I need help I can't go to bed until I finish this​

Answer:

The water level is rising at the rate 0.238 cm per second

Step-by-step explanation:

Let the radius and height of water at time t be r and h respectively.

Height of cup =H= 8 cm

Radius of cup = R = 4 cm

By symmetry

[tex]\frac{r}{h}=\frac{4}{8} \\r=\frac{1}{2}h ---1[/tex]

Volume of water at time t , [tex]V= \frac{1}{3} \pi r^2 h[/tex]

[tex]\frac{dV}{dt}=\frac{1}{3}\pi 2r \frac{dr}{dt} h+\frac{1}{3} \pi r^2 \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{3}\pi r (2 \frac{dr}{dt} h+ r \frac{dh}{dt})[/tex]

With 1

[tex]\frac{dr}{dt}=\frac{1}{2} \frac{dh}{dt}[/tex]

So,

[tex]\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) (2 (\frac{1}{2} \frac{dh}{dt}h)+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( \frac{dh}{dt}h+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( h+\frac{1}{2}h) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi h(\frac{3h}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi (\frac{3h^2}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{12}\pi 3h^2 \frac{dh}{dt}[/tex]

We are given that Water is poured into a conical paper cup at the rate of 3 cubic centimeters  (cm) per second (s).

We are supposed to find how fast the water level is rising at the instant the water is 4 cm deep.

So,[tex]\frac{1}{12}\pi 3(4)^2 \frac{dh}{dt}=3\\\frac{dh}{dt}=\frac{3 \times 12}{\pi 3(4)^2 }=0.238[/tex]

Hence the water level is rising at the rate 0.238 cm per second

The radius in terms of height is [tex]\mathbf{r =\frac 12h}[/tex], while the water level increases at 0.239 cm per second when the height is 4 cm

(a) Radius in terms of height

The given parameters are:

[tex]\mathbf{h = 8cm}[/tex] --- height

[tex]\mathbf{r = 4cm}[/tex] --- radius

The above parameters can be written as:

[tex]\mathbf{r :h =4cm : 8cm}[/tex]

[tex]\mathbf{r :h =4 : 8}[/tex]

Express as fractions

[tex]\mathbf{\frac rh =\frac 48}[/tex]

[tex]\mathbf{\frac rh =\frac 12}[/tex]

Multiply both sides by h

[tex]\mathbf{r =\frac 12h}[/tex]

(b) How fast the water is rising

The volume of a cone is:

[tex]\mathbf{V = \frac 13 \pi r^2h}[/tex]

Differentiate with respect to time

[tex]\mathbf{V' = \frac 13 \pi(2rh\ \frac{dr}{dt} + r^2\frac{dh}{dt})}[/tex]

When the water is 4cm deep, then the radius is 2cm using [tex]\mathbf{r =\frac 12h}[/tex]

So, we have:

[tex]\mathbf{V' = \frac 13 \pi(2 \times 2 \times 4\times \frac{dr}{dt} + 2^2\frac{dh}{dt})}[/tex]

[tex]\mathbf{V' = \frac 13 \pi(16 \frac{dr}{dt} + 4\frac{dh}{dt})}[/tex]

Also, we have:

[tex]\mathbf{r =\frac 12h}[/tex]

Differentiate with respect to time

[tex]\mathbf{\frac{dr}{dt} = \frac{1}{2}\frac{dh}{dt}}[/tex]

So, we have:

[tex]\mathbf{V' = \frac 13 \pi(16 \times \frac{1}{2}\frac{dh}{dt} + 4\frac{dh}{dt})}[/tex]

[tex]\mathbf{V' = \frac 13 \pi(8\frac{dh}{dt} + 4\frac{dh}{dt})}[/tex]

[tex]\mathbf{V' = \frac 13 \pi(12\frac{dh}{dt})}[/tex]

Expand

[tex]\mathbf{V' = 4\pi\frac{dh}{dt}}[/tex]

The volume increases at 3 cm^3 per second.

