The line integral you need to compute is
[tex]\displaystyle\int_C\langle2xy^2,4x^3+y\rangle\cdot\mathrm d\vec r[/tex]
By Green's theorem, this is equivalent to the double integral,
[tex]\displaystyle\iint_D\left(\frac{\partial(4x^3+y)}{\partial x}-\frac{\partial(2xy^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_D(12x^2-4xy)\,\mathrm dx\,\mathrm dy[/tex]
where [tex]D[/tex] is the region with boundary [tex]C[/tex]. This integral is equal to
[tex]\displaystyle\int_0^\pi\int_0^{\sin x}(12x^2-4xy)\,\mathrm dy\,\mathrm dx=\int_0^\pi(12x^2\sin x-2x\sin^2x)\,\mathrm dx=\boxed{\frac{23\pi^2}2-48}[/tex]
(5x^3-6-15x) / (10+5x)?
I need help please...
Answer:
(x^2 -2x +1) -16/(5x+10)
Step-by-step explanation:
The quotient and remainder can be found by polynomial long division or by synthetic division.
___
For synthetic division, it is recommended to divide the dividend and divisor by the leading coefficient of the divisor (5), so the divisor coefficient is 1. This results in a divisor of (x+2) and a remainder of -16/5. The simplified remainder becomes ...
(-16/5)/(x+2) = -16/(5x +10)
See the attachments for the various methods of computing the quotient.
Simplify 3b^−4/b^0. Write the expression using only positive exponents.
HURRY
Answer:
3/b^4
Step-by-step explanation:
b^0 = 1
3b^(-4) / b^0 = 3b^(-4) / 1 = 3b^-4
Since you are instructed to write only positive exponents, the answer is 3/b^4
what is the discriminant of the polynomial below 4x^2-20x +25
Answer:
The discriminant D=0
Step-by-step explanation:
For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is
[tex]D=b^2-4ac.[/tex]
In your case, for the polynomial [tex]4x^2-20x+25,[/tex]
[tex]a=4;[/tex][tex]b=-20;[/tex][tex]c=25;[/tex][tex]D=(-20)^2-4\cdot 4\cdot 25=400-400=0.[/tex]Answer:
The answer is 0 D
What is the value of x, given that OP||NQ
x= 7
x=9
x=12
x= 24
Answer:
Step-by-step explanation:
It is x=24
Answer:
(C) [tex]x=12[/tex]
Step-by-step explanation:
Given: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36.
To find: The value of x.
Solution: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36, thus using the proportionality theorem, we get
[tex]\frac{ON}{OM}=\frac{PQ}{PM}[/tex]
Substituting the given values, we have
[tex]\frac{7}{7+21}=\frac{x}{x+36}[/tex]
Upon solving the above equation, we get
[tex]\frac{7}{28}=\frac{x}{x+36}[/tex]
[tex]\frac{1}{4}=\frac{x}{x+36}[/tex]
[tex]x+36=4x[/tex]
[tex]x=12[/tex]
Hence, the value of x is 12 and option C is correct.
Please help I've failed this many times
Answer:
x-intercept (9, 0)y-intercept (0, 17.5)Step-by-step explanation:
You can compute the slope from two of the points, then write the point-slope form of the equation of the line.
slope = (change in y)/(change in x)
= (15 -20)/(3 -1) = -5/2
Then the equation of the line, using the first point) is ...
y = m(x -h) +k . . . . . . for slope m through point (h, k)
y = -5/2(x -1) +20
The x-intercept is the value of x where y=0:
0 = -5/2(x -1) +20 . . .put 0 where y is in the equation, then solve for x
0 = (x -1) -8 . . . . . . . . multiply by -2/5 (the inverse of the x-coefficient)
9 = x . . . . . . . . . . . . . simplify, add 9
The x-intercept is (9, 0).
__
The y-intercept is the value of y where x=0:
y = -5/2(0 -1) +20 . . . . . . put 0 where x is in the equation, then solve for y.
y = -2.5 +20 = 17.5
The y-intercept is (0, 17.5).
