Using Green's Theorem to evaluate the given line integral with the given conditions and vertices gives us; -30
How to evaluate an Integral with Green's Theorem?
The line integral of a vector-valued function along the edges of a rectangle or any other closed curve can be found by converting the line integral into a double integral. We apply Green's theorem to do this. The resulting double integral is integrated over the two-dimensional region bounded by the same closed curve.
Green's Theorem can be applied as follows:
∮_c (P.dx + Q.dy) = ∫∫_R ((dQ/dx) - (dP/dy))dA
The vertices of the rectangle (1,1), (3,1), (1,4), and (3,4).
Applying Green's Theorem to the given function gives;
∮_c (ln x + y) dx - x² dy
= ∫14∫13 Dx(-x2) -Dy(ln(x) +y) dx dy
= ∫₁⁴∫₁³ (-2x - 1) dx dy
= -3·[x² +x]₁³
= -30
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3. The time for a swing to move forward and backward can be determined by the formula
T = 2√√√15₁
T represents the time, in seconds, taken by the swing to move through one
complete cycle (forward and back) and L represents the length of the rope supporting the swing.
9.8
Determine the length of the rope supporting a swing that takes 3.4 seconds to move through one
complete cycle. Show all steps and round the answer to the nearest tenth of a metre.
Step-by-step explanation:
T = 2×pi × sqrt(L/9.8)
now we know the time the swing should take for a complete back and forth cycle : 3 4 seconds.
the only unknown variable is now L (the length of the rope) :
3.4 = 2×pi × sqrt(L/9.8)
3.4/(2pi) = sqrt(L/9.8)
(3.4/(2pi))² = L/9.8
3.4²/(4pi²) = L/9.8
11.56/(4pi²) = L/9.8
2.89/pi² = L/9.8
9.8 × 2.89/pi² = L = 2.869618563... m ≈ 2.9 m
Find the area of a triangle with base of 6m and height of 15m
Answer:
45 meters
Step-by-step explanation:
[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]
⊱________________________________________________________⊰
Answer:
A=45 m²
Step-by-step explanation:
The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].
where :
[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]
Substitute the values,
[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]
Done !! Hope this made sense to you :)
[tex]\small\boldsymbol{Calligraphy}[/tex]
⊱______________________________________________________⊰
Check the box labeled Show Segment Parallel to BC. Notice that intersects two sides of creating a smaller triangle, . How is related to ? How do you know?
write the equation of the line that is parallel to the line represented by 5 x + 2 y = 6 and passes through the point (1, 5.5).
Answer:
[tex]y=-2.5x+8[/tex]
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. So, first, transform the given equation into the slope-intercept form, [tex]y=mx+b[/tex].
[tex]5x+2y=6[/tex]
[tex]2y=-5x+6[/tex]
[tex]y=-\frac{5}{2} x+3[/tex]
Then, determine the equation of a line that has a slope of [tex]-\frac{5}{2}[/tex] and passes through (1, 5.5). Substitute all the known values and solve for b.
[tex]y=mx+b[/tex]
[tex]5.5 = -\frac{5}{2} *1+b[/tex]
[tex]5.5=-2.5+b[/tex]
[tex]b=8[/tex]
Therefore, the answer is [tex]y=-2.5x+8[/tex].
A piece of wood is 5 m long. It is cut into pieces. The lengths of the pieces are in the ratio 4:3:2:1. The longest piece is then cut in the ratio 4:1 so that there are now five pieces. How long is the smallest piece?
Answer:
0.4
Step-by-step explanation:
4+3+2+1 =10
5m÷10 =0.5
(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)
2 : 1.5 : 1 : 0.5
longest piece= 2 (2m)
4+1= 5
2÷5= 0.4
(0.4×4=1.6, 0.4×1=0.4)
1.6 : 0.4
so the shortest piece is 0.4!
Factor the expression.
3r2 – 75
Answer:
3(r + 5)(r - 5)
Step-by-step explanation:
Both 3 and 75 are divisible by 3, so we take out a 3.
3(r^2 - 25)
Next, we can factor r^2 - 25. It's a difference of squares.
