Parameterize each leg by
[tex]\vec r_1(t)=(1-t)(4\,\vec\imath)+t(-4\,\vec\imath)=(4-8t)\,\vec\imath[/tex]
[tex]\vec r_2(t)=(1-t)(-4\,\vec\imath)+t(4\,\vec\jmath)=(-4+4t)\,\vec\imath+4t\,\vec\jmath[/tex]
[tex]\vec r_3(t)=(1-t)(4\,\vec\jmath)+t(4\,\vec\imath)=4t\,\vec\imath+(4-4t)\,\vec\jmath[/tex]
each with [tex]0\le t\le1[/tex].
The line integrals along each leg (in the same order as above) are
[tex]\displaystyle\int_0^1((4-8t)\,\vec\jmath)\cdot(-8\,\vec\imath)\,\mathrm dt=0[/tex]
[tex]\displaystyle\int_0^1(16t(t-1)\,\vec\imath-4\,\vec\jmath)\cdot(4\,\vec\imath+4\,\vec\jmath)\,\mathrm dt=\int_0^1(64t(t-1)-16)\,\mathrm dt=-\frac{80}3[/tex]
[tex]\displaystyle\int_0^1(16t(1-t)\,\vec\imath+(8t-4)\,\vec\jmath)\cdot(4\,\vec\imath-4\,\vec\jmath)\,\mathrm dt=\int_0^1(64t(1-t)-4(8t-4))\,\mathrm dt=\frac{32}3[/tex]
###
The total line integral then has a value of -16. We can confirm this by checking with Green's theorem. Notice that [tex]C[/tex] as given as clockwise orientation, while Green's theorem assumes counterclockwise. So we must multiply by -1:
[tex]\displaystyle\int_{-C}\vec f\cdot\mathrm d\vec r=-\iint_D\left(\frac{\partial(x-y)}{\partial x}-\frac{\partial(xy)}{\partial y}\right)\,\mathrm dA=-\int_0^4\int_{y-4}^{4-y}(1-x)\,\mathrm dx\,\mathrm dy=-16[/tex]
as required.
To calculate a line integral over a curve in a vector field, parametrize each segment of the curve, substitute these parametrizations into the integral and evaluate the resulting integral over the range of the parameters. Without knowing the paths between the points in question, a specific solution can't be given. However, basic calculus techniques would be used to evaluate these integrals.
Explanation:The objective here is to find the line integral of the given vector field f⃗=xyi⃗ + (x−y)j⃗ along each segment of the triangle defined by the points (4,0), (-4,0) and (0,4). The vector field involves two variables, x and y. A line integral is a type of integral where a function is integrated along a curve. In this vector field, the function is defined in two variables x and y. Our first step in calculating the line integral is to parametrize each path between these points. Then, we substitute these parametrizations into the integral, which is then evaluated with respect to the parameter. Let's evaluate the line integral over the three segments of the triangle.
Unfortunately, without further information on the specific functional forms of the paths between these points, a concrete solution can't be provided. However, usually, this process involves applying the formula for a line integral over a vector field and using fundamental calculus techniques to simplify and evaluate these integrals. If the paths between points were straight lines, for example, the path parametrizations would be simple linear functions.
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what is the probability of selecting a number that is a multiple of 15?
Answer:
well since there are infinite numbers the probability is hard to solve. is there like a:
what is the probability of selecting a number that is a multiple of 15 in a hat that has paper with numbers from 1- 100
kind of thing?
Step-by-step explanation:
(4Q) What is the amplitude and period of f(t)= -2cos (3t)
ANSWER
d. The amplitude is 2
period:
[tex]\frac{2\pi}{3} [/tex]
EXPLANATION
The given function is
[tex]f(t) = - 2 \cos(3t) [/tex]
This function is of the form,
f(t) = a cos(bt)
The amplitude of this function is |a|
where a=-2
[tex] | - 2| = 2[/tex]
The period of this function is given by,
[tex]T= \frac{2\pi}{b} [/tex]
But b=3,
[tex]T= \frac{2\pi}{3} [/tex]
Option D is correct.
Achilles ordered a pizza with 16 slices. Every hour, he ate half of the remaining slices. Let f(n) be the number of slices Achilles ate in the nth hour since he got it.
f is a sequence. What kind of sequence is it?
A. Arithmetic
B. Geometric
Write an explicit formula for the sequence.
f(x)=?
