Complete question is;
A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?
Answer:
Diameter is decreasing at the rate of 5/(2πr) cm/hr
Step-by-step explanation:
We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;
dV/dt = -50 cm/hr
Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;
V = πr²h
dV/dr = 2πrh
Now,to find the rate at which the diameter is decreasing, we'll write;
dr/dt = (dV/dt)/(dV/dr)
dr/dt = -50/(2πrh)
We are given;
Diameter = 200 cm
Radius; r = 200/2 = 100 cm
Thickness; h = 10 cm
Thus;
dr/dt = -50/(2π × r × 10)
dr/dt = -5/(2πr) cm/hr
The rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex] and this can be determined by using the given data.
Given :
A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 [tex]\rm cm^3/hr[/tex].
The following steps can be used in order to determine the rate at which grindstone diameter decreases:
Step 1 - According to the given data, the rate at which grindstone volume decreases is:
[tex]\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}[/tex] --- (1)
Step 2 - The formula of the volume of the cylinder (grindstone) is given below:
[tex]V = \pi r^2 h[/tex]
Step 3 - Differentiate the above expression with respect to 'r'.
[tex]\dfrac{dV}{dr} = 2\pi r h[/tex] --- (2)
Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:
[tex]\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}[/tex]
[tex]\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\[/tex]
[tex]\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}[/tex]
So, the rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/12748872
A. 2,−4, 6,−8
B. −1/3, −1/6, 1/2, 1
C. −11/0, 0.2, 3/10, 1/4
D. −11/2,−0.75,−0.25, 1/12
E. −8,−34,−3, 1/4
Please tell me all of the answers that are correctly in order from least to greatest.
Answer:
The answer is D
Step-by-step explanation:
Cant be C because one of them is undefined.
Cant be A because 2 is greater than -4
can't be B because -1/3 is closer to 0 than -1/6
can't be E because -8 is closer to 0 than -34
D is all in order.
Answer:
d
Step-by-step explanation:
because I'm tired and tried trying to dosn hem
Find the sequence whose nth term is 4n + 5 also prove that the sequence is an AP
-2/3x^2-1=17 can y'all help me please !!!
The answer is ±3[tex]\sqrt{3\\}[/tex]
First, you should make one side of the quadratic 0. You can do this by subtracting 17 from both sides, making the equation
2/3x^2 - 18 = 0
To make everything an integer, you can multiply both sides by 3/2, making the equation
x^2 - 27 = 0
By adding 27 to both sides, you get
x^2 = 27
Now you are practically done! By taking the square root of both sides, you get
x = ±3[tex]\sqrt{3\\}[/tex]
Walking100
a) How many students ride in a tricycle, motorcycle and car going to their school
b) How many students ride in both a motorcycle and a tricycle?
c) How many students ride in both a motorcycle and a car?
d) How many students ride in both a car and tricycle?
e.)How many students go to school
in a car only;
in a motorcycle only;
30
Complete question :
The Venn diagram relating to the question can be found in the picture attached below :
Answer:
A.) 15 ; b.) 17 ; c.) 20 ; d.) 19 ; e.) 55 ; 67; 76 ;100 ; F.) 369
Step-by-step explanation:
Let :
Cars = C ; Motorcycle = M ; Tricycle = T ; Walking = W
a) How many students ride in a tricycle, motorcycle and car going to their school
Intersection of the 3 modes;
(C n M n T) = 15 ; it is the number which sits in between all the three circles.
B.) How many students ride in both a motorcycle and a tricycle?
(M n T) = 17 ; number in the middle of both circles representing motorcycle and tricycle
C.) How many students ride in both a motorcycle and a car?
(M n C) = 20 ; number in the middle of both circles representing motorcycle and Car
D) How many students ride in both a car and tricycle?
(C n T) = 19 ; number in the middle of both circles representing Car and tricycle
e.)How many students go to school
in a car only = 55
in a motorcycle only = 67
Tricycle only = 76
Walking = 100
F.) How many Grade Seven students of Koronadal National Comprehensive High School are there in all?
(100 + 67 + 76 + 55 + 19 + 20 + 17 + 15) = 369
polar decomposition of complex matrx
Answer:
hope it helps you
Step-by-step explanation:
The right polar decomposition of a matrix A ∈ Cm×n m ≥ n has the form A = UP where U ∈ Cm×n is a matrix with orthonormal columns and P ∈ Cn×n is positive semi-definite. Definition 2.2 (Left Polar Decomposition).