_____
Comment on the problem
Your question page seems to offer both lesson and video help. Either or both may be better than the written solution here.
What is the x-intercept and the y-intercept of the line in the graph
Answer:
x intercept= 3
y=-2
Step-by-step explanation:
the intercept is the point when the line crosses the axis
a rectangle is 6 meters longer than it is wide. The area of the rectangle is 315 square meters. find the length
Answer:
The length is 21 meters
Step-by-step explanation:
* Lets use variable to represent the dimensions of the rectangle
- The length of the rectangle is 6 meters longer than its width
# Let the width of the rectangle = x meters
∴ The length of the rectangle = x + 6 meters
- The area of the rectangle = Length × width
∵ The area of the rectangle = 315 meters²
∵ The length of the rectangle = x + 6
∵ The width of the rectangle = x
∴ x(x + 6) = 315 ⇒ open the brackets to solve the equation
∴ x² + 6x = 315 ⇒ subtract 315 from both sides
∴ x² + 6x - 315 = 0
- Lets factorize the quadratic equation to find the value of x
∵ The last term of the quadratic is negative
∴ The brackets have different sign
# x² = x × x ⇒ 1st terms in the two brackets
# -315 = -15 × 21 ⇒ 2nd terms in the two brackets
# x × -15 = -15x ⇒ 1st term in the first bracket and 2nd term in
the second bracket
# x × 21 = 21x ⇒ 1st term in the second bracket and 2nd term
in the first bracket
# 21x - 15 x = 6x ⇒ the middle term of the quadratic equation
∴ The factoriz of x² + 6x - 315 = 0 is
(x + 21)(x - 15) = 0
∴ x + 21 = 0 OR x - 15 = 0
# x + 21 = 0 ⇒ subtract 21 from both sides
∴ x = -21 ⇒ neglect this answer because there is no negative
value for the dimensions
# x - 15 = 0 ⇒ add 15 to both sides
∴ x = 15
- The value of the width is x
∴ The width = 15 meters
- The value of the length is x + 6
∴ The length = 15 + 6 = 21 meters
the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months.
1.8(1.02)^12t
What does the value 1.8 represent?
Answer:
1.8 represents the initial number of the club members in hundreds.
Step-by-step explanation:
* Lets revise the exponential grows
- If a quantity grows by a fixed percent at regular intervals,
the pattern can be depicted by this function.
- The function of the exponential growth is:
y = a(1 + r)^x
# a = initial value (the amount before measuring growth)
# r = growth rate (most often represented as a percentage and
expressed as a decimal)
# x = number of time intervals that have passed
* Now Lets study the problem to solve it
- The club's total number of members will grow exponentially
each month
- The expression to model the number of club members, in
hundreds, after advertising for t months is
1.8(1.02)^12t
* Lets compare between this model and the function above
# a = 1.8 ⇒ initial number of members in hundreds
# r = 1.02 - 1 = 0.02 ⇒ growth rate
# x = 12t ⇒ number of time intervals
* 1.8 represents the initial number of the club members in hundreds.
The unit of measurement for angles, it is equal to 1/360th of a complete revolution.
Answer:
degree
Step-by-step explanation:
The degree is the unit of measurement for angles; it is equal to 1/360th of a complete revolution.
The municipal swimming pool in Chandler, Arizona has three different ways of paying for individual open swimming. Sam, Jane, and Suzy are trying to decide which way to pay.
• Early Pay: Pay $45.00 before Memorial Day; swim any number of days
• Deposit Plus: $12.00 deposit plus $4.00 per day
• Daily Pay: $6.00 per day
1. Write an equation for each method of payment. Write your equations in slope-intercept form so that x is the number of days and y is the cost.
a. Early Pay:
b. Deposit Plus:
c. Daily Pay:
2. If Sam goes swimming 4 times, what would he need to pay with each payment plan? Which is the best payment method for him?
3. If Sam goes swimming 8 times, what would he need to pay with each payment plan? Which is the best payment method for him?