So, we have:

[tex]\mathbf{3 = 4\pi\frac{dh}{dt}}[/tex]

Divide both sides by 4

[tex]\mathbf{0.75 = \pi\frac{dh}{dt}}[/tex]

Divide both sides by pi

[tex]\mathbf{0.239 = \frac{dh}{dt}}[/tex]

Rewrite as:

[tex]\mathbf{\frac{dh}{dt} = 0.239}[/tex]

Hence, the water level increases at 0.239 cm per second when the height is 4 cm

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Answer:

Step-by-step explanation:

This is a trick. Since it's y=4. there is no slope, the slope is 0

Answer:

m= 6/7

decimal form m= 0.857

Step-by-step explanation:

hope this helps

Answer:

m=6/7

m=0.857...

Step-by-step explanation:

-4m - 6 + 6-m = -5 + 2m - 1​

-5m-6+6=-5+2m-1

-5m=-5+2m-1

-5m=2m-5-1

-5m=2m-6

-5m-2m=2m-6-2m

-7m=-6

divide both sides by -7

x=6/7

Answer:

Step-by-step explanation:

i hopes this helps

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^3+3x^2<x+3

(-∞,-3)∪(-1,1)

Answer:

the answer is A

Step-by-step explanation:

hope this help

Answer:

There are 6 blocks in each row

Step-by-step explanation:

The total number of blocks is 42 and the number of rows is 7. So the equation would be 42 ÷ 7.

So, 42 ÷ 7 = 6. There are 6 blocks in each row.

Hope this Helps!

Total number of row is 6 row.

Given that;

Total number of block = 42 block

Total number i=of block in each row = 7

Find:

Total number of row

Computation:

Total number of row = Total number of block / Total number i=of block in each row

Total number of row = 42 / 7

Total number of row = 6

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Answer:

0.325

Step-by-step explanation:

thats it

Answer:

0.325 kg

Step-by-step explanation:

You move the decimal point three places to the left, and end up with 0.325 kg.  :)

Answer:

6x+y=-8 because it will be y=-6x-8 having same slope with the line given

Answer:

its the second number to the right of the decimal

Answer:

two zeroes at the end and if it is a number like 2400 the hundreths place is the 400

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given

A= 260ft^2

W= 2x + 4

B=8x + 2

Step two:

A=L*W

260=(2x+4)*(8x + 2)

open bracket

260=16x^24x+32x+8

16x^2+56x-252=0

Solving using quadratic formula

the roots are

x=-6.0

x= 2.6

Hence the value of x= 2.6ft

Answer:

Here you go sorry.

Step-by-step explanation:

Question 1.

y = 4x - 8 has a slope of 4. Since parallel lines have equal slopes, the slope of your new line will also be 4.

Now, you have a point (3,9) and a slope 4. Use the Point-Slope Form for the equation of a line.

y - y1 = m(x - x1)

y - 9 = 4(x - 3)

y - 9 = 4x - 12

y = 4x - 3

Question 2.

Since it is parallel, it must have the same slope.

y = (1/2)x + b

Find b from the given point.

4 = (1/2)(2) + b

b = 3

y = (1/2)x + 3

Answer:

$46325 in total for the car

Step-by-step explanation:

Answer:

-7y+8x

Step-by-step explanation:

-7y+8x

Answer:

thx

Step-by-step explanation:

Answer:

no.

Step-by-step explanation:

b ∩ c   is the values that appear in both  b  and  c.

b ∪ c   is all the values in  b and  c.

Answer:

The Cheetah's initial speed is 19.4 miles per hour

Step-by-step explanation:

Since the Cheetah is initially running and then gradually increases its speed by 50.6 miles per hour to reach a top speed of 70 miles per hour, let the Cheetah's initial speed be u.

Also, let the increase in the Cheetah's speed be Δu and let v be the Cheetah's final speed.

