Given :
Salt is poured from a container at 10 cm³ s-¹ and it formed a conical pile whose height at any time is 1/5 the radius of the above.
To Find :
At what rate is the height of the cone increasing when the height is 2 cm form the base of the cone.
Solution :
We know, volume of a cone is given by :
[tex]V = \dfrac{\pi r^2h}{3}[/tex]
Also, h = r/5
r = 5h
[tex]V = \dfrac{\pi (5h)^2h}{3}\\\\V = \dfrac{\pi 25h^3}{3}[/tex]
Differentiating above equation w.r.t h, we get :
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{\pi 25h^3}{3})\\\\\dfrac{dV}{dh} = 25\pi h^2\dfrac{dh}{dt}\\\\\dfrac{dh}{dt}= \dfrac{\dfrac{dV}{dh}}{25\pi h^2 }\\\\\dfrac{dh}{dt}=\dfrac{10}{25\times 3.14\times 2^2}\\\\\dfrac{dh}{dt}=0.032\ cm/s[/tex]
Hence, this is the required solution.
Given the following list of data, find the median.
1,3, 1.23, 2, 4, 22, 13, 26. 8
Answer:
solution
or, (N+1) th item
_
2
or ,8+1 th item
_
2
or,9
_
2
or,4.5 th item hence the median is4
The median of the given numbers will be 8.5.
What is the median?The Median is the middlemost value of the numbers arranged in ascending orders. If the number of the data is an odd number so the median will be a middle number if the number of the data is even then the median is the mean of the middle two numbers.
The given data is:-
1 , 1.23 , 2 , 3 , 4 , 13 , 22 , 26.8
The total numbers of the data are 8 so the median will be calculated as:-
Median = ( 4 + 13 ) / 2
Median = 17 / 2
Median = 8.5
Therefore the median of the given numbers will be 8.5.
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What is the value of sin {3sin^-1 (2/5)} ?
Answer:
[tex]\displaystyle \frac{118}{125}[/tex]
Step-by-step explanation:
Trigonometry
Calculate
[tex]\sin (3\sin^{-1}(2/5))[/tex]
We use the formula for the sine of triple angle:
[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]
And recall:
[tex]\sin \sin^{-1}x=x[/tex]
For this problem, we set:
[tex]x=\sin^{-1}(2/5)[/tex]
Thus:
[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]
[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]
[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]
[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]
Picture below
mathematics
Answer:
false
Step-by-step explanation:
5/9 is .5 repeating
VWXY is a parallelogram. Find the measure of XY and WY
Answer:
WY = 30
XZ = 10.5
Step-by-step explanation:
Paralellogram's diagonal's bisect eachother
Therefore,
[tex]n + 7 = 3 n[/tex]
Move the n over,
2n = 7
Divide both sides by 2,
n = 3.5
WY = 2(ZY) because definition of bisector
Simplify...
WY = 2(4n+1)
WY = 2(4(3.5)+1)
WY = 2(15)
WY = 30
You asked for XY, but the question asks for XZ, so I'm going to give XZ.
With n = 3.5 from above,
XZ = 3n
XZ = 3(3.5)
XZ = 10.5
The measure of XY and WY are; WY = 30 and XZ = 10.5
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Since Paralellogram's diagonal's bisect each other
Therefore,
2n = 7
Divide both sides by 2;
n = 3.5
WY = 2(ZY)
because definition of bisector
Simplify;
WY = 2(4n+1)
WY = 2(4(3.5)+1)
WY = 2(15)
WY = 30
we asked for XY,
With n = 3.5 from above,
XZ = 3n
XZ = 3(3.5)
XZ = 10.5
The measure of XY and WY are; WY = 30 and XZ = 10.5
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For the triangles shown, which detail would have to be given to prove them congruent by the Angle Angle Side congruence criteria?
Answer:
The measure of the angle labeled d
Step-by-step explanation:
I took the quick check for "angle angle side postulate"
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of milligrams and standard deviation of milligrams for a sample of cigarettes. Construct a % confidence interval for the mean nicotine content of this brand of cigarette.
Answer:.
Step-by-step explanation:.
Which of the following letters have perpendicular line segments.
A E F H MNV X Z
Answer:
I think it's E, F, H
Step-by-step explanation:
Hope you got it.
Merry Christmas...
I need help plssssss.....
Y=log base(rootx) x find dy/dx
Given:
[tex]y=\log_{\sqrt{x}}x[/tex]
To find:
The value of [tex]\dfrac{dy}{dx}[/tex].
Solution:
We have,
[tex]y=\log_{\sqrt{x}}x[/tex]
It can be written as
[tex]y=\log_{\sqrt{x}}(\sqrt{x})^2[/tex]
Using property of log, we get
[tex]y=2[/tex] [tex][\because \log_aa^x=x][/tex]
Now, differentiate both sides with respect to x.
