Answers
Answer:
(i) (x√x)/3 -(√x)/2
(ii) f(x) = x³/27 +3x -5
Step-by-step explanation:
You want the value of the integral in each case. One integral is indefinite, the other has conditions specified.
In each case, the power rule applies:
[tex]\displaystyle \int{x^n}\,dx=\dfrac{x^{n+1}}{n+1}[/tex]
(i) indefinite integralThe integral can be rewritten as the sum of two integrals involving half powers.
[tex]\displaystyle \int{\dfrac{2x-1}{4\sqrt{x}}}\,dx=\dfrac{1}{2}\int{x^{\frac{1}{2}}}\,dx-\dfrac{1}{4}\int{x^{-\frac{1}{2}}}\,dx=\dfrac{x^{\frac{3}{2}}}{2\left(\dfrac{3}{2}\right)}-\dfrac{x^{\frac{1}{2}}}{4\left(\dfrac{1}{2}\right)}\\\\=\boxed{\dfrac{1}{3}x\sqrt{x}-\dfrac{1}{2}\sqrt{x}}[/tex]
(ii) f'(x)=ax²+bYou are given the derivative and three conditions:
f'(x) = ax² +bf'(3) = 4f(3) = 5f(0) = -5Together with the integral, the conditions give rise to three equations in the three unknown coefficients.
[tex]\displaystyle f(x) = \int{ax^2+b}\,dx=\dfrac{a}{3}x^3+bx+c[/tex]
Then the equations we can write for a, b, c are ...
f'(3) = 4 ⇒ a(3²) +b = 4
f(3) = 5 ⇒ (a/3)(3³) +b(3) +c = 5
f(0) = -5 ⇒ a(0³) +b(0) +c = -5
The last equation gives the value of c = -5, so the remaining equations become ...
9a +b = 4
9a +3b = 10
Subtracting the first from the second, we have ...
(9a +3b) -(9a +b) = (10) -(4)
2b = 6
b = 3
Using this in the first equation, we find 'a' to be ...
9a +3 = 4
a = 1/9
Then f(x) is ...
[tex]\boxed{f(x)=\dfrac{1}{27}x^3+3x-5}[/tex]
Related Questions
A large hotel orders bars of soap to Stocketts rooms once per year if the hotel goes through an average of 750 bars of soap each week how many bars of soap should the hotel order per year
Answers
The hotel should order 39000 bars of soap if the hotel goes through on an average of 750 soaps each week.
In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).
Average is calculated by dividing the sum of the data by the frequency of the data.
Average=sum ÷ frequency
For example if the average of the data set {1,2,3,5,10}=(1+2+3+5+10)÷5=21÷5=4.2
Now for the given question average is given as 750 bars of soap.
We know that there are 52 weeks in a year. ∴ frequency=52
Hence sum of all the averages will give the total number of soap ordered by the hotel in a year.
Sum=average × frequency
or, sum=750 × 52
or, sum=39000 bars of soap.
hence the hotel orders 39000 bars of soap in one year.
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what are the nouns in a large family once lived across the street
Answers
The nouns in the sentence is "family" and "street"
Nouns are the naming word, it is used to name anything in this world. we use noun to refer person, place and things. A noun is a word that generally functions as the name of a specific object or set of objects, such as living creatures, places, actions, qualities, states of existence, or ideas
In the given sentence " A large family once lived across the street"
the nouns are " family" and "street"
Final answer, family and street are the nouns in the given sentence.
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 95?
Answers
Using the concept of linear equation we can conclude that the number of marbles sold by Mark is 23 and the number of marbles sold by Don is 72.
What is a linear equation?An equation is said to be linear if the highest power of the variable is 1. It is also called as one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variable is x and A is the coefficient of x, while B is a constant.
Let the number of marbles Mark sells be ‘x’
then, the number of marbles Don sells can be given by ‘3x+3’
Total number of marbles sold=95
We can for equation by adding the number of marbles Mark sells and the number of marbles Don sells to the total number of marbles sold. The equation formed is
x+3x+3=95
4x+3=95
4x=95-3
4x=92
x=23
The number of marbles Mark sells =23
Number of marbles Don sells=3x+3
Substituting value of ‘x’
Number of marbles Don sells=(3×23)+3
Number of marbles Don sells=69+3
Number of marbles Don sells=72
Thus, the number of marbles sold by Mark is 23.