3(r + 5)(r - 5)
Brainliest, please :)
I just need help on what the answer is and understanding this question, thank you.
The graph represents the potential area of a concrete rectangle, based on length and width.
Which inequality in vertex form represents the graphed region?
A)y less-than negative 2 (x + 16) squared minus 32
B)y less-than negative one-half (x minus 16) squared + 32
C)y less-than negative 2 (x minus 16) squared + 32
D)y less-than negative one-half (x + 16) squared minus 32
The inequality of the graph is y < -1/2(x - 16)^2 + 32
How to determine the inequality?A quadratic function is represented as:
y = a(x - h)^2 + k
The vertex of the graph is
(h, k) = (16, 32)
So, we have:
y = a(x - 16)^2 + 32
The graph pass through the point
(x, y) = (12, 24)
So, we have:
24 = a(12 - 16)^2 + 32
Evaluate the like terms
-8 = a(-4)^2
This gives
16a = -8
Divide by 16
a = -1/2
Substitute a = -1/2 in y = a(x - 16)^2 + 32
y = -1/2(x - 16)^2 + 32
The graph is a less than graph.
So, we have
y < -1/2(x - 16)^2 + 32
Hence, the inequality of the graph is y < -1/2(x - 16)^2 + 32
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a box contains 7 red balls and 2 blue balls. how many more blue balls do you need to add to the box to make the probobility of pulling a red ball 0.5
A) 2
B) 3
C) 4
D) 5
E) None Of The Above
Using the probability concept, the number of blue balls you need to add is:
D) 5.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A probability of 0.5 is reached if the number of red balls is the same as the number of blue balls. Current the difference is of 7 - 2 = 5, hence 5 blue balls must be added.
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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 190 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.65 cm, y= 81.36 kg, r= 0.309, P-value= 0,002, and y= 106+1.15x. Find the best predicted value of y (weight) given an adult male who is 156 cm tall. Use a 0.10 significance level.
The best predicted weight of a person that is 156 cm is 285.4kg
We have the regression equation asy= 106+1.15
When the adult male is 156 cm tall the weight of this person would be calculated as:
y= 106+1.15*156
y = 106 + 179.4
y = 285.4
Hence we can arrive at the conclusion that the best predicted weight of a person that is 156 cm is 285.4kg
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answer as soon as possible
The area of the equilateral triangle is 110.9 cm
How to find area of a triangle?area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
tan 60 = opposite / adjacent
tan 60 = 8√3 / x
x = 8√3 / √3
x = 8
hence,
b = 8 + 8 = 16
Therefore,
area of a triangle = 1 / 2 × 16 × 8√3
area of a triangle = 64√3
area of a triangle = 110.851251684
area of a triangle = 110.9 cm
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A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. A total of 10 cars were rented which can hold 66 people altogether. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.
The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;
x + y = 10
x + y = 105x + 7y = 66
Simultaneous equationSmall car = 5 peopleLarge car = 7 peopleTotal cars = 10Total number of people = 66Let
Number of small cars rented = x
Number of large cars rented = y
x + y = 10
x + y = 105x + 7y = 66
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Rotate the given triangle 270° counter-clockwise about the origin.
[tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-1&[?]&[?]\\1&[?]&[?]\end{array}\right][/tex]
The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point (x, y) is rotated 270° counter-clockwise about the origin, the new point is (y, -x)
The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
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¿cuál es el número que no pertenece a esta suceción 99,105111,117,123,129,135,141,147,153
No hay ninguno de los nimbers que no pertenezca a la secuencia.
¿Qué número no pertenece a la secuencia?
Sabemos que una secuencia tiene que ver con un arreglo de números en un orden definido. Todos los números en una secuencia deben tener la misma razón común o diferencia común.
Si miramos todos los números que están escritos en la secuencia, la diferencia común aquí es seis. Se sigue entonces que todos los números son parte de la sucesión y no hay ninguno de los números que no pertenezca a la sucesión.
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To save $5,000 for a vacation in 3 years, how much money must be invested each
year if the investment earns 5% interest compounded annually? Round to the
nearest dollar.
$15,762
$1,586
$3,000
$1,667
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]
The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
How are annual payments or cash flows calculated?The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.