WILL GIVE BRAINLIEST ANSWER (if it is right)
Answer:
it's a geometric sequence. the explicit formula is: 8 times 1/2^n-1
Answer:
B. Geometric. [tex]f(n) =16\cdot \left(\frac{1}{2}\right)^{n}[/tex], [tex]\forall n \in \mathbb{N}_{O}[/tex]
Step-by-step explanation:
The problems shows a geometric sequence, since the statement describes succesive halves that are consumed by Achilles. The formula is:
[tex]f(n) =\Sigma_{i=1}^{n} 16\cdot \left(\frac{1}{2}\right)^{i}[/tex], [tex]\forall n \in \mathbb{N}[/tex]
Which conic section does the equation below describe?
[tex]\frac{(x-9)^2}{4} + \frac{(y+2)^2}{25} =1[/tex]
A. Hyperbola
B. Circle
C. Ellipse
D. Parabola
Answer: Option C. Ellipse
Step-by-step explanation:
The general equation of an ellipse has the following form:
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1[/tex]
Where the point (h, k) is the center of the ellipse
In this case we have the equation
[tex]\frac{(x-9)^2}{4} + \frac{(y+2)^2}{25} =1[/tex]
Note that its shape matches that of a ellipse with center (9, -2)
[tex]a=\sqrt{4} \\a=2\\\\\\b=\sqrt{25}\\b=5[/tex]
Therefore the answer is the obtion C
Answer:
C
Step-by-step explanation:
Justin is married with one child. He works 40 hours each week at a rate of $16 per hour. His wife began working part time after their daughter was born, but still contributes about $350 to the cash inflow each month. Their monthly cash outflow is generally about $3,000. They have a balance of $2,000 in their savings account. Justin has retirement contributions taken out of his paycheck at work. They have renter’s, car and life insurance coverage. Based on this information, what part of their financial plan should Justin and his wife work on? a. managing income b. managing liquidity c. protecting assets d. retirement Please select the best answer from the choices provided A B C D
Answer:
a. Managing Income
Step-by-step explanation:
Justin and his wife should pay more attention to managing liquidity (option B). This means they need to better manage their income, savings, and expenses to be able to save more money. Their current spending seems to be higher than their income which is not sustainable in the long term.
Explanation:Based on the information provided, option B, managing liquidity, is the area that Justin and his wife should focus on for their financial planning. Liquidity refers to the ability to cover immediate expenses or debts. Given they typically spend $3,000 per month and their combined income seems less than their outflow, it suggests that they might be having challenges saving money. Therefore, focusing on managing liquidity could help them better track their cash flow and enhance their savings plan.
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Given that lines b and c are parallel, select all that apply. Which pairs of angles are supplementary?
1 and 4
5 and 6
2 and 8
3 and 6
Supplementary angles, totaling 180 degrees, are demonstrated by ∠2 and ∠4, as well as ∠3 and ∠5, in the context of lines b and c, as depicted in the diagram.
Supplementary angles are pairs of angles whose measures add up to 180 degrees. In the context of lines b and c, the identified supplementary angle pairs are ∠2 and ∠4, as well as ∠3 and ∠5. These pairs satisfy the condition that the sum of their measures equals 180 degrees. Visually, this relationship is evident in the provided diagram, reinforcing the concept of supplementary angles. Specifically, the equation ∠2 + ∠4 = 180° and ∠3 + ∠5 = 180° illustrates the supplementary nature of these angle pairs. Understanding supplementary angles is crucial in geometry, as it provides a fundamental principle for evaluating the relationships between angles formed by intersecting lines. In the given scenario, the angles ∠2, ∠4, ∠3, and ∠5 exhibit supplementary properties, emphasizing their collective role in forming a straight line and contributing to the overall understanding of geometric configurations.
The correct question maybe :-
Given in the attachment
.....?????...........
You need 3a^3 to equal a^3, so you would need at subtract 2a^3.
Since the problem is addition, add - 2a^3:
3a^3 + -2a^3 = 3a^3 - 2a^3 = a^3
Then you have -5b^3 and you need it to equal b^^3, so you would need to add 6b^3:
-5b^3 + 6b^3 = b^3
First box would be -2
Second box would be 6
Find the value of x in the triangle shown below.
x =
In the triangle it has 74, 20, and x degrees
Answer:
86
Step-by-step explanation:
Angles in a triangle add up to 180 degrees
add 74 with 20 to get 94
subtract 94 from 180 to get the value of x
180-94=86
The value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.