While, the number of marbles sold by Don is 72.
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Find the value of x in each chase
Answers
Answer: x=11
Step-by-step explanation: 180-14 7= 33= angle EFB (angle in a straight line add up to 180)
Angle FBC= EFB= 33 (Alternate angles)
Angle DEB = EBC= 4x
4x- Angle FBC (33) =x
33= 3x
11=x
Sports Depot's is implementing a new strategy to increase sales of tennis balls. The basic idea is to sell tennis balls in large quantities to nonprofit groups, who resell the balls to raise money. For example, a service organization at a local college bought 2,000 tennis balls printed with the college logo. Sports Depot charged $.50 each for the tennis balls, plus a $500 one-time charge for the stamp to print the logo. The service group plans to resell the tennis balls for $2.50 each and contribute the profits to a shelter for the homeless. A. What is the service organization's average cost for the printed tennis balls it buys from Sports Depot?
Answers
The average cost price of 2000 printed tennis balls will be $1500.
What is an expression?The mathematical expression is the combination of 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 be used to denote the logical syntax's operation order and other properties.
Given that a local college's service organization purchased 2,000 tennis balls with the school's logo on them. Tennis balls cost $.50 each from Sports Depot, and a one-time stamp costing $500 was added on top of that.
Total cost = ( 2000 x 0.5 ) + 500
Total cost = 1000 + 500
Total cost = $1500
Therefore, the average cost price of 2000 printed tennis balls will be $1500.
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find the range 7,1,7,2,1,3,4,3
Answers
Answer: 6
Step-by-step explanation: How do you find a range?
You can find the range from numbers by subtracting the highest number from the lowest.
Here we have 7, 1, 7, 2, 1, 3, 4, 3.
You can put these in order:
1, 1, 2, 3, 3, 4, 7, 7.
Our highest number is 7 and our lowest is 1.
7-1=6.
6 is your range.
A line with slope 12 passes through the point (−6, 14)
Answers
Answer:
Step-by-step explanation:
Point slope form y-y₁ = m(x-x₁)
y-14 = 12(x + 6)
y-14 = 12x + 72
y = 12x + 86
i need help with this
Answers
The equations of the parabolas are given as follows:
a) f(x) = -(x + 6)² - 2.
b) g(x) = (1/32)(x - 6)² + 2
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In item a, the vertex is at (-6,-2), hence:
f(x) = a(x + 6)² - 2
When x = -8, f(x) = -6, hence we use it to find a as follows:
-6 = 4a - 2
4a = -4
a = -1.
Hence:
f(x) = -(x + 6)² - 2.
In item b, the vertex is at (6,2), hence:
g(x) = a(x - 6)² + 2
When x = -2, g(x) = 4, hence we use it to find a as follows:
4 = 64a + 2
64a = 2
a = 1/32.
Hence:
g(x) = (1/32)(x - 6)² + 2
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.55 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 2.12 and 2.98 ?
Answers
Using the Empirical Rule, 68% of the students have grade point averages that are between 2.12 and 2.98.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For this problem, we have that:
2.55 - 0.43 = 2.12.2.55 + 0.43 = 2.98.Hence 68% of the students have grade point averages that are between 2.12 and 2.98.
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You are given the equation 11 = 2x + 3 with no solution set.
Question A: Determine two values that make the equation false.
Question B: Explain why your integer solutions are false. (Also If you can please show me how to do this one)
Answers
Answer:
Step-by-step explanation:
By solving this algebraic equation we get x=4 that
2x=11-3 2x=
x=8/
x=
so by putting 4 in above equation the answer will be true
But we have to find where the equation gets false so put any number except 4 in above equation i.e the simple case putt zero x=
11=2(0)+
11=
which is false also putt x=1 the equation will be also false.
o when we putt any number except 4 in that equation we it will be false.
Answer:
x = 4
Step-by-step explanation
11=2x+3
11-3=2x+3-3
A printer is printing photos. For every 6 photos, the printer takes 3 minutes.
Complete the table below showing the number of photos and the time it takes to print them.
Answers
The printer will print 8photos in 4min and 18photos in 9min ; 12 photos in 6min and 20 photos in 10min .
In the question
it is given that , Printer takes 3min to take 6 photos
So , in 1 min it will print 6/3 photos .
