Rearrange b = c + xd to make x the subject of the formula.

Please explain this problem!!!

9966 [12]

tis a little of plain differentiation.

we know the radius of the cone is decreasing at 10 mtr/mins, or namely dr/dt = -10, decreasing, meaning is negative.

we know the volume is decreasing at a rate of 1346 mtr/mins or namely dV/dt = -1346, also negative.

so, when h = 9 and V = 307, what is dh/dt in essence.

we'll be needing the "r" value at that instant, so let's get it

$V=\cfrac{1}{3}\pi r^2 h\implies 307=\cfrac{\pi }{3}r^2(9)\implies \sqrt{\cfrac{307}{3\pi }}=r$

now let's get the derivative of the volume of the cone

$V=\cfrac{1}{3}\pi r^2 h\implies \cfrac{dV}{dt}=\cfrac{\pi }{3}\stackrel{product~rule}{ \left[ \underset{chain~rule}{2r\cdot \cfrac{dr}{dt}}\cdot h+r^2\cdot \cfrac{dh}{dt} \right]} \\\\\\ -1346=\cfrac{\pi }{3}\left[2\sqrt{\cfrac{307}{3\pi }}(-10)(9)~~+ ~~ \cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\right]$

$-\cfrac{4038}{\pi }=-\cfrac{180\sqrt{307}}{\sqrt{3\pi }}+\cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\implies \left[ -\cfrac{4038}{\pi }+\cfrac{180\sqrt{307}}{\sqrt{3\pi }} \right]\cfrac{3\pi }{307}=\cfrac{dh}{dt} \\\\\\ -\cfrac{12114}{307}+\cfrac{180\sqrt{3\pi }}{\sqrt{307}}=\cfrac{dh}{dt}\implies -7.920939735970634 \approx \cfrac{dh}{dt}$

5 0

2 years ago

A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles. HINT [See Example 7.

kirill115 [55]

Answer:

There are 12 sets of four marbles include all the red ones.

Step-by-step explanation:

Given : A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles.

To find : How many sets of four marbles include all the red ones?

Solution :

Number of red marbles = 3

Number of green marbles = 2

Number of lavender marbles = 1

Number of yellow marbles = 4

Number of orange marbles = 5

We have to form sets of four marbles include all the red ones,

For position of getting red ones we have three red marbles i.e. $^3C_3$

For the fourth one we have 12 choices i.e. $^{12}C_1$

Total sets of four marbles include all the red ones is

$=^3C_3\times ^{12}C_1$

$=1\times 12$

$=12$

Therefore, There are 12 sets of four marbles include all the red ones.

5 0

3 years ago

What is the slope of the following graph?

mel-nik [20]

I dont know if this helps since no one else is answering I’d like to help
To find slope.. the M in the slope formula of y=Mx+b represents slope

So as long as you know what point on the graph represents what then it should be easy

In most cases.. finding slope is where the line meets on the x axis

6 0

3 years ago

Please Help!!

Mrrafil [7]

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can.
If they join to work together they can complete the job in 3 hours. 
1/x + 1/(x - 8) = 1/3 
3(x - 8) + 3x = x(x - 8) 
x^2 - 14x + 24 = 0 
(x - 12)(x - 2) = 0 
Solutions: 
x = 2 
x = 12 
Jimmy can complete the job on his own in 12 hours.

6 0

3 years ago

In a recently administered iq test, the scores were distributed normally, with mean 100 and standard deviation 15. what proporti

iragen [17]

To solve for proportion we make use of the z statistic. The procedure is to solve for the value of the z score and then locate for the proportion using the standard distribution tables. The formula for z score is:

z = (X – μ) / σ

where X is the sample value, μ is the mean value and σ is the standard deviation

when X = 70

z1 = (70 – 100) / 15 = -2

Using the standard distribution tables, proportion is P1 = 0.0228

when X = 130

z2 = (130 – 100) /15 = 2

Using the standard distribution tables, proportion is P2 = 0.9772

Therefore the proportion between X of 70 and 130 is:

P (70<X<130) = P2 – P1

P (70<X<130) = 0.9772 - 0.0228

P (70<X<130) = 0.9544

Therefore 0.9544 or 95.44% of the test takers scored between 70 and 130.

6 0

3 years ago

Rearrange b = c + xd to make x the subject of the formula.​

Rearrange b = c + xd to make x the subject of the formula.