What is a triangle?A triangle is a closed 2-dimensional polygon with three angles and three straight sides.
According to the Triangle Angle Sum Theorem, the sum of the three interior angles in a triangle is always 180°.
Hence,
angleA + angleB + angleC = 180°
Given the data in the question;
First angle in the triangle A = 74°Second angle in the triangle B = 20°Third angle in the triangle C = xWe substitute our given values into the expression above.
angleA + angleB + angleC = 180°
74° + 20° + x = 180°
94° + x = 180°
x = 180° - 94°
x = 86°
Hence, the value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.
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a parabola is the set of all points that:
Answer:
Option C.
Step-by-step explanation:
Option C. A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.
The correct option is option C.
A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.
The parabola is symmetric about its axis.
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A rectangular prism is 3 inches long, 5 inches wide, and has a height of 6 inches. What is its surface area?
a.63 in2
b. 90 in2
c.120 in2
d.126 in2
Answer:
the answer is D.126
Step-by-step explanation:
Use the formula A=2(wl+hl+hw)
A series is: a summation of quantities whose positions are based upon the natural numbers any list of numbers an arrangement of quantities whose positions are based upon the natural numbers
Answer:
any list of numbers, an arrangement of quantities whose positions are based upon the natural numbers.
Step-by-step explanation:
Answer with explanation:
A Series is:
⇒a summation of quantities whose positions are based upon the natural numbers
This can be explained in the following way
Consider , the arrangement of Quantities
a, a a, a a a, a a a a, a a a a a, a a a a a a, a a a a a a a, a a a a a a a a,..........
1 , 1+1=2 , 1+1+1=3 , 1+1+1+1= 4 , 1+1+1+1+1=5 , 1+1+1+1+1+1=6 , 1+1+1+1+1+1+1=7 , 1+1+1+1+1+1+1+1=8
Here, Alphabet "a" are Quantity.
⇒1,2,3,.....are position of Quantity represented by Natural Number.
In terms of Summation , it can be written as:
1+2+3+4+5+6+7+8.............
[tex]=\sum_{k=1}^{n} k[/tex]
Yasmin ran 6 2/3 miles on wednesday.On saturday she ran 2 1/4 times as far as she did on wednesday.How far did Yasmin run on saturday
For this case we have to:
Wednesday:
[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]
Saturday:
He ran [tex]2 \frac {1} {4}[/tex] times more than on Wednesday, that is:
[tex]\frac {20} {3} + \frac {4 * 2 + 1} {4} =\\\frac {20} {3} + \frac {9} {4} =\\\frac {20 * 4 + 9 * 3} {12} =\\\frac {107} {12} =\\8 \frac {11} {12}[/tex]
Thus, on Saturday, he ran [tex]8 \frac {11} {12}[/tex]miles
Answer:
[tex]8 \frac {11} {12}[/tex]
HELP PLEASE
The spinner below shows 5 equally sized slices. Kala spun the dial 500 times and got the following results. Fill in the table below. Round your answers to the nearest thousandth.
Answer:
0.382
0.4
option (a)
Step-by-step explanation:
Formula to calculate probability
a)
probability = number of times event occur / total number of trials
Experimental probability of landing on white = 191/500 = 0.382
b)
probability = favourable outcome / total outcome
Theoretical probability of landing on white = 2/5 = 0.4
c)
As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.
The student must calculate frequencies, relative frequencies, and probabilities based on the results from spinning a dial. The frequencies are the counts of outcomes, relative frequencies are these counts divided by total spins, and probabilities are based on the assumption of a fair spinner.
Explanation:The question is about filling in a table with the results from spinning a dial 500 times. This tasks involves calculating frequencies, relative frequencies, and probabilities which are fundamental concepts in probability and statistics. Since we do not have the actual results, I will explain the process of completing the table:
Determine the frequency of each outcome by counting the number of times it occurred in the 500 spins.To find the relative frequency, divide the frequency of each outcome by the total number of spins (500 in this case).Round the relative frequencies to the nearest thousandth as directed.The probability of each outcome, assuming the spinner is fair, would be 1 divided by the number of slices (1/5 for a spinner with 5 slices).Example Calculation for Frequency:If an outcome occurred 100 times in 500 spins, the frequency is 100. To calculate the relative frequency, divide 100 by 500, which equals 0.2. Round this to the nearest thousandth to get 0.200.