4. If Sam goes swimming 12 times, what would he need to pay with each payment plan? Which is the best payment method for him?
5. Jane and Suzy decide to look at the different options available for individual open swimming. Jane enjoys swimming and would like to go to the pool on most days, but Suzy doesn’t know how many times she will go swimming this summer as she doesn’t really enjoy the summer heat and the pool atmosphere. Please explain in paragraph form which option would be best for Jane and which option would be best for Suzy. Explain your answer.
Any help would be greatly appreciated, I've been doing work all day and my mind is blank when I look at these questions. Thank you in advance.
1. a Early Pay: y = 45
b. Deposit Plus: y = 12.00 + 4.00x
c. Daily Pay: y = 6.00x
2. Early pay = $25
Deposit Plus = 12.00 + 4.00(4) = 12.00 + 16.00 = $28.00
Daily Pay = 6.00(4) = $24.00
Daily Pay is the cheapest one.
3. Early Pay = $45
Deposit Plus = 12.00 + 4.00(8) = 12.00 + 32.00 = $44.00
Daily Pay = 6.00(8) = $48.00
Deposit Plus is the cheapest one.
4. Early Pay = $45
Deposit Plus = 12.00 + 4.00(12) = 12.00 + 48.00 = $60.00
Daily Pay = 6.00(12) = $72.00
Early Pay is the cheapest one.
5. Since Jane likes to swim most days, it would be cheaper for her to do the Early pay option, because the price is a one time fee and she can swim every day.
Since Suzy doesn't really like to go swimming and might only go a couple times, it would be best for her to do the daily pay, that way she didn't spend any money up front if she doesn't swim at all.
Find the length of the radius of a circle whose center is at (12, 5 ), and one point on the circle is ( -6, -18 ). Round to the nearest hundredth of the units.
The answer is:
The radius of the circle is 29.21 units.
Why?To solve the problem, we need to remember that the radius of a circle is the distance from its center to any point of the circle.
We can use the following equation to calculate the distance between the center and the given point:
[tex]distance=radius=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]
So, we are given the information:
[tex]Center(12,5)\\Point(-6,-18)[/tex]
Where,
[tex]x_1=12\\y_1=5\\x_2=-6\\y_2=-18[/tex]
Now, substituting and calculating, we have:
[tex]radius=\sqrt{((-6)-(12))^{2}+((-18)-(5)^{2}}\\\\radius=\sqrt{(-18)^{2}+(-23)^{2}}=\sqrt{324+529}=\sqrt{853}=29.21units[/tex]
Hence, we have that the radius of the circle is 29.21 units.
Have a nice day!
Answer:
AB = 29.23
Step-by-step explanation:
Points to remember
Distance formula
Distance between two points (x₁, y₁) and (x₂, y₂) is given by
Distance = √[(x₂- x₁)² + (y₂ - y₁)²]
To find the radius
Center = (12, 5) and point on the circle = (-6, -18)
Radius = √[(x₂- x₁)² + (y₂ - y₁)²]
= √[(12 - - 6)² + (5 - -18)²]
= √[(12 + 6)² + (5 +18)²]
=√[18² + 23²] = √[324 +529 ] = 29.23
What is the area of a cylindrical ring where the diameter of the cross section is 6.3 in and the center line has a length of 48 in
Answer:
The area of cylinder 949.536 in²
Step-by-step explanation:
Points to remember
Curved surface area of cylinder = 2πrh
Where r - radius of cylinder
h - Height of cylinder
To find the area of cylinder
Here r = diameter/2 = 6.3/2 = 3.15 in
h = 48 in
Area = 2πrh
= 2 * 3.14 * 3.15 * 48
= 949.536 in²
Therefore area of cylinder 949.536 in²
if g(x)= 2x -1 then g(4)=
g(4)=2×4_1
8-1
=9
hence the answer is 9
hope it helps you!!!!!!!!!