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(2)[/tex]
[tex]\dfrac{dy}{dx}=0[/tex] [tex][\because \dfrac{d}{dx}(Constant)=0][/tex]
Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is 0.
Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).
a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?
b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.
c. Please state whether the following statement is always true, and give a brief explanation. If c=c, the newsvendor solution is the mean.
Complete Question
Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).
a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?
b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.
c. Please state whether the following statement is always true, and give a brief explanation. If [tex]C_o =C_i[/tex], the news vendor solution is the mean.
Answer:
a
[tex]N = 46728[/tex]
b
[tex]n = 47728[/tex]
c
Yes it is always true
Step-by-step explanation:
From the question we are told that
The regular price of the jersey is [tex]P_r = \$ 80[/tex]
The cost of producing a jersey is [tex]C= \$ 40[/tex]
The left-over price of the jersey is [tex]P_o = $ 30[/tex]
The mean is [tex]\mu = 40000[/tex]
The standard deviation is [tex]\sigma = 8000[/tex]
The cost of lost customer goodwill is [tex]C_g = \$ 10[/tex]
Generally the fund that LCF will loss for one jersey if they order for too many jersey (i.e more than they need )is mathematically represented
[tex]C_o = P_o - C[/tex]
=> [tex]C_o = 40 - 30[/tex]
=> [tex]C_o = \$ 10[/tex]
Generally the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented
[tex]C_i = P_r - C[/tex]
=> [tex]C_i = 80 - 40[/tex]
=> [tex]C_i = \$ 40[/tex]
Generally the critical ratio is mathematically represented as
[tex]Z = \frac{C_i }{ C_i + C_o}[/tex]
=> [tex]Z = \frac{40}{ 40 + 10}[/tex]
=> [tex]Z = 0.8[/tex]
Generally the critical value of [tex]Z = 0.8[/tex] to the right of the normal curve is
[tex]z = 0.841[/tex]
Generally the optimal quantity of jersey to order is mathematically represented as
[tex]N = \mu * [z * \sigma][/tex]
=> [tex]N = 40000 * [0.841 * 8000][/tex]
=> [tex]N = 46728[/tex]
Considering question b
Generally considering the factor of customer goodwill the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented as
[tex]C_k = C_i + C_g[/tex]
=> [tex]C_k = 40 + 10[/tex]
=> [tex]C_k = \$ 50[/tex]
Now the critical ratio is mathematically represented as
[tex]Z = \frac{C_k }{ C_k + C_o}[/tex]
=> [tex]Z = \frac{50}{ 50 + 10}[/tex]
=> [tex]Z = 0.833[/tex]
Generally the critical value of [tex]Z = 0.833[/tex] to the right of the normal curve is
[tex]z = 0.966[/tex]
Generally the optimal quantity of jersey to order is mathematically represented as
[tex]n = \mu * [z * \sigma][/tex]
=> [tex]n = 40000 * [0.966 * 8000][/tex]
=> [tex]n = 47728[/tex]
Considering question c
When [tex]C_o =C_i[/tex] then
The critical ratio is mathematically represented as
[tex]Z = \frac{C_k }{ C_k + C_k}[/tex]
=> [tex]Z = \frac{1}{ 2}[/tex]
=> [tex]Z = 0.5[/tex]
Generally the critical value of [tex]Z = 0.5[/tex] to the right of the normal curve is
[tex]z = 0[/tex]
So
The optimal quantity of jersey to order is mathematically represented as
[tex]n = \mu * [z * \sigma][/tex]
=> [tex]n = 40000 * [0* 8000][/tex]
=> [tex]n = 40000 = \mu[/tex]
Hence the statement in c is true
subtract 3 from 4 times m
Answer:
-1
Step-by-step explanation:
not sure if the equation is 3-4m or 3-4 but it's -1 if the equation is 3-4
in eleven years ted will be 22 years old how old is he now?
Answer:
11
Step-by-step explanation:
22-11=11
HELPP PLEASE ILL NAME YOU BRAINLIEST!!!
can u pls help me with this question asap
Answer:
$13.50
Step-by-step explanation:
5 bags is 22.50 so 22.50/5 = 4.50 for 1 bag. Multiply that by 3 for 3 bags and get $13.50
Each patron pays an annual fee of $36 to the library at the library collects $20,304 for an annual fee how many patrons are there
slove for x
(6x+4)+81+41
how can you isolate the varible f
Answer:
Step-by-step explanation:
The basic technique to isolate a variable is to “do something to both sides” of the equation, such as add, subtract, multiply, or divide both sides of the equation by the same number. By repeating this process, we can get the variable isolated on one side of the equation.
