Assuming the region is of uniform density, compute the mass of the region and its moments.
If n > m, then in the interval [0, 1] we have f(x) ≤ g(x). This means the mass is
[tex]M=\displaystyle\int_0^1(g(x)-f(x))\,\mathrm dx=\left(\frac{x^{m+1}}{m+1}-\frac{x^{n+1}}{n+1}\right)\bigg|_0^1=\frac1{m+1}-\frac1{n+1}[/tex]
The moments are
[tex]M_x=\displaystyle\int_0^1\frac{g(x)^2-f(x)^2}2\,\mathrm dx=\frac12\left(\frac{x^{2m+1}}{2m+1}-\frac{x^{2n+1}}{2n+1}\right)\bigg|_0^1=\frac12\left(\frac1{2m+1}-\frac1{2n+1}\right)[/tex]
[tex]M_y=\displaystyle\int_0^1x(g(x)-f(x))\,\mathrm dx=\int_0^1(x^{m+1}-x^{n+1})\,\mathrm dx=\left(\frac{x^{m+2}}{m+2}-\frac{x^{n+2}}{n+2}\right)\bigg|_0^1=\frac1{m+2}-\frac1{n+2}[/tex]
Then the centroid is
[tex](\overline x,\overline y)=\left(\dfrac{M_y}M,\dfrac{M_x}M\right)=\boxed{\left(\dfrac{(m+1)(n+1)}{(m+2)(n+2)},\dfrac{(m+1)(n+1)}{(2m+1)(2n+1)}\right)}[/tex]
Answer and I will give you brainiliest
Answer:
x = 60 degree
Step-by-step explanation:
90 + 90 + 2x - 10 + 2x + 2x + 10 = 540 degree (sum of 5 interior angles)
180 + 6x = 540
6x = 540 - 180
x = 360/6
x = 60 degree
a triangular prism is 37 millimeters long and has a triangular face with a base of 42 millimeters and a height of 28 millimeters.The other two sides of the triangle are each 35 millimeters.What is the surface area of the triangular prism?
No links pls
Answer: 4145.43
Have a great day! ;)
If four pounds of potatoes cost $6.00, how much would 10 pounds of potatoes cost
Answer:
I think is 15 dollars.
Step-by-step explanation:
each pound cost 1.5 multiply it by 10
Answer:
$15
Step-by-step explanation:
4 pounds are $6
10pounds are $?
1 pound would be $1.5, because 6/4 = 3/2= 1.5
If one pound is 1.5 dollars, 10 pounds would be 10*1.5=$15
Consider the following function:
f(3) = log2(x + 3)
Which interval has the smallest average rate of change in the given function?
O (0,2
O 4,6]
O [2,4
O (6,8)
In the function f(x) = log2(x + 3)), the smallest average rate of change in the function is in the interval, (6,8)
What is a logarithmic function ?The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.
Formulae for logarithmic function are,
LogAB = LogA + LogB
Logₐaᵇ = b
Given that,
A logarithmic function,
f(x) = = log2(x + 3)
Rate of change = Change in values of function/change in x
= [F(b) - F(a)]/ b-a
For the interval, (0, 2)
f(0) = Log2(0 + 3) = Log(6)
f(2) = Log2(2 + 3) = Log(10)
Rate of change = Log(10) - Log(6) /2
= 0.11
Similarly, for the intervals, (4, 6), (2, 4), (6,8)
Hence, the smallest average rate is for the interval, (6, 8)
To know more about Logarithmic function check:
https://brainly.com/question/27389970
#SPJ1
Which one hurry
A.50
B.80
C.90
D.100
Answer:
I think its
im not sure
Step-by-step explanation:
What is the order of rotational symmetry of this shape .for brainlest
Answer:
4.
Step-by-step explanation:
The orientation of the shape is the same 4 times during 360 degree turn.
Answer:
4
Step-by-step explanation:
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
Which function has the same y-intercept as the function
Y=2/3x-3?
Answer: 6x - 7y = 21
Step-by-step explanation:
sorry if its wrong
Plzzz help I only have 20 minutes
Answer:
n+6+2n+3+90=180
3n+99=180
3n=81
n=27
33 plus 90+57=180
Answer:
the value of n is 27 degree
Step-by-step explanation:
n+6+2n+3+90=180 degree (being linear pair)
3n+9+90=180
3n=180-99
3n=81
n=81/3
n=27
A linear pair is a pair of adjacent angles formed when two lines intersect.
for which of the following equations (-4, -3 ) not a solution
A. 2y - 3x = 6
B. -3x = 4y
c. y = 1 + x
D. 5x + 2y = -26
what is the largest six-digit base five number? How do you know?