Answer:
g(4) = 7
Step-by-step explanation:
To evaluate g(4) substitute x = 4 into g(x), that is
g(4) = (2 × 4) - 1 = 8 - 1 = 7
Jessica has some markers. She has 5 more black markers than blue markers. She has 4 times as many red markers as black markers. She has 8 blue markers. How many markers does Jessica have altogether? asap 60 points
Answer:
73 markers
Step-by-step explanation:
let b = blue markers
black markers = b+5
red markers = 4* black markers
= 4 * (b+5)
= 4b+20
The total markers is blue + black + red
b + b+5 + 4b+20 = 6b+25
We know she has 8 blue markers
black markers = b+5 = 8+5 = 13
red markers = 4b +20 = 4*8 +20 = 32+20 = 52
The total markers =6b+25= 6(8) + 25 = 48+25 = 73
98 POINTS!! PLS HELP!
2 Plain, 3 Cinnamon raisin, 4 Poppy seed, 2 French toast, 1 Wheat.
1. Whats the probability of (Not Cinnamon raisin) Explain.
1b. Probability of (Plain, Wheat, or Poppy) Explain how you got this answer.
Show work
1. 9/12 because all of them added together is 12 but cinnamon raisin is 3 so 12-3 gives u 9 and the total is 12 so 9/12
1b. Plain(2) wheat(1) poppy(4) 2+1+4=7. The total is again 12 so 7/12
Find the slope of the line if it exists
The answer to the problem is Undefined slope .
An architect created the blueprints for the Chin's house. The scale factor is 1 inch: 40 inches. The length and width of the living room on the blueprint are 4 inches and 8 inches respectively. WHat is the area of the actual living room?
Step 1: Find the area of the living room on the blueprint with the formula Area = length x height
A = 4 x 8
A = 32
Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in the 32 inches is times 40 <<< Does that make sense?), so...
40 x 32 = 1,280
Hope this helped!
Answer:
The measurements for the actual room are, in inches, 160 x 320
Step-by-step explanation:
If you want the computed area, then multiply those numbers together since A=bh. I assumed you were just looking for the measurements of the actual room. Set up a ratio for the scale first, the model info in the numerator and the actual room info in the denominator:
[tex]\frac{m}{a}: \frac{1}{40}[/tex]
Here, the m is the model on paper and the a is the actual room. So if the length of the room on paper is 4 inches, that will go on top with the model stuff and we will solve for the missing equivalent length of the actual room:
[tex]\frac{m}{a} :\frac{1}{40} =\frac{4}{x}[/tex]
Cross multiply to get that the length of the actual room is 160 inches long. Divide by 12 if you need that number in feet.
Doing the same with the width:
[tex]\frac{m}{a} :\frac{1}{40}=\frac{8}{y}[/tex]
Cross multiply to get that the width of the actual room is 320 inches. Again, if you need that in feet, divide by 12.
Which graph could represent the amount of green beans when selling at a unit rate of G dollars per pound?
Answer:
see attached
Step-by-step explanation:
The function that tells you the number of dollars you spend on a given number of pounds creates graphs with the coordinates (pounds, dollars).
If you want 1 pound to correspond to G dollars, then a point on the graph will be ...
(1, G)
Answer:
(1,g)
Step-by-step explanation:
hope this helps
NEED HELP ! 20 POINTS
Use Demoivres Theorem to find ( 1 - i )^10
a. 32 - 32i
b. -32i
c. -32 + 32i
d. 32
If [tex]z=1-i[/tex], then [tex]|z|=\sqrt{1^2+(-1)^2}=\sqrt2[/tex] and [tex]\arg z=-\dfrac\pi4[/tex] because [tex]z[/tex] lies in the fourth quadrant.
By DeMoivre's theorem,
[tex]z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i[/tex]
so the answer is B.
Answer:
B
Step-by-step explanation:
edge 2020
Consider the function f(x) = sin(x) and the function g(x) shown below.
Answer:
C
Step-by-step explanation:
g(x) = f(x - π/3), so g(x) is f(x) shifted to the right π/3 units.
Answer C.