In 1 min printer prints 2 photos
Hence in 4 min printer will print 2+2+2+2 = 8photos.
and in 9 min printer will print 2+2+2+2+2+2+2+2+2 = 18photos
Given in the question
that printer prints 6photos in 3min
So , it will print 1 photo in 3/6min
For printing 1 photo printer takes 1/2 min.
Hence for printing 12 photos it will take 12*(1/2) = 6 min
and for printing 20 photos it will take 20*(1/2) = 10min
Therefore , the printer will print 8photos in 4min and 18photos in 9min ; 12 photos in 6min and 20 photos in 10min .
The complete table is shown below
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What is the value of the expression −51 − 17 − (−37)?
Answers
Answer:
-31
Step-by-step explanation:
2 negatives make a positive so you have -51-17+37 which equals -31
Determin whether the relation defines a function, and give the domain and range.
Answers
If the relation has its domain in the x-axis and its range in the y-axis, then the relation is not a function. But if its domain is in the y-axis and its range is in the x-axis, then the relation is a function.
Is a given relation a function?
Relations are characterized by three elements:
An input set known as domain.An output set known as range.Relationships between elements of the domain and elements of the range.A relation is a function if and only if each element of the domain is related only to one element of the range. It must be mentioned that the answer may differ depending on what we assume as domain and range.
If the x-axis represents the domain and the y-axis represents the range, then relation is not a function, but if the x-axis is the range and the y-axis is the domain, the given relation is a function.
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Bisecting something achieves which of the following? Select all that apply.
*
Adds circles to a line segment.
Cuts in half.
Makes two equal pieces.
Moves an object along a path.
Answers
When something is bisected, the following is achieved:
Cuts in half.Makes two equal pieces.What happens when something is bisected?When an object is bisected, it means that it is being cut in half.
Cutting something in half means that you will leave two equal pieces. Bisecting therefore leads to something being cut in half.
Bisecting is used in various mathematical formulas such as when bisecting angles.
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what is the greatest common side length what does it represent?
Answers
The greatest common side represents the congruent squares in a rectangular shaped grid.
What is greatest common side?
The greatest common side or the greatest common factor defines the two images which has exactly same shape as well as shape size. And it is also known as congruent which means same. It uses the integer factor algorithms for the calculation.
The congruent comes in different shapes like square, parallelogram, rhombus, rectangular etc. In all these types, some sides are exactly equal.
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Solve for w.
-(w + -46) = 82
W =
Answers
distribute
-w + 46 = 82
subtract 46 from both sides
-w = 36
multiply by -1
w = -36
Which statement is true about the end behavior of the
graphed function?
0 As the x-values go to positive infinity, the function's
values 90 to negative infinity.
As the x-values go to zero, the function's values go
to positive infinity.
As the x-values go to negative infinity, the function's
values are equal to zero.
O As the x-values go to positive infinity, the function's
values go to positive infinity.
Answers
Answer: B) as the x-values go to negative infinity, the functions values go to positive infinity.
Step-by-step explanation:
Solve for the following equation . x^6-9x^3+10=0
Answers
Answer:
x = ∛10x = -∛10/2 +(∛10√3)/2ix = -∛10/2 -(∛10√3)/2ix = -1x = 1/2 -(√3)/2ix = 1/2 +(√3)/2iStep-by-step explanation:
You want to solve the 6th-degree equation x^6 -9x^3 +10 = 0.
QuadraticThe equation is basically quadratic in x^3. Substituting z = x^3, we have ...
z^2 -9z +10 = 0
(z -10)(z +1) = 0 . . . . . factored form
z = 10, z = -1 . . . . . . . values of z that make the factors zero
CubicsNow, we have two cubic equations to solve:
x^3 = 10 ⇒ x = ∛10x^3 = -1 ⇒ x = ∛(-1) = -1The real root is given by the cube root function. The imaginary roots are that value multiplied by 1∠±120° = (-1/2 ±(√3)/2i). Then the six roots are ...
x = ∛10x = -∛10/2 +(∛10√3)/2ix = -∛10/2 -(∛10√3)/2ix = -1x = 1/2 -(√3)/2ix = 1/2 +(√3)/2i__
Additional comment
The product ∛10√3 can be simplified to ...
[tex]\sqrt[3]{10}\sqrt{3}=(10^{2/6})(3^{3/6})=(10^23^3)^{1/6}=\sqrt[6]{2700}\approx 3.7315903[/tex]
Pls help with question
Answers
1) The composite function is f ° g (x) = x / (2 + x). The domain of the composite function is all real numbers except - 2 and the range of the composite function is all real numbers except 1.