Now, the final speed, v = initial speed, u + change in speed, Δu

So, v = u + Δu

So, the Cheetah's initial speed is u = v - Δu

Now, v = 70 mi/h and Δu = 50.6 mi/h

Substituting v and Δu into the equation, we have

u = v - Δu

u = 70 mi/h - 50.6 mi/h

u = 19.4 mi/h

So, the Cheetah's initial speed is 19.4 miles per hour

Answer:

the answer is c I think, I'm sorry if it is wrong, but I'm pretty sure it's right

Answer:

C

Step-by-step explanation:

Step-by-step explanation:

Here you go,

number 7 = 26

number 9 = 66

number 8 = 79

number 6 = 31

Answer:

Y= -3/2x-8

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

First find out how many beads cover 1 inch of the string which is 4 beads then multiply that number, 4, by the length of the string, 13. You should get 52.

Answer: 52

Part A

Why?

So for this question. You can write a ratio what will the balance be what information do they give you that you can register as a ratio? Well, what will the ratio be?

OK, THE WORK IS HERE!--v

So 12 beads are the ratio.

Now what do we want to know? Well, we want to know how to solve it.

1. 12b= __

3in= 13in <---------well-known way people use it to solve

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

2. 12b divided by 12 = 1b

3in divided by 12= ____->ANSWER: 0.25 <----- Not that many people do it this way

for 2. solve-v

1b = ___ ANSWER: 52

0.25 13in 1 We can do this 13 divided by 0.25 which is 52

SO FOR PART A THE ANSWER IS 52

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

ANSWER: Part B is __

Why?

-1in off here----------------------------1in off here-

And she wants to keep The middle part and we know this whole thing is 13 but the middle part = 11. Sooooooo...

1b = ___ANSWER 8

0.25 = 2in so now we can do this: 2 divided by 0.25 which we get 8

ANSWER FOR PART B IS 8

The statement that describes the graph of the system of equations is:

C. The lines intersect at (1.6, 1.4).

Here, we have,

To determine the description of the graph of the system of equations:

1.5x + 0.2y = 2.68

1.6x + 0.3y = 2.98

We can start by comparing the slopes of the two lines.

The equations are in the form y = mx + b, where m represents the slope.

In the first equation, the slope is 0.2, and in the second equation, the slope is 0.3.

Since the slopes are different, we can conclude that the lines are not parallel (option A) or overlapping at all points (option B).

To determine the point of intersection, we can solve the system of equations.

By using any appropriate method, we find that the lines intersect at (1.6, 1.4) (option C).

Therefore, the statement that describes the graph of the system of equations is:

C. The lines intersect at (1.6, 1.4).

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Answer:

Step-by-step explanation:

10.6_

Answer:

96/9  or  10   6/9  or  10     2/3

Step-by-step explanation:

Lets make common denominators first LCM(9,1)=9

8/1 x 9/9 = 72/9

24/9 + 72/9 = 96/9

Answer: 96/9  or  10   6/9  or  10     2/3

Hope this helps :D

Answer:

Step-by-step explanation:

Find the measure of the vertex angle ∠ABD of an isosceles triangle

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem

∠ABD=∠BAD= ----> the angles of the base are equals

Find the measure of the vertex angle

∠ABD= ------> the sum of the internal angles of a triangle is equal to

Step 2

Find the measure of the angle  ∠CBD in the equilateral triangle

we know that

A equilateral triangle has three  equal sides and three equal angles

The measure of the internal angle in a equilateral triangle is

so

∠CBD=

Step 3

Find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC=

therefore

the answer is

the measure of the angle ∠ABC is

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

a is the answer

Answer:

A

IS YOUR ANSWER

I HOPE IT HELPS MATE

I WILL ALWAYS HELP YOU UNDERSTANDING YOUR ASSINGMENTS

HAVE A GREAT DAY

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Answer: Number of children  = 168

Number of adults = 120

Step-by-step explanation:

Let x = Number of children and y = Number of adults

As per given,

x+y=288          (i)

2.25x+6.80y =1194       (ii)

Multiply 2.25 on both sides in (i)

2.25x+2.25y= 648       (iii)

Eliminate (iii) from (ii)

4.55y=546

[tex]\Rightarrow y=\dfrac{546}{4.55}\\\\\Rightarrow\ y=120[/tex]

Put y= 120 in (i)

x+120=288

⇒ x=288-120

⇒ x= 168

Hence, Number of children  = 168

Number of adults = 120

Answer:

D

Step-by-step explanation: