Write as a ratio in simplest form: 14 feet to 2 yards

Answer:

[tex]\frac{1}{\pi} \frac{\text{ft}}{\text{min}}[/tex] is the rate at which the water is rising when the water is 6 ft deep.

Step-by-step explanation:

See the attached diagram that I drew to represent this problem.

To solve related rates problems, let's use the recommended steps:

I already drew the diagram; see attached image.

I labeled the quantities we are given in the problem. h = 10 ft, and r = 5 ft. We are also told that the change in volume is 9 ft³/min; dV/dt = 9 ft³/min.

We want to find dh/dt when h = 6.

We know that we are dealing with a cone in this problem, and we are given the volume of the cone. Therefore, we can use the formula for the volume of a cone in order to relate all of the quantities in the same equation.

Since we only want the two variables, V and h, we can solve for r in terms of h and substitute this value for r in the formula.

This is because when we perform implicit differentiation, we do not have the change in r (dr/dt) but we do have dh/dt, which is what we are trying to solve for.

We know that r = 5 ft, and h = 10 ft. Therefore, we can say that [tex]\frac{r}{h}=\frac{5}{10} \rightarrow \frac{r}{h} = \frac{1}{2}[/tex]. Multiply h to both sides to solve for the variable r: [tex]r=\frac{h}{2}[/tex].

Substitute this into the volume of a cone equation:

Simplify this equation.

Perform implicit differentiation on the volume equation.

Substitute known values and solve for dh/dt to find the change in height, or the rise in water level, when the water is 6 ft deep (h = 6).

We know that:

Plug these values into the implicitly differentiated volume equation.

Answering the question in context:

Since dh/dt = 1/π when h = 6 ft, we can say that the water is rising at a rate of [tex]\frac{1}{\pi} \frac{\text{ft}}{\text{min}}[/tex] when the water is 6 ft high.

Hey there!

We can create some variables to denote some of the things we are working with.

v = volume

h = height

r = radius

We know that [ dv/dt = (π/3)r²h ]. We also know that [ r/h = 5/10 = 1/2 ] which resembles the parts of a triangle.

Solution:

v = π/3*h/2²

h = πh³/(4)(3)

~Differentiate both sides

dv/dt = (3πh³/4*3)(dh/dt)

~Simplify

dh/dt = (4dv/dt)/πh²

~Use chain rule

(4)(9)/π6²

1/π

Thus, the speed of the water level rising is [ 1/π ft/min ] when the water is 6ft deep.

Best of Luck!

Answer:

f(x)=(x+2)(x-7)(x-5)(x-5)

Step-by-step explanation:

With the use of the roots and leading coefficient, you can easily write out the polynomial as I have above.

Answer:

f(x)= (x-7)(x-5)(x-5)((x+2)

Step-by-step explanation:

Edge answer D

Answer:

-60...make me brainlistt

Step-by-step explanation:

Answer:

7 but im not sure

Step-by-step explanation:

Answer:

its A and B

Step-by-step explanation:

Do NOT hit none of the above, that's wrong

the answer to the equation is -280

Answer:2[tex]\sqrt{6}[/tex]because it is a 45 45 90

Step-by-step explanation:

Answer:

Area  = 10

Step-by-step explanation:

([tex]\sqrt{50}[/tex]×[tex]\sqrt{8}[/tex])  ÷ 2 = 10

Answer: 3.0 meters

Step-by-step explanation:

3000 millimetres  is the same as 3 meters.  

3 as a decimal is the same as 3.0

Answer: 1-20 can be made with four 2's  when you use a power on the 2's like this 2 to the power of 4 + (2 to the power of 2+2 to the power of 2)= 20

Step-by-step explanation:

Answer:

56 feet

Step-by-step explanation:

If 1 inch = 2 feet, we can first find the actual dimensions of his room by multiplying the number of inches by 2.

6(2)

= 12

8(2)

= 16

So, the actual dimensions of his room are 12 feet by 16 feet.

To find the perimeter, use the perimeter formula, P = 2l + 2w.

Plug in the length and width:

P = 2l + 2w

P = 2(12) + 2(16)

P = 24 + 32

P = 56

So, the perimeter of his actual room is 56 feet.

Answer:

oof

Step-by-step explanation:

Answer:

Correct

Step-by-step explanation:

Answer:

68,359,375. Using a calculator, you can multiply each new number by 5.

11th term of the given geometric sequence is [tex]a_{n}= 7(5^{n-1})[/tex]

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Given geometric sequence = 7,35,175,..

Nth term of the geometric sequence [tex]a_{n}=a_{1}.r^{n-1}[/tex]

[tex]a_{1}=7[/tex]

[tex]r=\frac{35}{7}=5[/tex]

Nth term of the geometric sequence

[tex]a_{n}= 7(5^{n-1})[/tex]

Hence, the Nth term of the given geometric sequence is  [tex]a_{n}= 7(5^{n-1})[/tex]

Learn more about Geometric sequence here

https://brainly.com/question/13008517

#SPJ2

Answer:

5 and 1/3 cups of soil

Step-by-step explanation:

Hello there, in this problem we can solve for the amount of soil that Katie will need by multiplying the factor for one of them by the number of pots we have, 8. We get 16/3 cups of soil, or 5 and 1/3 cups of soil.

Hope this helps!

-HM

Answer:

Katie need 5.6 cups of soil.

Step-by-step explanation:

To solve this equation, we just need to multiply 8 by 2/3. Though to make this equation easier, I will turn 2/3 into a decimal by dividing the numerator (2) by the denominator (3.)