Question 4
1 pts
What is the midpoint of the segment containing the endpoints (-3.3) and
05.1:
Answer:
1, 2
Step-by-step explanation:
Given parameters;
Endpoints = (-3, 3) and (5, 1)
Unknown:
The midpoint of the segment = ?
Solution:
The midpoint between two endpoints is given as;
x[tex]_{m}[/tex], y[tex]_{m}[/tex] =( [tex]\frac{x_{1} + x_{2} }{2}[/tex] , [tex]\frac{y_{1} + y_{2} }{2}[/tex])
x and y are coordinates
x₁ = -3
x₂ = 5
y₁ = 3
y₂ = 1
x[tex]_{m}[/tex], y[tex]_{m}[/tex] = [tex]\frac{-3 + 5}{2}[/tex], [tex]\frac{3+ 1}{2}[/tex]
x[tex]_{m}[/tex], y[tex]_{m}[/tex] = 1, 2
Your family goes to dinner. The meal costs $55 for all of you. You pay 7% sales tax and leave a 9% tip. What is the total cost of the meal after tax and tip?
Answer:
8.80 dollars
Step-by-step explanation:
(2fg)7 simplify the expression
Answer:
14 f g
Step-by-step explanation:
Multiply 7 by 2 .
Ben solved a fraction division problem using the rule “multiply by the reciprocal.” Look at his work.
StartFraction 7 Over 20 EndFraction divided by two-fifths. StartFraction 20 Over 7 EndFraction times two-fifths = StartFraction 40 Over 35 EndFraction = StartFraction 8 Over 7 EndFraction = 1 and StartFraction 1 Over 7 EndFraction
Did he solve the problem correctly?
Yes. He solved the problem correctly.
No. He multiplied the dividend by the divisor.
No. He multiplied the denominators instead of finding a common denominator.
No. He multiplied with the reciprocal of the dividend instead of with the reciprocal of the divisor.
Answer:
(d) No. He multiplied with the reciprocal of the dividend instead of with the reciprocal of the divisor.
Step-by-step explanation:
The problem should have been written ...
[tex]\dfrac{7}{20}\div\dfrac{2}{5}=\dfrac{7}{20}\times\dfrac{5}{2}\qquad\text{the reciprocal of the divisor is used}[/tex]
Instead, Ben wrote it as ...
[tex]=\dfrac{20}{7}\times\dfrac{2}{5}\qquad\text{the reciprocal of the dividend is erroneously used}[/tex]
_____
Additional comment
Ben will get the reciprocal of the proper answer: 8/7 instead of the correct value of 7/8.
Answer:
D) No. He multiplied with the reciprocal of the dividend instead of with the reciprocal of the divisor.
Step-by-step explanation:
How many of the 20% acidic solution be added to create the needed 30% acidity in the final mixture
............................................................(18x-8) (4x+16)
Answer:
[tex](18x-8)(4x+16)=72x^2+256x-128[/tex]
That's really all you can do to that equation, I think.
Hope this helps!
Jan designs a new logo for Kim's website. Kim pays Jan $45 for 5 hours of work. How much will Kim pay Jan for 15 hours of work?
am not sure but i think its 135$
i divided 45 by 5 to get the pay per hour
then multipled 9 by 15 to get the answer
am not the best in maths so its better u get someone to check if before u submit.
Answer:
675
Step-by-step explanation:
$45✖15 hours=675
so you see what we did here is multiply the money amount by the hour .
HOPE IT HELPS :)PLEASE GIVE ME brilliant!!!pLeAse hurry i must finish right now
look at screenshot
please answer all of #2
Answer:
Sorry can't do this
Step-by-step explanation:
Answer:
uhhhhhhhhhhhhhhhhhhhhhhhhh 4
Step-by-step explanation:
1. The perimeter of a rectangular rug is 40 feet. The length is 4 feet less
than twice the width.
a. Find the length and the width of the rug
b. Find the area of the rug.
2. The sum of three numbers is 45. The second number is 8 less than the
first and the third number is 5more than twice the first. Find the three
numbers.
I need help with both questions please help.
Angela earns $11.50 per hour. If she works more than 40 hours a week she earns double time. This week she worked a total of 48 hours. How much was her total weekly paycheck?