Answer:
999999.9>repeating
Step-by-step explanation:
.1 more and it will be 7 digits and not 6 Hope this helps :D
9514 1404 393
Answer:
444444₅ = 15624₁₀
Step-by-step explanation:
It will be 1 less than the smallest 7-digit base-5 number. That number is 5^6 = 15625, so the largest 6-digit base 5 number is 15624 in decimal. In base 5, it is 6 of the largest base-5 digits:
444444₅ = 15624₁₀
__
The digits of the number cannot be any larger than the largest base-5 digit. The base-5 digits are 0 to 4, so the largest is 4.
A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data:
16 11 12 10 0 12 8 4 1 0
13 0 2 4 2 6 17 11 10 14
8 3 10 7 1 13 4 7 1 13
5 5 12 2 16 13 9 9
Complete the frequency distribution for the data.
Hours Frequency Relative Frequency
0-2
3-5
6-8
9-11
12-14
15-17
Step-by-step explanation:
The complete frequency distribution table for the data has been attached to this response.
The frequency column contains values that are the number of times the given range of hours appear in the data. For example, numbers in the range 0 - 2 hours, appear 9 times in the data. Also, the numbers in the range 3 - 5 appear 6 times. The same logic applies to other ranges.
The relative frequency column contains the ratio of the number of times the given range of hours appear in the data, to the total number of outcomes. The total number of outcomes is the sum of all the frequencies on the frequency column. This gives 38 as shown.
So, for example, to get the relative for the numbers in the range 0-2, divide their frequency (9) by the total outcome or frequency (38). i.e
9 / 38 = 0.24
Also, to get the relative for the numbers in the range 3-5, divide their frequency (6) by the total outcome or frequency (38). i.e
6 / 38 = 0.16
Do the same for the other ranges.
PLS HELP ASAP!
Shown below is a cylinder. Calculate the volume using 3.14 for π
Answer:
V = 678.24 cm^3
Step-by-step explanation:
Formula for volume of a cylinder:
the radius is half of the diameter (12/2 = 6)
[tex]V = \pi r^{2} h\\V = \pi 6^{2} 6\\\\V = 678.24[/tex] cm^3
Answer:
678.24 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We know the diameter
r =d/2 = 12/2 = 6
V = 3.14 * 6^2 * 6
678.24 cm^3
Choose (two) statements (the original conditional statement and converse)
that could form the biconditional "An object measures 12 inches if and only if it is 1 foot long."
A. If an object is 1 foot long, then it measures 12 inches.
B. If an object does not measure 12 inches, then it is not 1 foot long.
C. An object is not 1 foot long if it does not measure 12 inches.
D. If an object measures 12 inches, then it is 1 foot long.
PLEASE HELP !!
Answer:
Ssss
Step-by-step explanation:
Kolyan buys water for $2.60. He also buys biscuits The ratio cost of biscuits: cost of water= 3:2 Find the cost of the biscuits.
Answer:
1.733
Step-by-step explanation:
Given ratio ,
=> 3:2
According to the Question ,
=> $ 2.60 / x = 3/2
=> x = $ 2.60 × 2/3
=> x = $ 1.733
Answer:
≈ $1.73
Step-by-step explanation:
[tex]\frac{2.6}{y} :\frac{3}{2}[/tex]
y × 3 = 2 × 2.6
3y = 5.2
3y ÷ 3 = 5.2 ÷ 3
[tex]y=1\frac{11}{15}[/tex]
y = 1.7333333333333
1.7333333333333 rounds to $1.73
A set of eight cards contains one joker. Player A chooses 5 cards at random,
Player B takes the remaining three cards. What is the probability that Player A has the joker?
Player A discards 4 cards and Player B discards two cards. It is known that the joker has not been discarded, what is the probability that Player A has the joker?
Answer:
56%
Step-by-step explanation:
because of the 56% it had to be true to be in the question at all.
Jane Peterson has taken Amtrak to travel from New York to Washington, DC, on six occasions, of which three times the train was late. Therefore, Jane tells her friends that the probability that this train will arrive on time is 0.50. Would you label this probability as empirical or classical? Why would this probability not be accurate?
Answer:
a) This probability as empirical Probability.
b) This probability is not accurate because this experiment must be repeated a large number of times for empirical probabilities should be accurate.
Step-by-step explanation:
On 6 occasions, of which three times the train was late. that means 3 times the train is on time.
Empirical probability = Number of outcomes satisfying event / No.of trails
= 3/6 = 0.5.
a) This probability as empirical Probability.
b) This probability is not accurate because this experiment should be repeated a large number of times for empirical probabilities should be accurate.
(5 QUESTION 4 If 1 foot = 0.37 metres and 1 mile - 5.180 feet. Find the number of kilometres in 15 miles.
Answer:
there are 24.14 kilometers in 15 miles
I need to solve for X Y and Z please and thank you
9514 1404 393
Answer:
x = 5y = 30z = 8Step-by-step explanation:
The rhombus has several relevant properties.