Which operation is NOT closed for polynomials?
es )
A)
add a trinomial to a trinomial
B)
divide a binomial by a trinomial
multiply a binomial by a binomial
D)
subtract a binomial from a trinomial
Answer:
B)
divide a binomial by a trinomial
Step-by-step explanation:
As we know that the polynomials are very closed to the addition, subtraction and the multiplication but the same cannot be happen under the division as the division of two polynomials could not become a polynomial it is not necessary
Now if we divide the binomial from a trinomial so it would give a rational expression and contain a negative exponent and negative exponent is not allowed under the same
Therefore the option B is correct
-4(x+6)-2(-3x-9) simplify
Answer:
-4x-24+6x+18
Step-by-step explanation:
use distributive property to simplify -1(4+x)=6
Answer:
[tex]\huge\boxed{\boxed{x=-10}}[/tex]
Step-by-step explanation:
Hello.
The Distributive Property states that
a(b+c)=ab+ac
Simplify:
-1(4+x)=6
-4-x=6
Add 4 to both sides:
-4+4-x=6+4
-x=10
Divide both sides by -1 in order to get rid of the minus sign:
x=-10
And we're done!
I hope it helps & have an outstanding day!
~ST2710 :)
Complete the statement with the appropriate symbol.
1.42 _____ 1.420
=
>
Answer:
=
Step-by-step explanation:
After the decimal point if the zeros are on the right side they do not have any value.
Answer: = because 0 has no value
Complete the statement with the appropriate symbol.
1.42 ___=__ 1.420
>
<
=
Step-by-step explanation: = because the 0 has no value.
A pound of sweet potatoes costs $1.81 at Walmart. Shelly buys 14.6 pounds to make a sweet potato pie. How much money
will she spend at Walmart?
Answer:
$26.43
Step-by-step explanation:
A pound = $1.81. Multiply the price per pound by however many pounds Shelly is buying.
Answer:
26.426
Step-by-step explanation:
1.81x14.6=26.426
Solve: 2x + 3x? - 11x-6=0
Answer:
To solve the following equation we must first combine like terms Recognize the easiest way to manipulate the equation Lastly rearrange to isolate for x: usually done with division2x+3x-11x-6=0
Combine like x variables
-6x-6=0
Add 6 to the right side
-6x = 6
Divide by -6
x=-1
Rate positively and give brainlist
Answer:
x = - 1
Step-by-step explanation:
2x + 3x - 11x - 6 = 0
-6x = 6
x = - 1
LOOK AT PICTURE, THEN ANWSER, WHOEVER IS CORRECT I WILL MARK BRAINIEST:)
Answer:
C
Step-by-step explanation:
It has to be either A or C because the function is decreasing as you move left to right, this only occurs when the number inside parenthesis is less than 1.
It isn't A because if you plug in x=0, the value is 2, but on the graph it is greater than 2.
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What is the difference between Susan’s and Jim’s lawn-care businesses in the amounts they charge for 10 hours of work?
Answer:
Let's assume that Susan's graph is linear. Then, we can do linear interpolation. Let y be the amount charged for 10 hours of work done:
(7-10)/(7-11) = (168-y)/(168-264)
y = $240
For Jim's Lawn care, let's find the constant slope using points (1,20) and (2,40):
m = (20 - 40)/(1-2) = 20
Then, since the y-intercept is zero, the linear equation is:
y = 20x
Substituting x = 10 hours,
y = 20(10) = $200
The difference between the two would then be:
Difference = $240 - $200 = $40
What is the elevation of the deck where Winston ate dinner?
plz helppp
Question:
What is the elevation of the deck where Winston ate dinner?
Answer:
The surf shop was higher and the distance would be 12.8 feet above the oceans surface.
12.8
Step-by-step explanation:
Please Help thank you I appreciate it
Answer:
48in sq
Step-by-step explanation:
8*12/2=8*6=48
Answer:
48in
Step-by-step explanation:
A triangle like this is like half of a rectangle. The rest fits in the upper left and right. So to find the area of the triangle, we're going to start be pretending it's a recrangle.
Our rectangle is 12 by 8.
12 x 8 = 96
If this were a rectangle, the area would be 96in.
Since it's a triangle and that's only half of a rectangle, the area is half of that.
96 / 2 = 48
The area of this triangle is 48in.
What is the length of x?
Answer:
The length of 'x' is 4
Step-by-step explanation:
We can use the pythagorean theorem to solve this.
The pythagorean theorem is:
[tex]a ^{2} + b^{2} = {c}^{2} [/tex]
[tex]a ^{2} + b^{2} = c^{2} \\ {3}^{2} + {b}^{2} = 5^{2} \\ 9 + {b}^{2} = 25 \\ \frac{ - 9 \: \: \: \: \: \: \: \: = - 9}{b ^{2} = \sqrt{16} } \\ b = 4[/tex]
Therefore x = 4
Anyone know this answer?
the answer is =10
10
10
10
Macy wants to sell her old Playstation 4 games on decluttr.com. The wtbsite charges sellers a comission of 20%
for items sold on their website. If Macy sells a Playstation 4 game on the website for $35.00. How much willshe
actually receive?
Answer:
$28
Step-by-step explanation:
The website charges 20%, so Macy receives 80%.
Then:
80% x 35=.8 x 35=28 ....................