This can be achieved using the future value and present value formulas or factors.
We can also use an online finance calculator, as follows:
Data and Calculations:Future value = $5,000
Investment period = 3 years
Annual compound interest = 5%
N (# of periods) = 3 years
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $5,000 ($4,531.56 + $468.44)
Results:
PMT = $1,510.52
Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)
Total Interest = $468.44
Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
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answer me with step by step details please
Answer:
31 3/4 %
Step-by-step explanation:
There are 100 squares so each square is a percent. There at 31 full squares colored and it looks like 3/4 of 1 square.
Consider the equation x+4=−2x+19. Let f(x)=x+4and g(x)=−2x+19. The graph of each function is shown. Coordinate plane with the graphs of two lines. The horizontal x axis labeled from negative three to nine in increments of one. The vertical y axis labeled from negative two to nineteen. The line f of x passes through ordered pairs zero comma four and two comma six. The line g of x passes through the ordered pairs zero comma nineteen and one comma seventeen. At what point do the graphs intersect? Enter your answer in the box.
The point of intersection of both graphs will have the coordinate (5, 9).
What is the Point of Intersection of the Graph?
We are given the functions;
f(x) = x + 4
g(x) = -2x + 19
Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;
x + 4 = -2x + 19
x + 2x = 19 - 4
3x = 15
x = 15/3
x = 5
Thus;
f(x) = 5 + 4 = 9
g(x) = -2(5) + 19 = 9
Thus, the point of intersection of both graphs will have the coordinate (5, 9)
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Choose the equation that matches
the graph.
a.y = 3x - 2
b. y = 3x-2
c. y = 3x+2
d. y = 3x + 2
e. y = (1/3)x-2
Answer:
it matches with equation a
The total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16
what is the price of each cap?
what is the price of what umbrella ?
If the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16 then the price of one umbrella is $8 and price of one cap is $4.
Given that the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16.
We have to find the price of one umbrella and one cap.
We have to form equations first to find the price of umbrella and cap.
Equation of two variables look like ax+by=c. It can be a linear equation, quadratic equation or a cubic equation.
let the price of umbrella be x and price of cap is y.
We know that total cost is equal to price of one unit multiplied by the units.
According to question.
2x+y=20----------1
x+2y=16-----------2
Multiply equation 2 by 2 and then subtract resulted equation from equation 1.
2x+y-2x-4y=20-32
-3y=-12
y=-12/-3
y=4
put the value of y in equation 2 to get the value of x.
x+2y=16
x+2*4=16
x+8=16
x=16-8
x=8
Hence the price of one umbrella is $8 and the price of one cap is $4.
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Who knows the answer for this problem please solve asap
The value of x to the nearest hundredth is 4.14
Side-angle-side theoremThe given diagram is a right triangle with the following parameters
Opposite side to 16 degrees = x
Hypotenuse = 15
Using the expression below
sin theta = x/15
sin16 = x/15
x = 15sin16
x = 4.135
Hence the value of x to the nearest hundredth is 4.14
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The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
By definition of the zeros of ta quadratic function, for 5.5 seconds the ball is in the air before it hits the ground.
Zeros of a functionThe points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
In summary, the roots or zeros of the quadratic function are those values of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.
Time the ball is in the air before it hits the groundIn this case, the height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t² + 88t, where "t" is the time it is in the air.
When the ball hits he ground, he height h has a value of zero. This is h=0. Replacing in the previous expression for the height you get:
0= -16t² + 88t
It can be solved by extracting the term "t" as a common factor:
0= t×(-16t + 88)
The Zero Product Principle says that if the product of two numbers is 0, then at least one of the factors is 0. Then:
t= 0
or
0= -16t + 88
Solving: -88= -16t
(-88)÷ (-16)=t
5.5= t
Finally, this means that for 5.5 seconds the ball is in the air before it hits the ground.
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Evaulate u^2-4u+2 when u=-2
You can just replace [tex]u[/tex] with 2:
[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]
Alternatively, you can complete the square.
[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]
When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.
Jermy deposited money into a savings account that pays a simple annual interest rate of 1.6%. He earned 55.04 in interest after 4 years. How much did he deposit?.