The sides are all the same lengthDiagonals are perpendicular bisectors of each otherDiagonals divide the rhombus into congruent trianglesThe last of these relations can be used to find x:
7x° = 35°
x = 35°/7° = 5
The second of the relations can be used to find y:
3y° = 90°
y = 90°/3° = 30
The first of the relations can be used to find z:
10z -8 = 5z +32
5z = 40 . . . . . . . . . add 8-5z
z = 40/5 = 8
Please help me please ! Quick
Answer:
4,2 is tge answer due to the interaction point plus it says the solution is at the interaction.
Answer:
C. I think
Step-by-step explanation:
Help meeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
the answer is in the above image
use the app
WOLFRAM ALPHA it helps a lot
Answer:
[tex] \frac{1}{ 2^{1} } + \frac{1}{ {3}^{2} } + \frac{1}{ {4}^{3} } + \frac{1}{ {5}^{4} } + ... \\ \frac{1}{2} + \frac{1}{9} + \frac{1}{64} + \frac{1}{625} + ... \\ = \frac{226201}{360000} \\ = 0.6283..[/tex]
[tex]\frac{1+siny}{cos y}+\frac{cos y}{1+sin y}[/tex]
[tex]\frac{cot x}{tanx+cot x}=cos^2x[/tex]
csc^2θ·tan^2θ - 1 = tan^2θ
Step-by-step explanation:
a)
[tex] \frac{1 + \sin y}{ \cos y} + \frac{ \cos y}{1 + \sin y} = \frac{1 + 2 \sin y + \sin^{2} y + \cos ^{2} y}{ \cos y(1 + \sin y)} [/tex]
[tex] = \frac{2 + 2 \sin y}{ \cos y (1+ \sin y)} = \frac{2}{ \cos y} = 2 \sec y[/tex]
b)
[tex] \frac{ \cot x}{ \tan x + \cot x} = \frac{ \cos x}{ \sin x( \frac{ \sin x}{ \cos x} + \frac{ \cos x}{ \sin x} )} [/tex]
[tex] = \frac{ \cos x}{ \frac{ \sin^{2} }{ \cos x} + \cos x } = \frac{ \cos x}{ \frac{ \sin ^{2} x + \cos^{2} x}{ \cos x} } [/tex]
[tex] = \cos ^{2} x[/tex]
c) Note that cscx = 1/sinx so
[tex] \csc^{2} \theta \tan^{2} \theta - 1= \frac{1}{ \cos^{2} \theta } - 1[/tex]
[tex] = \frac{1 - \cos^{2} \theta }{ \cos \theta} = \frac{ \sin^{2} \theta}{ \cos ^{2} \theta } = \tan^{2} \theta[/tex]
What is the slope of the line described by the equation below?
y=-x+ 8
O A. -8
O B. -1
O C. 8
O D. 1
Answer:
-1
Step-by-step explanation:
See Image below:)
Answer:
-1
Step-by-step explanation:
i need y’all to help me asap!!!!!!
Answer:
-1
Step-by-step explanation:
f(0) = -5^0 = -1
Factor the expression completely. 28x2 + 20
Answer:76
Step-by-step explanation:
Maria has 24 dollars. If cokes are 3 dollars and
hotdogs are 4 dollars, which inequality represents the
possibilities of how she can spend the 24 dollars:
Answer:
do 24 divide 3
then 24-4
have maria debate if she wants large quantities of hot dogs or cokes
PLEASE HELP, AND HOW DO U SOLVE THESE TYPE OF QUESTIONS
9514 1404 393
Answer:
625
Step-by-step explanation:
The ordered pair is an (x, y) pair. You are given the value of x. Put it in the equation and do the arithmetic.
y = 5^4 = 625
The ordered pair is (4, 625). The missing value is 625.
_____
Additional comment
The exponentiation function on many calculators is done using a key labeled ...
[tex]\boxed{y^x}[/tex]
You can do it the long way by recognizing that 5^4 = 5·5·5·5 or 25·25.
I need the answer. Plzzzzzz
Answer:
J
because there is only one number in between 10-19 which is 18. One number in between 20-29 which is 26. 2 numbers in between 40-49 which is 46 and 47. 3 numbers in between 50-59 which is 53, 54, 59. and 1 number in between 70-79 which is 75
Step-by-step explanation:
Brainly?
Use the following data and graph the best-fit quadratic curve. What is a good approximation for the value of c?
2
1
3
-2
Answer:
3=a(-3-(-2))^2+2
Step-by-step explanation:
Answer:
3=a(-3-(-2))^2+2
Step-by-step explanation:
What is the range of the data?
Evaluate: (g + ƒ)(2)
From the graph,
g(2) = 4 ( from the coordinate (2,4))
[ The green line represent the function g(x)]
f(2)= 0
[ The red line represent the function f(x)]
(g + ƒ)(2) = g(2)+f(2) = 4+0 = 4
OPTION A is the correct answer
