Answer:
a) dA/dt = 125,42 mm/min
b) dh/dt = - 1,78 mm/min
Step-by-step explanation:
The volume of the cylinder is:
V(c) = π*r²*h ( r and h radius of the base and heigh respectively )
Then the surface area is: Area of the base : π*r²
Plus lateral area : h*2*π*r
A(c) = π*r² + 2*π*r*h
With the help of differentials we obtain:
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt (1)
In this equation and at time t we know:
r = 18 mm dr/dt = 2 mm/min h = 8 mm dh/dt = ??
dA/dt = increasing rate of the surface area ( with respect to time)
To find dh/dt we know:
V(c) is constant, then
V(c) = π*r²*h then h = V(c) / π*r²
dh/dt = - [V(c)*2*π*r*dr/dt ] / π²*r⁴
By subtitution of V(c)
dh/dt = - [ π*r²*h *2*π*r*dr/dt ] / π²*r⁴
dh/dt = - [2*π²h*r³*dr/dt ] /π²*r⁴
dh/dt = - [2*h* dr/dt ] / r
dh/dt = - 2*8*2 / 18 mm/min
dh/dt = - 1,78 mm/min
By subtitution in equation (1)
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt
dA/dt = 2*π*18*2 + 2*π*8*2 + (- 2*π*18*1,78 )
dA/dt = 226,20 + 100,53 - 201,31
dA/dt = 125,42 mm/min
Following are solutions to the given points:
Formula:
Cylinder volume [tex]v = \pi r^2 h...............(i)[/tex]
[tex]\to \frac{dr}{dt} = 2 \frac{mm}{min}\\\\ \to \frac{dh}{dt} = -2 \frac{mm}{min}\\\\ \to h=8\\\\ \to r=18 \\\\[/tex]
Part A:
Calculating the circular area of the surface:
[tex]\to A=\pi r^2\\\\[/tex]
So, [tex]\frac{dA}{dt}=2 \pi r \frac{dr}{dt}.........(ii)[/tex]
Therefore
[tex]\to \frac{dA}{dt}= 2\pi \times 18 \times 2= 72 \pi \ \frac{mm^2}{min}\\\\[/tex]
Part B:
[tex]\to \frac{dh}{dt}= - 2 \frac{mm}{min}[/tex]
Learn more:
brainly.com/question/19667963
et.
n
4. Elena's account balance with her parents is
-$5.50. She adds a certain amount of
money to her balance by mowing the lawn.
Elena now has an account balance less than
$20. Determine a possible amount she
earned mowing the lawn. Then interpret the
solution. (Example 1) moll end to bi
Answer:
-$5.50>x>$20
Elena has more than -$5.50 but less than $20.
Step-by-step explanation:
Ok, so the question says that Elena has -$5.50 in her account. That means that she owes someone ( the bank) $5.50.
Elena then mows the lawn which may have paid off her debt. But we don't know that for sure.
All they give us is that Elena has less than $20 in her bank account.
So your answer may look like this:
-$5.50>x>$20
Elena has more than -$5.50 but less than $20.
Elena earned, amount more than -$5.50 and less than $20 by mowing the lawn.
What is Inequality?If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.
For example, x>3 (x should be greater than 3)
Given,
Account balance of Elena with her parents = -$5.50.
Which means she is in debt of $5.50.
Elena then adds a certain amount of money to her balance by mowing the lawn,
which may have paid off her debt, that is not sure.
But,
Account balance of Elena after mowing the lawn is more than - $5.50 less than $20.
Let the money Elena earned by Elena earned mowing the lawn = x
Then,
Possible amount she earned mowing the lawn = -$5.50 < x <$20.
Hence, Possible amount Elena earned mowing the lawn is
between -$5.50 and $20 = -$5.50 < x < 20.
Learn more about inequality here:
https://brainly.com/question/28823603
#SPJ2
To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail.
(a) What percent of values must be chopped off from each tail for a 95% confidence interval?
(b) If the bootstrap distribution contains values for 1000 bootstrap samples, how many should be chopped off at each end to produce a 95% confidence interval?
