For any given [tex]0\le y\le4[/tex], a cross section in that plane is a circle whose diameter is [tex]x=\sqrt{10}\,y^2[/tex] with thickness [tex]\Delta y[/tex]. Such a cross section contributes a volume of [tex]\pi \left(\frac x2\right)^2 \, \Delta y = \frac{5\pi}2 y^4 \, \Delta y[/tex].
As [tex]\Delta y\to0[/tex] and the number of cross sectional cylindrical disks increases without bound, the infinite sum of their volumes converge to the volume of the solid, given by the definite integral
[tex]\displaystyle \frac{5\pi}2 \int_0^4 y^4 \, dy = \frac{5\pi}2 \cdot \frac{4^5}5 = \boxed{512\pi}[/tex]
Solve the equation below for p:
9p-12=-3p+24
Answer:
p= 3
Step-by-step explanation:
Answer:
p = 3
Step-by-step explanation:
Solving for the value of p,
→ 9p - 12 = -3p + 24
→ 9p + 3p = 24 + 12
→ 12p = 36
→ p = 36/12
→ [ p = 3 ]
Thus, the value of p is 3.
the sum of an arithmetic series is given be Sn= 6n-3n2. find the common difference and the first 4 terms of the sequence
The common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively
How to determine the valueGiven that the sum of an arithmetic sequence is 6n-3n²
Let the first term of the sequence be a1The second term of the sequence be a2The third term of the sequence be a3The fourth term be a4d denotes common difference of the sequenceS1 = a1 = 6(1) - 3(1)² = 6 - 3 = 3
S4 = a1 + a2 + a3 + a4 = 6(4) - 3(4)² = -24
a1 + a2+ a3 + a4 + d = -24
4(a1) + d = -24
4(3) + d = -24
12 + d = -24
d = -24 + 12
d = -12
The first four terms are;
T2 = 3 + (2-1) -12
T2 = 3 -12
T2 = -9
T3 = 3 + 2(-12)
T3 = 3 - 24
T3 = -21
T4 = 3 + 3(-12)
T4 = 3 - 36
T4 = -33
Thus, the common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively
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select ALL expressions equal to -10(4x - 5).
A. 4x - 50
B. -40x -50
C. -40x + 50
D. -50 -40x
E. 50 - 4x
F. 50 - 40x
Answer: C, F
Step-by-step explanation: this is a form of distribution meaning you have to distribute -10 to the numbers inside the parenthesis. -10x4= -40x and -10 x -5= 50 therefor it is -40x+50. This answer can work as commutative meaning -40x+50 can also be written as 50-40x
The coordinates of point T are (0,5). The midpoint of ST is (6,-2) find the coordinates of point S
The coordinates of point S are (12,₋9)
Given, coordinates of T are (0,5)
midpoint of ST is (6,₋2)
When it is necessary to determine the precise center point between two specified points, the midpoint formula is used. So you may use this method to determine the point that divides a line segment specified by two points in half.
coordinates of S are = ?
we know the midpoint formula is (x₊x₁)/2 , (y₊y₁)/2
The midpoint calculation is the same as averaging two numbers. As a result, by adding any two integers together and dividing by two, you may find the midpoint between them.
substitute the given values in the formula.
(6,₋2) = (x₊0)/2 , (y₊5)/2
for the x value of S:
x/2 = 6
x = 12
for the y value of S:
y₊5/2 = ₋2
y ₊ 5 = ₋4
y = ₋4 ₋ 5
y = ₋9
Therefore the coordinates of S are (12,₋9)
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L = {0,20,40,80,100}
M = {5,10,15,20,25}
N = {10,20,30,40,50}
Sets L, M, and N are shown above. Which of the following sets represents LU (MnN) (the union of L with the interesection of sets M and N)?
The sets represents L ∪ (M ∩ N) is {0 , 10 , 20 , 40 , 80 , 100}.
What is domain and range ?
The bis the set of possible input values, and the range is the set of all possible output values of the graph.