860
1376
2976
3440
Answer: THE ANSWER IS A) $860
Step-by-step explanation: I GOT A 100 ON THE TEST
A function and its inverse are shown on the same graph. A function and its inverse are shown on the same graph.
Which statement describes the relationship between the function and its inverse?
The slope of f–1(x) is the same as the slope of f(x).
The slope of f–1(x) is the opposite as the slope of f(x).
The x-intercept of f–1(x) is the same as the y-intercept of f(x).
The x-intercept of f–1(x) is the opposite as the y-intercept of f(x).
Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
Which statement is the correct one?
On the image, we can see two linear equations, such that the orange one is f(x) and the blue one is the inverse.
If you follow the orange line, you can see that the y-intercept of f(x) is y = 1.If you follow the blue line, you can see that the x-intercept of the inverse is x =1.Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
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Need help with this math question
The correlation coefficient is -0.87; strong correlation
How to determine the correlation coefficient?The given parameters are:
x = Time spent working out
y = lbs Overweight
Next, we enter the table of values in a graphing tool.
From the graphing tool, we have the following summary:
X Values
∑ = 27.1Mean = 2.71∑(X - Mx)2 = SSx = 22.569Y Values
∑ = 89Mean = 8.9∑(Y - My)2 = SSy = 778.9X and Y Combined
N = 10∑(X - Mx)(Y - My) = -114.19R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -114.19 / √((22.569)(778.9))
r = -0.8613
Approximate
r = -0.87
This means that the correlation coefficient is -0.87
Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0
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correct the error 4⁴- 4³=4¹
The error is that
[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]
Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.
NO LINKS!!! Please help me with this problem
Answer:
length: 8end points: (-8, 1), (0, 1)Step-by-step explanation:
In the quadratic form ...
(x -h)² = 4p(y -k)
The value 4p is the length of the latus rectum. It also tells the distance between the vertex (h, k) and the focus (h, k+p).
ApplicationThe value of 4p is given as 8. This means p = 8/4 = 2.
The length of the latus rectum is 8.
The end points of the latus rectum have the same y-value as the focus:
y = k +p = -1 +2 = 1
The end points of the latus rectum have x-values that are h±2p.
x = h ± 2p = -4 ± 2·2 = {-8, 0}
The end points of the latus rectum are (-8, 1) and (0, 1).
What is the measure of angle A?
250
140
70
110
Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°
What is the Angle of Intersecting Tangents Theorem?Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).
Measure of one of the intercepted arcs = 250°
The second intercepted arc = 360 - 250 = 110°
Positive difference of the intercepted arcs = 250 - 110 = 140°
Measure of angle A = 1/2(140)
Measure of angle A = 70°
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Answer:
the answer is 70. hope this helps <3
Step-by-step explanation:
Christine has scored 73, 85, 70, and 63 on her previous four tests. What score does she need on her next test so that her average (mean) is 73?
Answer:
74
Step-by-step explanation:
(73 + 85 + 70 + 63 + x)/5 = 73.
You find the average by adding all of the test scores and dividing that number by the number of tests. We had four test, so will will take that total, plus some mystery number (let's call it x), we divide that total by 5 because now there are 5 tests and not 4. We already know what we want the average to be, we want the average to be 73. We now have:
(291 + x)/5 = 73 Multiply both sides by 5
291 + x =365 Subtract 291 from both sides to get
x = 74
Answer: 74
Step-by-step explanation:
The mean is the average of all the values, which we find by finding the sum of each value and dividing by the total number of data points.
With 5 data points, we can use this equation to find, x, or the data point needed to obtain a mean of 73:
[tex]\frac{73+85+70+63+x}{5}=73\\ 291+x=365\\x=74[/tex]
4. (a)(i)Show that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix.
that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix
Write the recursive rule for the 5th term of the sequence: -7, -3, 1, 5, 9
Answer:
Step-by-step explanation:
Let [tex]x_{n}[/tex] represent the nth term in the sequence. Then [tex]x_{n-1}[/tex] represents the previous term
The first term, [tex]x_{1}[/tex] = -7
Each consecutive term is obtained by adding 4 to the previous term.
So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]