Answer:
a
[tex]\frac{\alpha }{2} = 2.5 \%[/tex]
b
[tex]N = 25[/tex]
Step-by-step explanation:
From the question we are told that
The number of bootstrap samples is n = 1000
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally the percentage of values that must be chopped off from each tail for a 95% confidence interval is mathematically evaluated as
[tex]\frac{\alpha }{2} = \frac{0.05}{2} = 0.025 = 2.5 \%[/tex]
=> [tex]\frac{\alpha }{2} = 2.5 \%[/tex]
Generally the number of the bootstrap sample that must be chopped off to produce a 95% confidence interval is
[tex]N = 1000 * \frac{\alpha }{2}[/tex]
=> [tex]N = 1000 * 0.025[/tex]
=> [tex]N = 25[/tex]
Answer:
Step-by-step explanation:
Hey
−4/3r=−7
what is the (r)?
Answer:
r = 21/3 ( Assuming the question is (-4/3) * r = 7)
Step-by-step explanation:
please solve 2x^2 -4x - 48 = 0
Answer:
-4, 6
Step-by-step explanation:
[tex]2x^2 -4x - 48 = 0 \\ \\ 2( {x}^{2} - 2x - 24) = 0 \\ \\ {x}^{2} - 2x - 24 = 0 \\ \\ {x}^{2} - 6x + 4x - 24 = 0 \\ \\ x(x - 6) + 4(x - 6) = 0 \\ \\ (x - 6)(x + 4) = 0 \\ \\ x - 6 = 0 \: \: or \: x + 4 = 0 \\ \\ x = 6 \: \:o r \: \: x = - 4 \\ \\ x = - 4, \: \: 6[/tex]
In his bank account, Jean-Paul has a balance of $0.00
His friend Albert has a bank balance of -$11.10
Which friend's bank account has more debt?
Choose 1 answer:
A. Jean-Paul
B. Albert
Which friend's bank balance has a greater absolute value?
Choose 1 answer:
A. Jean-Paul
B. Albert
A class of 25 students includes 12 boys. Does the ratio of
girls to students represent a fraction? Does the ratio of
boys to girls represent a fraction? How do you know?
Answer- The ratio of girls to students represents a fraction because it is a part- to-whole comparison. The ratio of boys to girl is not a fraction because it is part-to-part.
Answer:
Step-by-step explanation:
Sample Response: The ratio of girls to students represents a fraction because it is a part-to-whole comparison. The ratio of boys to girls is not a fraction because it is a part-to-part comparison.
Identify the solutions (roots) of the function y=x2 + 2x - 3
please help
Answer:
x=1,-3
Step-by-step explanation:
50 cm = .... m a. 50 x 106 m b. 50 x 10-3 m c. 50 x 101 m d. 50 x 10-2 m
9514 1404 393
Answer:
d. 50 x 10^-2 m
Step-by-step explanation:
"c" is the SI prefix for "centi-" meaning one hundredth, or 10^-2. Then ...
50 cm = 50×10^-2 m
Consider the following patter: -18, X, -10, -6, -2
The value of x in this pattern is
Answer:
-14
Step-by-step explanation:
(-6)-(-2)= -4
(-10)-(-6)= -4
therefore there is a 4 number Gap between them:
(-10) + (-4) = -14
E
Question 5/8
> NEXT
5
Cherie accepted a job through an employment agency. The job pays $1,100 weekly. The
agency charges 22% of her first three months, pay. How much money will the
employment agency receive for placing Cherie in her new job? (Round to the nearest
dollar.)
Answer: $2,904
1,100x4 than multiply by .22 then with that you multiply by 3.
$726 money will the employment agency receive for placing Cherie in her new job.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Cherie accepted a job through an employment agency
The job pays $1,100 weekly.
The agency charges 22% of her first three months, pay.
22% of 1100 we have to calculate.
First we have to convert 22% to decimal
22/100=0.22
0.22×1100=242
Now for three months we need to calculate.
3×242
$726
Hence, $726 money will the employment agency receive for placing Cherie in her new job.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ2
In ABC, if mA is six less than 7 times x, mB is five less than three times x, and mC is five less than four times x, find x and the measure of each angle
Answer:
a=92 b=37 c=51
Step-by-step explanation:
a= 7x-6
b=3x-5
c=4x-5
7x-6+3x-5+4x-5=180
14x-16=180
14x=196
x=14
True or false:triangle angle some theorem is when all of them interior (inside)angles of a triangle add up to 180°?