Answer:
11.50 x 40 regular hours is $460
double time is 11.50 x 2 = $23 an hour
She makes $23 an hour for 8 hours = $184
$460 + $184 = $644 paycheck
Enter an equation in standard form to model the linear situation.
A barrel of oil was filled at a constant rate of 6.7 gal/min. The barrel had 12 gallons before filling began.
Answer:
jdfjafdsds
Step-by-step explanation:
The GCF of two numbers is equal to the lesser of the numbers? Always,sometimes, or never true
Answer:
Sometimes
Step-by-step explanation:
To answer this question, I'll make use of the following illustrations:
GCF of 4 and 10
[tex]4 = 1 * 2 * 2[/tex]
[tex]10 = 1 * 2 * 5[/tex]
Hence:
The GCF is
[tex]GCF = 1 * 2[/tex]
[tex]GCF = 2[/tex]
GCF of 5 and 10
[tex]5 = 1 * 5[/tex]
[tex]10 = 1 * 2 * 5[/tex]
[tex]GCF = 1 * 5[/tex]
[tex]GCF = 5[/tex]
In the first scenario, the GCF is lesser than the smallest number.
In the second, the GCF is equal to the smaller number.
Hence:
The option that completes the question is "sometimes"
Three assembly lines Alpha, Beta, and Gamma make the same power transistor. Each of the assembly lines has its own level of efficiency. Resulting in inventory having 20% of the transistors from Alpha, 50% from Beta, and the remaining 30% from Gamma. Further the probability a transistor from Alpha will be defective is 0.02, a transistor from Beta will be defective is 0.06, and a transistor from Gamma will be defective is 0.04. If a random transistor from inventory is defective, what is the probability it came from Bet
Answer:
P [ β / Def] = 0,6521 or 65,21 %
Step-by-step explanation:
Tree diagram:
0,20 (α) Defective 0,02
0,50 (β) defective 0,06
0,30 (γ) defective 0,04
According to Baye´s Theorem
P [ A/B] = P[A] * P [ B/A] / P[B]
if we call
β = A and Defective = B then P[β] = P[A] and P[Defective] = P[B]
we get :
P [ β / Def] = P[β] * P [ def./β] / P[def]
Then
P[β] = 0,5
P[def/β] = 0,06
P [Defective] = 0,02* 0,2 + 0,06*0,5 + 0,04*0,3
P [Defective] = 0,004 + 0,03 + 0,012
P [Defective] = 0,046
P [ β / Def] = 0,5 * 0,06 / 0,046
P [ β / Def] = 0,6521 or 65,21 %
Explain how to estimate the product of 12/3/8 times 6/7/8.
Answer:
210 approximately.
Step-by-step explanation:
12/3/8 = 12*8/3 = 32
6/7/8 = 6*8/7 = 48/7 = 7 approximately
So the product is approximately 30*7 = 210.
LaTeX: Create\:an\:equation\:in\:slope\:intercept\:form\:that\:is\:parallel\:to\:y\:=\frac{\:1}{3}x\:+\:4\:and\:goes\:through\:the\:point\:\left(-3,\:1\right).C r e a t e a n e q u a t i o n i n s l o p e i n t e r c e p t f o r m t h a t i s p a r a l l e l t o y = 1 3 x + 4 a n d g o e s t h r o u g h t h e p o i n t ( − 3 , 1 ) .
Group of answer choices
LaTeX: y=\frac{1}{3}x+2 y = 1 3 x + 2 y = 1 3 x + 2 y = 1 3 x + 2
LaTeX: y\:=\:-3x\:+\:4 y = − 3 x + 4 y = − 3 x + 4 y = − 3 x + 4
LaTeX: y=\frac{1}{3}x y = 1 3 x y = 1 3 x y = 1 3 x
LaTeX: y=-3x-8
Answer:
[tex]y = \frac{1}{3}x +2[/tex]
Step-by-step explanation:
Given
Equation:
[tex]y = \frac{1}{3}x + 4[/tex]
[tex]Point: (-3,1)[/tex]
Required
Determine the equation of the point parallel to the given equation
First, we need to determine the slope of: [tex]y = \frac{1}{3}x + 4[/tex] using
[tex]y = mx + b[/tex]
Where m represents slope.