In the sets:
Union (∪) of two sets means all the elements in the two sets without repeating the same elements
Intersection (∩) of two sets means the common elements in the two sets
∵ Set L = {0 , 20 , 40 , 80 , 100}
∵ Set M = {5 , 10 , 15 , 20 , 25}
∵ Set N = {10 , 20 , 30 , 40 , 50}
We need to find L ∪ (M ∩ N)
At first find (M ∩ N)
M ∩ N means find the common elements of M and N
10 and 20 are common elements in M and N
M ∩ N = {10 , 20}
Now find the union of L and {10 , 20}
L ∪ {10 , 20} means all elements in L and {10 , 20} without repeating the same elements
L ∪ {10 , 20} = {0 , 10 , 20 , 40 , 80 , 100}
L ∪ (M ∩ N) = {0 , 10 , 20 , 40 , 80 , 100}
The sets represents L ∪ (M ∩ N) is {0 , 10 , 20 , 40 , 80 , 100}
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I need the quotient of this expression
The quotient of the expression [tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5}[/tex] is [tex]x^{2} - 3x + 7 + \frac{-20x+36}{x^{2}-5}[/tex].
In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.
A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
Constant: An absolute numerical number is referred to as a constant.
Variable: A symbol without a set value is referred to as a variable.
Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.
Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.
Consider the expression,
[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5}[/tex]
Now,
[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5} = x^{2}+\frac{-3x^{3}+7x^{2}-5x+1}{x^{2}-5}[/tex]
[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5} = x^{2} - 3x + \frac{7x^{2}-20x+1}{x^{2}-5}[/tex]
[tex]\frac{x^{4}-3x^{3}+2x^{2}-5x+1}{x^{2}-5} = x^{2} - 3x + 7 + \frac{-20x+36}{x^{2}-5}[/tex]
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The scatter plot shows the rental price versus area (in square feet) for 20
apartments that recently rented in an apartment complex.
The equation of the least squares regression line is given as:
Predicted Rental Price = 391+0.98· Area
Use the drop-down menus to complete the statements below about what this linear model tells you about the rental cost of apartments in the complex.
The linear model tells you about the rental cost of apartments in the complex that is $410.6
What is a linear equation?A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = MX + c. Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
A linear equation is given as y = MX + b
where m is the rate of change, b is the initial value of y, and, x are variables.
Assume that y represents the monthly rental price and x represents the square footage.
Given the equation:
Predicted Rental Price = 391+0.98· Area
For the rental price versus area (in square feet) for 20 apartments.
Predicted Rental Price = 391+0.98· Area
Predicted Rental Price = 391 +0.98· (20)
= 410.6
The linear model tells you about the rental cost of apartments in the complex that is $410.6
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Please help meeeeeeee
Answer: 19
Step-by-step explanation: 13+6=19
Which of the following values are solutions to the given
equation?
|x-5|=9
Be sure to select ALL numbers which are solutions.
(Select all that apply.)
x=3
x = 14
x = -2
x = 9
x= -14
x=-4
Step-by-step explanation:
x= 14 and x = -4 these are the answers
Find X and Y with these angles. Thank you
A 6-inch candle burns down in 6 hours. At what rate does the candle burn, in inches per hour??
Answer:
1 inch per hour.
Step-by-step explanation:
If a candle burns 6 inches in 6 hours, this means 1 inch of the candle melted every hour. Therefore, the candle burned/melted at a rate of 1 inch per hour.
Hope this helps!
Answer: the candle burns down at about 1 inch per hour
Step-by-step explanation: since if it is burning the whole time the equation you can do is 6 hours divided by 6 inches which is 1 hour by 1 inch
List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these.
The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis, y-axis and it is graphically shown.
What is a symmetry of a function?A symmetry of a function is a transformation that leaves the graph unchanged. Symmetric function is a function having several variables which remain unchanged for any type of permutation of the variable.
For the given situation, Symmetry with respect to x-axis
The point becomes (x, -y) as the point flips by itself up or down which changes its y coordinate to negative of whatever it was. And there is no motion is done horizontally so no change in x coordinate.
The interecpets are; (0, 6) (0, -6)
Thus this intercepts is symmetric to y-axis. this intercepts is not symmetric about origin.
Hence we can conclude that the intercepts is symmetric about x - axis.
Therefore, The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis and it is graphically shown.
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Is 3 irrational number integer real number whole number natural number irrational number
3 is a whole number, as it is a regular number, on the other hand decimals and negatives are a diffrent story! Have fun on Brainly!
A pump can dispose of sludge at the rate of 6,000 lb/h. How many pounds can be disposed of per minute?
Amount of sludge dispose per minutes is 100 lb.
What is Rate of change?
A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.