2) The composite function is g ° f (x) = 2 · x + 1. Both the domain and the range of the composite function is all real numbers.
How to use composition between two functions and find the domain and range of a function
Let a, b be functions, there is a composition when the independent variable of one of the functions is substituted by the other function. For instance,
a ° b (x) = a [b (x)]
The domain of a function is the set of x-values such that the function exists, whereas the range of it is the set of y-values.
If we know that f(x) = 1 / (2 · x + 1) and g(x) = 1 / x, then the composite functions and their domains are:
f ° g (x)
f ° g (x) = f [g (x)]
f ° g (x) = 1 / [2 · (1 / x) + 1]
f ° g (x) = 1 / [(2 + x) / x]
f ° g (x) = x / (2 + x)
The domain of the composite function is all real numbers except - 2 and the range of the composite function is all real numbers except 1.
g ° f (x)
g ° f (x) = g [f (x)]
g ° f (x) = 1 / [1 / (2 · x + 1)]
g ° f (x) = 2 · x + 1
Both the domain and the range of the composite function is all real numbers.
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1. You are buying tile for your bathroom floor and
baseboards for your bathroom walls. In the figure,
the entire polygon represents the layout of the
floor. Each unit in the coordinate plane represents
1 foot.
a. Find the area of the floor.
b. Find the perimeter of the floor.
c. The cost of the baseboard is $2 per foot. The
cost of the tile is $2.50 per square foot. Find
the total cost to buy tile and baseboards for
your bathroom.
Answers
The solutions to the questions are
The area of the floor is 65 square feetThe perimeter of the floor is 50 feetThe total cost to buy tile and baseboards for your bathroom is $145a. Find the area of the floor.The figure represents the given parameter.
On the figure, we have the following shapes:
Rectangle 1: 7 units by 5 unitsRectangle 2: 3 units by 10 unitsThe area is calculated as
Area = Area of rectangle 1 + Area of rectangle 2
So, we have
Area = 7 * 5 + 3 * 10
Evaluate
Area = 65
Hence, the area of the floor is 65 square feet
b. Find the perimeter of the floor.On the figure, we have the following shapes:
Rectangle 1: 7 units by 5 unitsRectangle 2: 3 units by 10 unitsThe perimeter is calculated as
Perimeter = Perimeter of rectangle 1 + Perimeter of rectangle 2
So, we have
Perimeter = 2 *(7 + 5) + 2 * (3 + 10)
Evaluate
Perimeter = 50
Hence, the perimeter of the floor is 50 feet
c. Find the total cost to buy tile and baseboards for your bathroom.The total cost is calculated as
Total Cost = Cost of baseball * Area of baseball + Cost of tile * Area of tile
So, we have
Total Cost = 2 * 7 * 5 + 2.5 * 3 * 10
Evaluate
Total Cost = 145
Hence, the total cost to buy tile and baseboards for your bathroom is $145
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Divide.
4857÷18
• 15
• 269 R 12
• 269
• 269 R 15
I’m confused as to what the R means.
Answers
Answer:
269 R 15
Step-by-step explanation:
R means remainder
So if u divide 4857 by 18 you will get 269 reminder 15.
Suppose the number of CD players a retail chain is willing to sell per week at a price of dollars is given by the function
S(p) =[tex]\frac{70p}{1p+2}[/tex]
Find the supply and the instantaneous rate of change of the supply with respect to price when the price is 40 dollars.
S(40) = already got (66.677)
S'(40) = ?
Answers
1) The supply when the price is 40 dollars would be; S(40) = 66.677
2) The instantaneous rate of change of the supply with respect to price when the price is 40 dollars is; 0.0794
How to find the instantaneous rate of change?