By comparison
[tex]m = \frac{1}{3}[/tex]
The equation of the point is calculated as thus:
[tex]y - y_1 = m(x - x_1)[/tex]
Where [tex](x_1,y_1) = (-3,1)[/tex]
So, we have:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 1 = \frac{1}{3}(x - (-3))[/tex]
[tex]y - 1 = \frac{1}{3}(x +3)[/tex]
[tex]y - 1 = \frac{1}{3}x +1[/tex]
Solve for y
[tex]y = \frac{1}{3}x +1 +1[/tex]
[tex]y = \frac{1}{3}x +2[/tex]
Pleas help I am brainliesting
Answer:
$2.22 i think
Step-by-step explanation:
Answer:
You would have $2.22 left.
Step-by-step explanation:
6.96 - (0.79 * 6)
6.96 - 4.74
2.22
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples. 30 + 5m; $36 30 + m; $36 30 + 5m; $24 30 + m; $24
Answer:
m + 30 ; $36
Step-by-step explanation:
Given that:
Total fruits needed = 15
Fruits needed :
Apple (m) ; cost = $3 per piece
Oranges (o) ; cost = $2 per piece
Amount spent on fruits :
[(cost of apple * number of apples) + (cost of orange *(total fruits - number of apples)]
3m + 2(15 - m)
3m + 30 - 2m
3m - 2m + 30
m + 30
Amount spent if 6 apples is purchased :
m = 6
m + 30
6 + 30 = $36
Kari is building a rectangular garden bed. The length is 6 feet. She has 20 feet of boards to make the sides. Write and solve an inequality to find the possible width of her garden bed.
Answer:
ahe using 12 feet of boards and threre 8 ft of board left so i guess the with will be 4.
Step-by-step explanation:
6+6 =12 for the lenghth
4+4=8= for the with
2y-5y=-10.
what are the x and y intercepts
Answer:
The y intercept is (0,2) and the x intercept is (5,0)
Step-by-step explanation:
Find the y-intercept by letting x = 0
2(0) + 5y = 10
5y = 10
y = 2 Therefore, the y-intercept is (0, 2)
Find the x-intercept by letting y = 0
2x + 5(0) = 10
2x = 10
x = 5 Therefore, the x-intercept is (5, 0)
Here is the graph!!
Denise is going to shop with the $250.00 that she earned from doing chores. She wants to save
20% of her money to put into a savings account. She buys a pair of jeans for $75.00 and a new
leather coat for $110.00, with 5% sales tax on both items. Does Denise still have the amount of
money she planned to put into her savings account?
Yes she does.
I just answered the question.
a) how would you work out 4 1/3 x 6?
The solution of the expression 4¹/₃ x 6 will be 26.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 4¹/₃ x 6. The expression of multiplication will be solved as below,
E = 4¹/₃ x 6
E = ( 13 / 3 0 x 6
E = 13 x 2
E = 26
Hence, the solution will be 26.
To know more about an expression follow
https://brainly.com/question/28773316
#SPJ2
PLEASE HELP I WILL GIVE BRAINLIEST!!!
Solve for x: 5x + 15 = 28 (5 points)
forty-three over five
thirteen over five
13
43
Answer:
x=3
or 13/5
Step-by-step explanation:
5x+15=28 (-15)
5x=13 (/5)
x=3
The cost of parking a motor home in a state park includes a one time fee of $180, plus a daily rate of $55 per day. Anthony prepaid for his stay and paid the state park commission a fee of $565. This paid for the one time fee as well as for a number of days. How many days of parking did Anthony pay for? Group of answer choices
Answer:
Anthony paid for 7 days of parking.
Step-by-step explanation:
From the information given, the cost of parking a motor home in a state park would be equal to the one time fee plus the result of multiplying the daily rate for the number of days:
c=180+55x, where c is the cost of parking the motor home and x is the number of days.
Now, you can replace c with 565 that is the amount Anthony prepaid and you can solve for x to be able to find the number of days he paid for:
565=180+55x
565-180=55x
385=55x
x=385/55
x=7
According to this, Anthony paid for 7 days of parking.
i need help with this equation: p+9=-1
Answer:
p = - 10
Step-by-step explanation:
Step 1:
p + 9 = - 1 Equation
Step 2:
p = - 1 - 9 Subtract 9 on both sides
Answer:
p = - 10
Hope This Helps :)
PLEASE HELP ME
My teacher is really bad at explaining this so I'm confused