Remember to round all your final calculated values appropriately as per the instructions given in the question.
Please help????!!!!!
Answer:
y =8
Step-by-step explanation:
[tex]y^{2} = 16*4[/tex]
Write the equation of a vertical line that passes through the point (3, –3).
x = – 3
y = 3
y = – 3
x = 3
Answer: last option.
Step-by-step explanation:
We know that the line is vertical and it passes through the point (3, -3).
Then, since it is vertical, the equation of this line will have the following form:
[tex]x = a[/tex]
Where "a" is the value of the x-coordinate (Because vertical lines passes through all points with the same x-coordinate)
Then, you can observe in the given point that the x-coordinate is 3. Therefore, the equation of the line is:
[tex]x=3[/tex]
ANSWER
[tex]x = 3[/tex]
EXPLANATION
The equation of a vertical line that passes through
[tex](x_1,y_1)[/tex]
is given by
[tex]x = x_1[/tex]
That is x equals the x-value of the point.
Since the vertical line passes through (3,-3).
Therefore the equation of a vertical line that passes through the point (3, –3).
[tex]x = 3[/tex]
A vehicle originally travelled at 30 kph. Now its speed is increased to 10 kph more than twice its original speed. What is the speed now?
Answer:
20kph
Step-by-step explanation:
10 * 2 = 20
Why do insurance companies charge more for women than men? Is that fair? Why or why not?
Answer:
because women are still commonly looked down upon, and men more superior. It is not fair due to the fact that women get paid less and men get hired for more jobs.
Step-by-step explanation:
ron got a new credit card with a credit limit of $4000. he then made the following purchases: $425.36, $358.33, $377.11, and $90.20. what is his available credit?
Answer:
The available credit is [tex]\$ 2,749[/tex]
Step-by-step explanation:
we know that
The available credit is equal to the credit limit minus the purchases
so
[tex]4,000-(425.36+358.33+377.11+90.20)=\$ 2,749[/tex]
The mass of a ball is 128 g. It has a density of 0.5 g/cm³.
What is the volume of the ball?
Show your work and place a box around your answer.
Answer:
The volume of the ball is 256 cm³
Step-by-step explanation:
we know that
The density is equal to the ratio of the mass by the volume
D=m/V
Solve for V
The volume is equal to the ratio of the mass by the density
V=m/D
In this problem we have
m=128 g
D=0.5 g/cm³
substitute
V=128/0.5=256 cm³
What is the phase shift and period for the function y = 3cos6(θ − 30°) + 4?
Phase shift = right 30°, period = 60°
Phase shift = right 30°, period = −60°
Phase shift = left 30°, period = 60°
Phase shift = left 40°, period = 30°
ANSWER
Phase shift = right 30°, period = 60°
EXPLANATION
See attachment.
The graph of y = cos x is transformed to y = a cos (x − c) + d by a vertical compression by a factor of 1/2 and a translation 3 units up. The new equation is:
Y = ½ cos (x + 3)
Y = 2 cos x + 3
Y = 2 cos x - 3
Y = ½ cos x + 3
Answer: Last Option
[tex]Y =\frac{1}{2}cosx + 3[/tex]
Step-by-step explanation:
If the graph of the function [tex]y=kf(x) +d[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <k <1[/tex] then the graph is compressed vertically by a factor k.
If [tex]|k| > 1[/tex] then the graph is stretched vertically by a factor k
If [tex]k <0[/tex] then the graph is reflected on the x axis.
If [tex]d> 0[/tex] the graph moves vertically upwards d units.
If [tex]d <0[/tex] the graph moves vertically down d units.
In this problem we have the function [tex]y = cosx[/tex]
And we know that The graph of [tex]y = cosx[/tex] is transformed with a vertical compression by a factor of 1/2 and a translation 3 units up
therefore it is true that [tex]0 <k <1[/tex] and [tex]k=\frac{1}{2}[/tex] and [tex]d =3> 0[/tex]
Therefore the new equation is:
[tex]Y =\frac{1}{2}cosx + 3[/tex]
To the nearest hundredth of a centimeter, what is the length of the hypotenuse?
A 45-45-90 triangle is half a square. So, the hypotenuse is the diagonal of the square.
The diagonal of the square is [tex]d\sqrt{2}[/tex], where d is the side of the square.