Here it is given that :
A pump can dispose of sludge at the rate of 6,000 lb/h, that is in one hour pump dispose 6000 lb of sludge.
it is known that 1 hour = 60 minutes
Therefore, to find the amount of sludge dispose by pump in ome minute we divide 6000 with 60 :
amount of sludge dispose in one hour = 6000 lb
amount of sludge dispose in 60 minutes = 6000 lb
amount of sludge dispose in 1 minutes = 6000 lb/60 = 100 lb
Therefore, amount of sludge dispose per minutes is 100 lb
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If you buy 100 shares of a stock that cost $30 per share and the value of the stock increase 10% each year for 3 years, what is the value of your stock after 3 years
Answer:
$3900
Step-by-step explanation:
100*30=$3000
10%=0.1 ---> 3*0.1=0.3
3000*1.3=$3900
Every pay period, Tamara pays 11% of her gross pay in taxes and an additional $200 in voluntary retirement deductions.
Write an equation that represents Tamara's net pay, where x represents her gross pay per pay period.
Of(x) = 0.89x - 200
Of(x) = 0.89x+ 200
Of(x) = 0.11x + 200
Of(x) = 0.11x-200
An equation that represents Tamara's net pay, where x represents her gross pay per pay period is: D. f(x) = 0.11x - 200
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
Mathematically, net pay can be calculated by using this formula:
Net pay = Gross pay - Deductions.
In order to solve this word problem, we would assign variables to the gross pay and then translate the word problem into algebraic equation as follows:
Let x represent the gross pay.
Translating the word problem into an equation, we have;
f(x) = 0.11x - 200
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how many proper subsets are there of the set {O,P,Q,R,S,T,U,V,W}
Answer:
37 subsets
Step-by-step explanation:
yeah just copy that and that's all
Rita bought 1/4 pound hamburger patties
for her family reunion picnic. She
bought 50 patties. How many pounds of
hamburgers did she buy?
Answer:
12 1/2 pounds
Step-by-step explanation:
You want to know the total weight of 50 hamburger patties that weigh 1/4 pound each.
Total weightThe weight of 50 patties will be the sum of their weights. That sum is most easily figured using multiplication.
(1/4 lb) +(1/4 lb) +(1/4 lb) +... +(1/4 lb) . . . . 50 repetitions
= 50 × (1/4 lb)
= (50/4) lb = 12.5 lb
Rita bought 12 1/2 pounds of hamburgers.
Lesson 3.1 worksheet please help thank you!
please refer to the picture!!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
According to given information,
g(x) = 4when, x is not equal to -2, that means g(x) = 4 for all values of x except " - 2 "
Therefore,
[tex]\qquad \sf \dashrightarrow \: g( - 5) = 4[/tex]
and
[tex]\qquad \sf \dashrightarrow \: g(3) = 4[/tex]
And, when x = -2, it's value is 2, hence :
[tex]\qquad \sf \dashrightarrow \: g( - 2) = 2[/tex]
Fifth grade
Rasheeds body mass was 120kg.He went on a diet and lost 1/6 of his body mass during the first month and 1/10 of his remaining mass during the second month.
What fraction of his original mass did Rasheed lose during the second
The fraction of the original mass that was lost in the second month is 1/12.
What is the fraction?A fraction is a non-integer that is made up of numerators and denominators. An example of a fraction is 1/6.
Weight lost in the first month = 1/6 x 120 = 20kg
Weight lost in the second month = 1/10 x (120 - 20)
= 1/10 x 100 = 10kg
Fraction of the original mass that was lost in the second month : weight lost in the second month / total mass
10 kg / 120 = 1/12
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PLEASE HELP Four different linear functions are represented below. Answer the following questions.
The closest y-intercept is in function 1 so in option (A), the Greatest y-intercept is +4 in function 3 so in option (C), Functions 1 and 2 will have a slope less than 3 option (A) and (B).
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
Given four functions,
The y-intercept is a point on the y-axis where the graph intersects therefore coordinate of x will be 0.
In function 1 ⇒ y-intercept = -1 in rest, all it is far from 1 therefore it is close to 0.
The y-intercept of function 3 is →
y = x + 4 ⇒ y = 0 + 4 = 4 which is greatest positive value among all.
The slope of any function associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope of function 1 has points (0,-1) and (1,-5)
(-5 + 1)/(1 - 0) = -4 < 3
The slope of function 2 →
(5 - 8)/(-1 + 2) = -3 < 3 rest all function have slope as > 3.
Hence "The closest y-intercept is in function 1, the Greatest y-intercept is +4 in function 3 , Functions 1 and 2 will have a slope less than 3".