Answer:
true
Step-by-step explanation:
The sum of interior angles is 180 degrees (Triangle Angle Sum Theorem). All interior angles of a triangle are more than 0° but less than 180°. The bisectors of all the three interior angles intersect inside a triangle at a point called the in-center, which is the center of the in-circle of the triangle.
There are 211 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 48 fans?
name the property shown by each statement: d x e x 0 = 0
Answer:
Commutative Property of Multiplication. Associative Property of Multiplication.
Step-by-step explanation:
37st term: 9, 3, -3, -9, -15
Answer:
Step-by-step explanation:
The first term (a) = 9
the 37th term is what we want (n = 37)
d = - 6
t_37 = 9 + (n - 1) * (-6)
t_37 = 9 + 36 * - 6
t_37 = 9 - 216
t_37 = - 207
i need help on this one
Answer:
Is g(x)
Step-by-step explanation:
We search the roots of the function on this way
(x-1)^2 (x+2) =0
(x-1)^2 =0
x-1=[tex]\sqrt{0}[/tex]
x=1 ////
(x+2)=0
x=-2 ////
So (1,0) and (-2,0) are the roots of the function (as the image)
Someone help plzzzzz
Answer:
for the first box the answer is 4x but I dont know the y intercept
Step-by-step explanation:
get 2 points the do y2-y1/x2-x1 then you get your x
If using the method of completing the square to solve the quadratic equation
x2 – 9x + 38 0, which number would have to be added to "complete the
square"?
=
Answer:
81/4
Step-by-step explanation:
Given the equation x^2 – 9x + 38 = 0
Subtract 38 from both sides
x^2 – 9x + 38 - 38= 0 - 38
x^2 - 9x = -38
Next is to complete the square, to do this we will add the square of the half of coefficient of x to both sides as shown;
Coefficient of x is - 9
Half of -9 will be (-9/2)
Squaring the result will give (-9/2)² = 81/4
Hence the number that would have to be added to "complete the
square" is 81/4 to have;
x^2 - 9x + 81/4= -38 + 81/4
(x-9/2)² = -38 + 81/4
Hence the required value is 81/4
PLS HELP IM IN THE MIDDLE OF A TEST PLSSSSSSSSSSSSSSSSSS AND GIVE ME THE RIGHT ANSWER PLSSSSSSS.
WILL GIVE BRAINLEST What expression can be used to determine the total cost of buying c pounds of cashews for $ 2.95 per pound and s pounds of sugar for $0.72 per pound? Choose the correct expression for determining the total cost.
2.95c -0.75s
3.67-(c+s)
2.95 + 0.72s
0.72 + 2.95s
Answer:
1pound of granola= $3.25
g pound of granola=g*3.25
=3.25g$
1 pound of flour = 0.74$
f pound of flour = f*0.74
= 0.74f$
The expression to determine the total cost of buying the above items= (3.25g+0.74f)
Step-by-step explanation:
Simplify. 23+4⋅8
A. 40
B. 80
C. 96
D. 160
Answer:
A i guess
Step-by-step explanation:
23 + 4 ⋅ 8
I got the answer 55 so see what is close to 55
Answer:
2 ^ 3 + 4 * 8 = 40
Step-by-step explanation:
So going by the order of operations, PEMDAS,
There are not parenthesis so we can skip that part.
exponents on the other hand we have 2^3. Don't be fooled. It's not 2 * 3. What you have to do is multiply 2 by itself 3 times. So 2 * 2 * 2 = 8. Step one Done!
The M in PEMDAS is multiplication! So we solve that part next! 4 * 8 = 32. Step 2 Done!
Now for the final step, for A in PEMDAS you have to add both sums together. 8 + 32 = 40
Final answer: 40
I hope this helps! <3
alice started at the origin and moved to the left and then down to plot a point. which quadrant and which possible point did alice plot at?
Answer:
OK
Step-by-step explanation:
LOL SO WHAT I . DID
IS ik the qudrents and just ask siri maybe she will help but i got qudrent 3
Select the correct answer.
Which inequality represents all the solutions of -2(3x+6) = 4(x +7)
Bouncing Baby Company sells their cribs for the following amounts to stores
Number of Cnbs
10
Price
$1320
50
S6600
Which of the following statements about the price of the cribs are true if the price remains proportional to the number of cribs Select TWO that apply.