In your case, we have
[tex]d\sqrt{2}=110\sqrt{2}\approx 155.56[/tex]
Answer:
88.39
Step-by-step explanation:
Find the missing part. l = 8, w = 4, h = 2 Find the diagonal (d) of the base
Diagonal of base is 8.94(approx)
If you need an explanation please contact me.
I apologize if this is not what you meant.
HELP PLEASE!!!
What is the solution to the system of equations below?
y=1/2x-4 and y=-2x-9
A) (-2,-5)
B) (-2,-3)
C) (2, -3)
D (2,-13)
PLEASE HELP THANKS!!
Answer:
(-2,-5)
Step-by-step explanation:
y=1/2x-4 and y=-2x-9
Just substitute one into the other and then solve for x. Then go back to get y.
1/2x-4=-2x-9
Add 4 on both sides
1/2x =-2x-5
Add 2x on both sides
2.5x=-5
Divide both sides by 2.5
x=-5/(2.5)=-2
Plug into y=-2x-9 to find y.
y=-2(-2)-9=4-9=-5.
Answer (-2,-5)
Answer:
A) (-2,-5)
Step-by-step explanation:
A small dog gets fed 3/4 cups of dog food twice a day. Using d for the number of days and f for the amount of dog food in cups, write an equation relating the variables. Use the equation to find how many days a large bag of dog food will last if it contains 210 cups of food?
The desired equation relating the variables is;
d = 4f/6Also, a large bag of dog food that contains 210 cups of food will last 140 days according to the equation.
According to the question;
The small dog gets fed 3/4 cups of dog food twice a day.
In essence; The dog is fed twice a day with 3/4 cups of dog food each time.
Therefore; The dog gets fed 2× (3/4) cups of dog food per day
a) The equation is therefore;
d = f/(6/4)d = 4f/6.b) To determine the number of days a large bag of dog food will last if it contains 210 cups of food;
d = 4f/6d = (4 × 210)/6d = 140 daysRead more:
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Jane will roll a number cube 30 times.How many times would Jane expect to roll a number larger than 4?
Answer:
Are there any options for an answer?
Step-by-step explanation:
Full question in the attached below. HELP QUICK .
Ms.Call is renting a truck for a day. The two choices she has are Company A and Company B.
Company A charges $35 per day plus $0.45 per mile
Company B charges $60 per day plus $0.25 per mile.
What is the minimum number of miles that Ms.Call would need to drive in order to make renting from Company B a better deal.
Answer:
125 miles
Step-by-step explanation:
Write formulas for the amount of $ that would be due each of the two companies and set these equal to one another prior to solving for the number of days:
A: $35 + ($0.45/mile)x
B: $60 + ($0.25/mile)x
Then $35 + ($0.45/mile)x = $60 + ($0.25/mile)x, or
($0.20/mile)x = $25
$25
dividing both sides by $0.20 yields x = ------------------- = 125 miles
$0.20/mile
The charges made by the two companies would become equal after the 125th mile. After that, Company B would become cheaper.
Ms. Call would need to drive at least 125 miles for the rental from Company B to be more cost-effective.
Explanation:To find out when Company B becomes a better deal, we need to set up an equality and solve it for the number of miles. We can create the equation as follows:
Company A cost = Company B cost.
So, $35 + $0.45x = $60 + $0.25x.
Here x represents the number of miles driven. If we simplify this equation, we have:
$0.20x = $25.
Thus, solving for x: x = 25/0.20 = 125
So, Ms. Call would need to drive at least 125 miles in order for Company B to be a better deal.
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A die with numbers 1 through 6 is rolled. What is the probability of getting a 4 on the first roll and then getting a 4 or a 6 on the second roll?
the probability is 1/18
given the geometric sequence where a1=3 and the common ratio is -1, what is the domain for n?
All integers where >_0
all integers where n>_0
all integers where n<_0
all integers where n>_1
Answer:
all integers where n ≥ 1
Step-by-step explanation:
n is a counting number, since it counts the terms of the sequence. It is in the set {1, 2, 3, ...}, any of the integers 1 or greater.
HELP SO I DONT FAIL THIS YEAR
Answer:
Option Z
The graph in the attached figure
Step-by-step explanation:
Let
x----> the number of chickens sandwiches
y----> the number of hamburgers
we know that
[tex]x+y\leq 40[/tex] ----> inequality A
[tex]4x+2y\geq 100[/tex] ----> inequality B
using a graphing tool
The solution is the triangular shaded area
see the attached figure