Apply distributive 15+22

The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]

We are give a cone with dimensions as seen in the diagram in the attached image.

The volume changes at the rate

[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]

the negative sign is used because the volume of water is reducing.

what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate

[tex]\frac{dh}{dt}|_{h=3cm}[/tex]

The relationship between the volume and the height is given by

[tex]V=\frac{1}{3}\pi r^2h[/tex]

but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this

[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]

substitute into the volume formula to eliminate [tex]r[/tex]

[tex]V=\frac{\pi h^3}{27}[/tex]

differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly

[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]

to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]

[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]

So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]

Learn more about related rate of change here: https://brainly.com/question/15576763

Explanation:

Consider ABCD is a rhombus

We know that

All sides are equal in rhombus i.e,

⇛AB=BC=CD=DA

and AC and BD are digonals

Given that

Diagonal and the side of the rhombus are equal.

⇛AB = BC = CD = DA = AC

Diagonal AC divides the rhombus into two triangles .

They are ∆ BAC and ∆ DAC

In triangle BAC

BA=BC=AC,(Given)

⇛∠ BAC=∠ABC= ∠ACB =60°→→→Eqn(i)

Similarly in ∆DAC ,

DA=DC=AC

⇛∠DAC=∠ACD=∠ADC=60°→→→Eqn(ii)

From eqn(i) and eqn(ii)

∠A=∠BAC+∠DAC=60°+60°=120°

and

∠B= ∠ABC = 60°.

and

∠C=∠ACB+∠ACD=60°+60°=120°

and

∠D =∠ADC=60°

∴ ∠A = 120° , ∠B = 60° ,∠C = 120° & ∠D = 60°

Answer:-The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°.

Note: [Figure refers in the attached file.

Answer: 23.76 miles

Step-by-step explanation:

You are basically finding the perimeter for question a

given that perimeter is [tex]\pi[/tex]d

Subsitute the values

So perimeter = [tex]\pi[/tex] x 5.5 = 5.5 [tex]\pi[/tex] miles = 17.28 miles (2.d.p)

For question b, the area of the surface of Crater lake is finding its area

Given that area of a circle is [tex]\pi r^{2}[/tex]

Substitute the values

Because 5.5 is the diameter, to find the radius, divide by 2 to get 2.75

Area = 2.75^2 x [tex]\pi[/tex] = 7.5625[tex]\pi[/tex] = 23.76 miles^2 (2.d.p)

Answer:

Step-by-step explanation:

When divide f(x)=ax³+bx²+cx+d by (x+3), the remainder is 4:

Then 2f(x) - 6 is:

As we see the remainder is 2

Answer: The cost per ticket is $12.

Step-by-step explanation:

Answer:

A. distributive

Step-by-step explanation:

You would multiply the 9 with the x to get 9x, and then you would multiply the 9 with the negative -5 to get 9x-45.

The point (4,6) means it took Ziah 4 minutes to run 6 blocks.

This is because any point is of the form (x,y) where in this case

x = number of minutes

y = number of blocks

Answer:

answer is in an image here

imageshare.best/image.php?id=JS9NDO

Explanation:

copy n paste in browser

not a bot btw

Answer:

5 miles

Step-by-step explanation:

add the points together.

it seems like each point is how many miles they ran each day.

1/4 + 2(1/2) + 3/4 + 3(1) = 5

Step-by-step explanation:

Option A is the correct answer

Answer:

A is correct

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] is 0.125

[tex]\frac{2}{3}[/tex] is 0.667

[tex]\frac{9}{10}[/tex] is 0.9

[tex]\frac{7}{6}[/tex] is 1.167

which from this you can see that A represents the order from smallest to largest

Answer: C. 95 is a composite number.

Step-by-step explanation:

You can look at the ones place of each number to see if any end in 0, 2, 5, or any other digit that indicates that the number is not prime. Since 95 ends in a 5, it can be divided by 5, making it have more factors than 1 and itself. Therefore, 95 is the composite number of the list of numbers.

Answer:95

Step-by-step explanation:composite numbers are numbers that have more factors than 1 and itself, factors are numbers you can multiply to get a number. 95 is a composite number since 1,95, AND 5 are all factors of 95 making it a composite number

The balance after ten years is $2,208.04.

When an amount of money is compounded quarterly, it means that the amount deposited and the interest earns interest every quarter. The formula that can be used to determine the balance in 10 years is:

FV = P (1 + r)^nm

$1000 x (1.02)^40 = $2,208.04

To learn more about future value, please check: https://brainly.com/question/18760477

Answer:

  see attached

Step-by-step explanation:

The one that matches the triangle shown in the attachment has the given vertices.

Answer:

Either (c) or (a), (B also looks like a good answer, but I'd go for c)

Step-by-step explanation:

If I'm inincorrect, I apologize!

Answer:

First you would divide 12 cars by 3 hours to see how many cars get washed per hour

Then you know that 4 cars get washed in one hour so you multiply it by $5.00 because you want to see how much money they earn in one hour

After you know they earn $20.00 per hour you multiply that by 8 because you want to see how much money they earn in eight hours

So your final answer is $160 for washing cars in 8 hours

The equation m(x + n) = n​ si solved for x will be given as x = n / m (1 - m).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation is given below.

m(x + n) = n​

By simplifying for x, then we have

x + n = n / m

     x = n / m - n

     x = (n - mn) / m

     x = n / m (1 - m)

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

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Explanation:

We have 6 slots to fill A,B,C,D,E,F

There are 6 choices for choice A, then 5 choices for slot B, 4 for C, and so on until we reach one choice for slot F. Count down by 1 each time a slot is filled.

Multiply out those values to get: 6*5*4*3*2*1 = 720

For more information, check out the concept of factorials.

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Another approach is to use the nPr permutation formula which is

[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]

where in this case n = 6 and r = 6.

Answer:

answer

Step-by-step explanation:

what are do u mean what is f and e explain properly and then people will tell u

Answer:

Second and fourth

Step-by-step explanation:

A line is in point-slope form when you write down as [tex]y-y_0=m(x-x_0)[/tex] - do not be distracted by the signs, +1 and +5 can both be written as -(-1) or -(-5) rispectively.

Answer:

x=12

Step-by-step explanation:

[tex](4x + 15) + (x + 5) = 180 \\ 5x + 20 = 180 \\ 5x = 60 \\ x = 12[/tex]

Answer:

12

Step-by-step explanation:

The answer is A.

A negative x a negative equals a positive so the square root of a negative value cannot be a negative value.

Answer:

m∠1 = 97

m∠2 = 83

m∠3 = 97

m∠4 = 83

Answer:

m∠1 = 97°

m∠2 = 83°

m∠3 = 97°

m∠4 = 83°

Step-by-step explanation:

180 - 97 = 83°

180 - 83 = 97°

Answer:

x + 23 = 2x - 41

Step-by-step explanation:

I'm not too sure how to explain the correctness of the answer but I know that it's:

x + 23 = 2x - 41