A. 6 cribs cost $600
B. 22 anos cost $2640
C. 40 cribs cost $5280
D. 55 cribs cost $7920
E. 80 cribs cost $10.500
F. 250 cribs cost $11 880
Answer:
Option C
Step-by-step explanation:
Since, Price of cribs (P) are proportional to the proportional to the number of cribs (N) sold,
P ∝ N
P = kN
Here 'k' is the proportionality constant
To get the value of proportionality constant,
Since, value of 10 cribs is $1320
1320 = k(10)
k = 132
Therefore, equation will be
P = 132N
Option A
If number of cribs = 6
P = 132(6) = $792
False.
Option B
For N = 22
P = 132(22) = $2904
False.
Option C
For N = 40
P = 132(40) = $5280
True
Option D
For N = 55
P = 132(55) = $7260
False
Option E
For N = 80
P = 132(80)
= $10560
False
Option F
For N = 250
P = 132(250)
= $33000
False
If the given options have been written correctly only one option, Option (C) is correct.
Which formula do we use to reflect over the y=x line
(x, y) → (y,x)
(x, y) → (-y, -x)
(x, y) = (-x, y)
(x, y) = (x, -y)
Answer:
the first one on the list because it said refect
The probability distribution below shows the number of kittens in a litter, Find the probability that a cat will have at most 4 kittens * 7 points
The probability that a cat will have at most 4 kittens is to be considered as the 0.83.
Calculation of the probability;= Probability of 2 + Probability of 3 + Probability of 4
= 0.20 + 0.35 + 0.28
= 0.83
Hence, The probability that a cat will have at most 4 kittens is to be considered as the 0.83.
Learn more about probability here: https://brainly.com/question/3066522
The probability that a cat will have at most 4 kittens is 0.83
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the number of kittens in the litter be = A
Now , when A = 2
The probability distribution is = 0.20
Now , when A = 3
The probability distribution is = 0.35
Now , when A = 4
The probability distribution is = 0.28
Now , when A = 5
The probability distribution is = 0.15
And , the probability that a cat will have at most 4 kittens is calculated by
P ( x ≤ 4 ) = P ( 2 ) + P ( 3 ) + P ( 4 )
= 0.20 + 0.35 + 0.28
= 0.83
Therefore , the probability that a cat will have at most 4 kittens is 0.83
Hence , The probability that a cat will have at most 4 kittens is 0.83
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ2
Can someone help with this please?
Answer:
a) Function 1 has the greatest y-intercept
b) Only function 2 has a slope less than -2
c) Function 4 has the least steep slope
Answer:
1. Function 1
2. Function 2
3. Function 4
Step-by-step explanation:
y-intercept: Function 1: 4, Function 2: 1, Function 3: -5, Function 4: -2
- Function 1 has the highest y-intercept
slope less than -2: Function 1: 2, Function 2: -4, Function 3: 5, Function 4: -1
- Function 2 has a slope lower than -2
least steep graph: Function 1: steepness 2, Function 2: steepness 4, Function 3: steepness 5, Function 4: steepness 1
- Function 4 has the steepest graph
The sum of two numbers is
60
and the difference is
10
. What are the numbers?
Answer:
35 and 25.
Step-by-step explanation:
x+y=60
x-y=10
Subtract eq1 by eq2
x-x+y-(-y) = 60-10
2y=50
y=25.
x+25=60
x=35
Hope this helps :D
#Team Rainbows
Lucy cuts 5 different pieces of fabric throughout the day .
1.125 M 475CM 245CM 5.875M 3.055M
What is the total amount of fabric she cut ?
(. )M
Answer: 1 625.5cm or 16.255m
Step-by-step explanation:
convert all m measurements into cm by multiplying, add all the cm measurements together. this equation is 12.5cm+ 475cm+ 245cm+ 587.5cm+ 305.5cm= 1625.5cm.
convert the cm measurements back to m measurements (i only assume because you said . m at the end)
The total amount of fabric she cut is 17.255 m .
The total length of the fabric can be determined by adding the length of the different pieces. Addition is determining the total value or summing two or more numbers.
In order to add the different lengths, the lengths have to be in meters.
100cm - 1 meter
475cm = 475 / 100 = 4.75m
245cm = 245 / 100 = 2.45m
Now that all the lengths are in the same units, they can now be added together; 1.125 + 5.875 + 3.055 + 4.75 + 2.45 = 17.255 m
To learn more about addition, please check: https://brainly.com/question/349488
What is the measure of angle 7?