What are the vertical and horizontal asymptotes for the function f(x)= x^2+x-6/x^3-1?
a) vertical asymptote: x = 1
horizontal asymptote: none
b) vertical asymptote: x = 1
horizontal asymptote: y = 0
c) vertical asymptote: x = –2, x = 3
horizontal asymptote: y = 0
d) vertical asymptote: x = –2, x = –3
horizontal asymptote: none
Answer:
Option B
Step-by-step explanation:
Given
f(x)= (x^2+x-2)/(x^3-1)
For vertical asymptotes we have to put the denominator of the function equal to zero:
x^3-1=0
x^3=1
So,
x=1
As the degree of denominator is greater than the degree of numerator, there will be only horizontal asymptote which will be y=0 because all the y values will be dragged down to the x-axis.
So the horizontal asymptote: y=0
And Vertical asymptote: x =1
Answer:
b
Step-by-step explanation:
Which is not a correct way to name the angle?
Answer:
The third one (QRP)
Step-by-step explanation:
it indicates that the angle is at point R, which it isn't! The letter in the middle shows where the angle is
Option C is not a correct way to name the angle. This is obtained by understanding the correct ways of naming an angle.
What are the correct ways of naming an angle?The correct ways of naming an angle are,
By its vertexBy three points (the middle point must be the vertex)By using numbersIn the given question,
Option A has three points and the middle point is the vertex.Option B is the vertex.Option C has three points but the middle point is not the vertex.Hence option C is not a correct way to name the angle.
Learn more about naming a triangle here:
brainly.com/question/26038114
#SPJ2
GEOMETRY!!! 15 PTSSSSS
Answer:
23) option c
JL ≈ 9.3
25) option c
y ≈ 9.6
Step-by-step explanation:
25)Given in the question that,
cos(21°) = 9 / y
y = 9/cos(21°)
y = 9.64
y ≈ 9.6(nearest tenth)
23)Given in the question that the hypotenuse of right angle triangle = 12
To find,
height of the right angle triangle
angle k = 39°
so by using trigonometry identity
cos(39) = opp/hypo
cos(39) = JL / KL
JL = cos(39)(12)
JL = 9.32
JL ≈ 9.3
Answer:
Q 23. Last option 7.6
Q 25 Third option
Step-by-step explanation:
To solve Q 23
From the figure we can write,
Sin 39 = Opposite side/Adjacent side
= JL/KL
= JL/12
JL= 12 * Sin 39
= 12 * 0.629 = 7.55
= 7.6
To solve Q 25
Cos 21 = 9/y
y = 9/Cos 21 = 9/0.9335
= 9.64
= 9.6
Find the solution set for the equation, given the replacement set.
5x + 2y = –3; {(–2, 9.5), (–3, 11.5), (–4, 8.5), (–5, 6.5)}
a.
{(–2, 9.5), (–3, 11.5)}
c.
{(–4, 8.5)}
b.
{(–3, 11.5)}
d.
{(–4, 8.5), (–5, 6.5)}
Answer:
c. {(–4, 8.5)}
Step-by-step explanation:
A plot of the equation and the offered points is attached.
__
It might be helpful to put the equation into slope-intercept form.
2y = -5x -3
y = -5/2x -3/2
This shows you that y will be an odd multiple of 1/2 only for even values of x. So, we only need to check the points (-2, 9.5) and (-4, 8.5).
At x=-2, y = -5/2(-2) -3/2 = 5 -3/2 < 9.5 . . . . . (-2, 9.5) is not a solution
At x=-4, y = -5/2(-4) -3/2 = 10 -3/2 = 8.5 . . . . (-4, 8.5) is a solution
Of the offered choices, the only one in the solution set is (-4, 8.5).
Can someone help and explain this problem to me? I’m stuck
a. 2 units
b. 3 units
c. 8 units
d. 9 units
Answer:
c. 8 units
Step-by-step explanation:
You are to find the y-intercepts of the two functions given, then report the difference between them. The y-intercept is the y-value when x=0.