2  ÷ 3 = 0.7 when rounded to the nearest tenth.

Now, let's multiply 0.7 by 8.

8 x 0.8 = 5.6

Therefore, Katie need 5.6 cups of soil.

Hope this helps! :)

Answer:

3/4 hour

Step-by-step explanation:

Answer:

of course.

he's the king of the court

Answer:

He's a great setter but he never gets an award like Oikawa does...

Step-by-step explanation:

*spoiler*

-

-

-

-

buuut he does get accepted to the Japan Youth Training camp where only elites go (Ushijima when there) ;)

Answer:

The result will be irrational, but 1.5128968253966 hours should be the answer.

Step-by-step explanation:

Answer:

linear, it can be solved for y

Answer:

A. Linear

Step-by-step explanation:

It's a straight line when you graph it etc. etc.

An apartment of the same square footage today is $716 unfurnished making a cost of living increase of 44.69%. If Della and Jim's apartment was $32 per month with furnishings included and they signed a lease for 13 months, what is the total weekly cost in 1905? Answer: $1340.80

Answer:

R=5/4

Or

R=1.25

Step-by-step explanation:

Answer:

The probability is  [tex]P( p < 0.9207) = 0.0012556[/tex]

Step-by-step explanation:

From the question we are told

  The population proportion is [tex]p = 0.96[/tex]

 The sample size is  [tex]n = 227[/tex]

 The number of graduate who had job is  k = 209

Generally given that the sample size is large enough  (i.e n >  30) then the mean of this sampling distribution is  

       [tex]\mu_x = p = 0.96[/tex]

Generally the standard deviation of this sampling distribution is  

    [tex]\sigma = \sqrt{\frac{p (1 - p )}{n} }[/tex]

=>  [tex]\sigma = \sqrt{\frac{0.96 (1 - 0.96 )}{227} }[/tex]

=>  [tex]\sigma = 0.0130[/tex]

Generally the sample proportion is mathematically represented as

      [tex]\^ p = \frac{k}{n}[/tex]

=> [tex]\^ p = \frac{209}{227}[/tex]

=> [tex]\^ p = 0.9207[/tex]

Generally probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is mathematically represented as

     [tex]P( p < 0.9207) = P( \frac{\^ p - p }{\sigma } < \frac{0.9207 - 0.96}{0.0130 } )[/tex]

[tex]\frac{\^ p - p}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \^ p )[/tex]

   [tex]P( p < 0.9207) = P(Z< -3.022 )[/tex]

From the z table  the area under the normal curve to the left corresponding to    -3.022  is

     [tex]P(Z< -3.022 ) = 0.0012556[/tex]

=> [tex]P( p < 0.9207) = 0.0012556[/tex]

Answer:

The equivalent expression is:

[tex]-16m^2n-\left(-25m^2n\right)+\left(-7m^2n\right)=2m^2n[/tex]

Step-by-step explanation:

Given the expression

[tex]-16m^2n-\left(-25m^2n\right)+\left(-7m^2n\right)[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a,\:-\left(-a\right)=a[/tex]

[tex]=-16m^2n+25m^2n-7m^2n[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-16m^2n+25m^2n-7m^2n=2m^2n[/tex]

[tex]=2m^2n[/tex]

Therefore, the equivalent expression is:

[tex]-16m^2n-\left(-25m^2n\right)+\left(-7m^2n\right)=2m^2n[/tex]

Answer:

x = 9

Step-By-Step Explanation:

1. 3x + 5 + 6x + 4 = 90

2. 9x + 9 = 90

3. 9 + -9

4. 90 + -9

5. 9x = 81

6.  x= 9                              Substituting X:

                                        3 X 9 + 5 = 27 + 5 = 32

                                        6 X 9 + 4 = 54 + 4 = 58       58 + 32 = 90, so X = 9

Answer:

Step-by-step explanation:

The reason I say the answer above is wrong is because their answer equals up to a angle of 100 degrees however your angle is equaling up to 90 degrees. First off we know this angle is going to be 90 degrees right so we put it into the eqution:

=90

but we don't know what x is in order to solve the degrees that add up to 90, so since these equations add up to 90 we put them into the equation:

(3x + 5)+ (6x + 4) = 90

we then add all the numbers that have the same variables or are simply numbers in the equation

3x + 6x and 5 + 4 to get 9x + 9 = 90

we then subtract 9 from both sides (because what you do to one side you do to the other) to get 81

the equation now looks like this: 9x = 81 so now we divide 9 from both sides to get x = 9

Now how do we know if x is really 9 well we plug it into the equations (3x + 5) and (6x + 4) making them look like this (3(9) + 5) and (6(9) + 4)

and you get (3(9) + 5)= 32

                     (6(9) + 4)= 58

and when you add them together you get 90

32 + 58 = 90

Sorry it took so long to answer back. I hope this helps you

Isolate the variable by dividing each side by factors that don't contain the variable.

h = −8

Statements 3, 4 and 5

Answer:

Statements 3, 4 and 5

Step-by-step explanation:

Answer:

y=1/3x+6

Step-by-step explanation:

Equations parallel to each other have the same slope so that rules out the fourth answer. Perpendicular equations have opposite and reciprocal slopes, which in this case would be [tex]\frac{-1}{3}[/tex], which rules out all of the others except for the third option.

I will find x, so 4x-4=180, so 4x=184, so x=46

Sorry if i answered wrong I don't understand what it is asking for.