We are given the function that represents the number of CD players a retail chain is willing to sell per week at a price of dollars as;
S(p) = 70p/(p + 2)
1) The supply when the price is 40 dollars would be;
S(40) = 70(40)/(40 + 2)
S(40) = 2800/42
S(40) = 66.677
2) The instantaneous rate of change would be gotten by finding the derivative of the supply function to get;
S'(p) = 140/(p + 2)²
Thus;
S'(40) = 140/(40 + 2)²
S'(40) = 0.0794
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Grandparents want to make a gift of $100,000 for their grandchild’s 20th birthday. How much would have to be invested on the day of their grandchild’s birth if their investment could earn: (a) 10.5% compounded continuously? (b) 11% compounded continuously? (c) Describe the effect that this slight change in the interest rate makes over the 20 years of this investment
Answers
Answer:
20
Step-by-step explanation:
20 yenara they hain aahe aahe
my answer is 20 i guess........
what is 0.037854921 to the nearest hundreth
Answers
Answer:
0.04
Step-by-step explanation:
I hope this is the answer you are looking for and I hope this helps!
the x intercept of a function always occurs where y is equal to zero
Answers
Line A: y = 1/2x + 2
Line B: y = -1/2x + 7
Line C: y = 2x + 4
Line D: y = 1/2x + 5/4
Which lines are perpendicular?
Answers
When the multiplication of two slopes of two lines is equal to -1, they are perpendicular to each other.
-1/2*2=-1
Therefore line B & C are perpendicular.
Which choice correctly uses compensation to multiply
4
×
38
?
A.
4
×
40
=
160
4
×
2
=
8
160
−
8
=
152
B.
4
×
40
=
160
4
×
2
=
8
160
+
8
=
168
C.
4
×
40
=
160
160
×
2
=
320
D.
4
×
40
=
160
4
×
2
=
8
160
×
8
=
1,280
Answers
It should be noted that using compensation to multiply 4 × 38 will be A. (4 × 40) - (4 × 2) = 152.
How to illustrate the information?Based on the information, it should be noted that the compensation strategy for multiplication has to do with the multiplication of numbers based on the multiple of 10 and the number will then be subtracted afterwards.
Therefore, it should be noted that using compensation to multiply 4 × 38 will be:
= (4 × 40) - (4 × 2)
= 160 - 8
= 152.
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Describing a Graph On a coordinate plane, points (1, 3), (5, 9), and (7, 12) are plotted. statements are true about this graph? Check all that apply. The three points do not form a straight line. The three points form a straight line. The graph passes through the origin. The graph does not pass through the origin. The graph shows a proportional relationship. The graph does not a show a proportional relationship.
Answers
The correct statements regarding the linear function in the graph are:
The three points form a straight line.The graph does not pass through the origin.The graph does not a show a proportional relationship.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the points, we have that:
When x changes by 4, y changes by 6.When x changes by 6, y changes by 9.When x changes by 2, y changes by 3.Hence these points form a straight line with a slope of 1.5, that is:
y = 1.5x + b.
When x = 1, y = 3, hence we use it to find b as follows:
3 = 1.5 + b
b = 1.5.
Hence the relation is:
y = 1.5x + 1.5.
Since the y-intercept is different of 0, we have that:
The graph does not pass through the origin.The graph does not a show a proportional relationship.More can be learned about linear functions at https://brainly.com/question/24808124
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Select all of the figures that appear to have at least four lines of symmetry.
1. CIRCLE
2. SQUARE
3. RECTANGLE
4. OVAL
5. TRIANGLE
Answers
Figures with at least 4 lines of symmetry are:
CircleSquareRectangleOvalWhat are lines of symmetry?A line of symmetry is a line that divides two equal and symmetrical parts of a shape or object. This line is also known as the axis of symmetry or the mirror line because it divides the figure symmetrically and the divided parts appear to be mirror reflections of each other. A line of symmetry is a line that exactly cuts a shape in half. This means that if you folded the shape along the line, both halves would exactly match. Similarly, if you placed a mirror along the line, the shape would not change.So, according to the given image, we can say that circle, square, rectangle, and oval can have at least 4 lines of symmetry.
Therefore, figures with at least 4 lines of symmetry are:
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Five more than the quotient of a number and 3 is 7
Answers
The expression for Five more than the quotient of a number and 3 is 7 is (n/3) +5 =7.
The unknown number y is 6.
How to find the unknown number?Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is called as an algebraic expression (or variable expression).
given that Five more than the quotient of a number and 3 is 7.
the unknown number is y.
variable = y
now find the value of y.
This statement should be transformed into an equation.
A number divided by three can be written as
y/3.
Adding 5 now results in equation is
(y/3) + 5.
This is supposed to equal 7, therefore the equation is
(y/3) +5 =7.
now solve the equation
deducting 5 from both sides, you can solve for y to get
y/3 = 2.
Multiply 3 to both sides so that y is 6.
n = 6.
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