For f(x), we have ...
f(0) = 3·2^0 = 3·1 = 3
__
For the table, we can see that x=0 is halfway between x=-2 and x=2, so the y-intercept can be expected to be halfway between y=3 and y=-13. That value for y is ...
g(0) = (3 + (-13))/2 = -10/2 = -5
That is, the y-intercept of g(x) is -5.
__
The difference between f(0) and g(0) is ...
f(0) -g(0) = 3 -(-5) = 8 . . . . units
Decimal Calculations (Multiplication). An employee earns a salary of $380 for a 40-hour work week. If the employee worked 40 hours plus 14 hours of overtime at the overtime rate of 12.50 for each hour overtime worked, find her total income for the week.
Answer:
$ 555
Step-by-step explanation:
Salary for a 40-hour work week = $380
Total income for the week will be = Salary of regular 40 hours + Salary of 14 hours overtime
Salary per hour for the overtime work = $ 12.50
So,
The salary for 14 hours of overtime will be = $ 12.50 x 14 = $ 175
Therefore,
Total income for the week will be = $ 380 + $175 = $ 555
Thus, for a 40 hour work week and 14 hours of overtime the total income of the week will be $ 555
The mean average of the following 4 math marks will become your report card marks 97,78,84, and 86 what will your report card mark be ?
Answer:
86.25
Step-by-step explanation:
97+84+78+86=345 then u divide by 4 which is 86.25
Solve the system of equations.
y = x + 6
y = x^2 + 8x + 16
Answer:
(-5,1)
(-2,4)
Step-by-step explanation:
y = x + 6
y = x^2 + 8x + 16
Since both equations are equal to y, we can set them equal to each other
x + 6 = x^2 + 8x + 16
Subtract x from each side
x -x + 6
= x^2 + 8x-x + 16
6 = x^2 +7x +16
Subtract 6 from each side
6-6 = x^2 +7x +16-6
0 = x^2 +7x +10
Factor
What 2 numbers multiply together to give us 10 and add together to give us 7?
5*2 = 10
5+2 =7
0 = (x+5) (x+2)
Using the zero product property
x+5 = 0 x+2 = 0
x = -5 x=-2
Now we need to find the y's that go with the x's
x=-5
y= x+6
y =-5+6
y=-1
(-5,1)
x=-2
y = -2+6
y=4
(-2,4)
The prism is 7 cubes wide, 10 cubes high, and 4 cubes deep. Each cube is 0.5 inch wide. What is the volume of the prism in cubic inches?
35 cubic in.
7/2=3.5
10*4=20/2=10
10*3.5=35
Some states are running out of license plate numbers. Delaware currently uses six-digit numbers in its license plate numbering system. The state of Washington recently stated that it needs to explore options to replace their current system of three numerical digits followed by three letters. New Jersey currently uses a system of one letter, two numerical digits, then three letters. How many license plate numbers can Delaware assign under their system?
a. 100,000 plate numbers
b. 101,000 plate numbers
c. 1,000,000 plate numbers
d. 110, 000 plate numbers
Answer:
c. 1,000,000 plate numbers
Step-by-step explanation:
Each of the 6 digits of a Delaware plate can take on any of 10 values, so there are ...
10×10×10×10×10×10 = 1,000,000
possible plate numbers.
Delaware can assign 1,000,000 license plate numbers under its six-digit numbering system, as each of the six places can have any digit from 0 to 9 giving 10^6 or one million possible combinations.
The question asks how many license plate numbers Delaware can assign under their six-digit numbering system. To find the number of possible combinations for a six-digit number where each digit can be any number from 0 to 9, we need to calculate 10 possibilities for each position (including the leading zero) multiplied together.
Therefore, the calculation follows this pattern: 10 imes 10 imes 10 imes 10 imes 10 imes 10, which equals 1,000,000 possible combinations. This is because each of the six places in the license plate number can have any of the ten digits from 0 to 9. So the answer to how many license plate numbers Delaware can assign under their system is 1,000,000 plate numbers.