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If f(x) = 3x - 1 and g(x) = x^2-4x, find f(g(x)).
A) 3x-1
____
x^2- 4x
B) 3x^2-12x-1
C) 3x^3-13x^2+4x
D) 9x^2-18x+5
Answer:
[tex] \large{ \boxed{ \tt{3 {x}^{2} - 12x - 1 }}}[/tex]
Please see the attached picture for full solution!
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round off to millions
9887674
69954943
47546804
Answer:
9,887,674 ≈ 10,000,000
69,954,943 ≈ 70,000,000
47,546,804 ≈ 48,000,000
Which equation has the solution x = 5?
A. 3x + 1 = 9
B. 18 - 2x = 9
C. 32 - 4x = 12
D. 25/x + 4 = 9
E. x/5 + 5 = 6
F. 11 + 6x = 22
Answer:
C. 32 - 4x = 12
Step-by-step explanation:
Samra's guardians invested money for her into a 529 College Savings Plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x)=
400(1.02. What is the meaning of the y-intercept in the context of the problem?
The initial value of the investment is $400.
The principal amount put into the savings plan is $1.02.
The percent rate of change is 400%.
The average rate of change that is occurring is 1.02.
In the context of the issue, the letter D represents the meaning of the y-intercept.
The value of the investment at the outset is determined to be $600.
How can we make sense of this information?Based on the data, the growth of the savings plan over the course of one year, denoted by the variable x, may be modeled using the exponential function f(x) = 600 * (1.04)x.
In this instance, the significance of the y-intercept in relation to the situation at hand is that the beginning value of the investment is equal to $600.
In conclusion, the choice D is the one that should be made.
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Answer:
(A) The initial value of the investment is $400.
Step-by-step explanation:
Got it right on my quiz.
Order the square root of 97 to the third power, 78/9, and the square root of 45 from greatest to least.
Answer:The answer would be the second
Step-by-step explanation:The square root of 97 to the third power is 955.3. 78/9 is 8.6 and the square root of 45 is 6.7.
8,702 mL = ______________ L
Answer:I think it's 8.702 L
Step-by-step explanation:
Can someone solve this equation please ? 3/4x + 7 = -8
Answer:
x = -20
Step-by-step explanation:
Solve for x:
(3 x)/4 + 7 = -8
Put each term in (3 x)/4 + 7 over the common denominator 4: (3 x)/4 + 7 = (3 x)/4 + 28/4:
((3 x)/4 + 28/4) = -8
(3 x)/4 + 28/4 = (3 x + 28)/4:
(1/4 (3 x + 28)) = -8
Multiply both sides of (3 x + 28)/4 = -8 by 4:
(4 (3 x + 28))/4 = -8×4
(4 (3 x + 28))/4 = 4/4×(3 x + 28) = 3 x + 28:
(3 x + 28) = -8×4
4 (-8) = -32:
3 x + 28 = -32
Subtract 28 from both sides:
3 x + (28 - 28) = -28 - 32
28 - 28 = 0:
3 x = -28 - 32
-28 - 32 = -60:
3 x = -60
Divide both sides of 3 x = -60 by 3:
(3 x)/3 = (-60)/3
3/3 = 1:
x = (-60)/3
The gcd of -60 and 3 is 3, so (-60)/3 = (3 (-20))/(3×1) = 3/3×-20 = -20:
Answer: x = -20
What polynomial must be added to -3c^{2} +3 -6c in order to get a sum of 2c^{2} -c+5
The polynomial that added to [tex]-3c^{2}+3-6c[/tex] in order to get a sum of [tex]2c^{2}-c+5[/tex] is [tex]5c^{2}+5c+2[/tex]
Given,
The first polynomial = [tex]-3c^{2}+3-6c[/tex]
The result = [tex]2c^{2}-c+5[/tex]
Then,
[tex]-3c^{2}+3-6c[/tex] + second polynomial = [tex]2c^{2}-c+5[/tex]
The second polynomial = [tex]2c^{2}-c+5[/tex] -( [tex]-3c^{2}+3-6c[/tex] )
[tex]=2c^{2}-c+5+3c^{2}+6c-3\\ =(2+3)c^{2}+(-1+6)c+(5-3)\\ =5c^{2}+5c+2[/tex]
Hence, the polynomial that added to [tex]-3c^{2}+3-6c[/tex] in order to get a sum of [tex]2c^{2}-c+5[/tex] is [tex]5c^{2}+5c+2[/tex]
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