒ In 1 hour = 24 / 8 chapters

⇒ In 1 hour = 3 chapters

That means, Isabel reads 3 chapters per hour with the same pace. The Question can be simply solved by using Unitary method $.$

Answer:

the unit rate, in chapters per hour, would be how many chapters in one hour --- but, for 23 chapters/78 hours = this fraction (23/78) is already in simplified (i.e., reduced) form --- i.e., 23 is prime, and 78 = 2(39) = 2(3)13, so 23 and 78 contain no factors in common --- so, the unit rate would be (23/78) chapters per hour --- if the problem had been, for example, 23 chapters in 69 hours, then the unit rate would have been (23/69) chapters per hour = (1/3) chapters per hour, or one chapter every 3 hours (though this is not a unit rate)

Step-by-step explanation:

im wrong but make sure u solve it and see if e

The distributive property combines (blank) and (blank) to make multiplying whole numbers simpler

Answers

The distributive property combines addition and multiplication to make multiplying whole numbers simpler.

It combines multiplication of simpler numbers with addition.
For example:
26 x 15 can be written as: 15(10+10+6)

Answer:

Step-by-step explanation:

Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.
a. x = 8, y = 17
b. x = 6, y = 8
c. x = 8, y = 10
d. x = 8, y = 6

Answers

D. X = 8 , Y = 6

3x - 14 = x + 2
3x - x = 2 + 14
2x = 16
2x / 2 = 16/2
x = 8

To check: 3x - 14 = x + 2 ; 3(8) - 14 = 8 + 2 ; 24 - 14 = 10 ; 10 = 10

4y - 7 = y + 11
4y - y = 11 + 7
3y = 18
3y / 3 = 18 / 3
y = 6

To check: 4y - 7 = y + 11 ; 4(6) - 7 = 6 + 11 ; 24 - 7 = 17 ; 17 = 17

Daniel wants to buy cookies for her friends. The area of a cookie is 113.04 in2. What is the circumference of the cookie?