Answer:
[tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex]
Step-by-step explanation:
Let be [tex]f(x) = \frac{3}{5}-\frac{8}{x}[/tex] and [tex]F[/tex] is the antiderivative of [tex]f(x)[/tex] such that:
1) [tex]F = \int {\left(\frac{3}{5}-\frac{8}{x} \right)} \, dx[/tex] Given.
2) [tex]F = \frac{3}{5} \int \, dx -8\int {\frac{dx}{x} }[/tex] ([tex]\int {[f(x)+g(x)]} \, dx = \int {f(x)} \, dx + \int {g(x)} \, dx[/tex])
3) [tex]F = \frac{3}{5} x - 8\cdot \ln |x| + C[/tex], where [tex]C[/tex] is the integration constant. ([tex]\int {k} \, dx = k\cdot x[/tex]; [tex]\int {\frac{dx}{x} } = \ln|x|[/tex], [tex]\int {k\cdot f(x)} \, dx = k\int {f(x)} \, dx[/tex]) Result.
a total of 309 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold
Answer: 103 adult tickets
Step-by-step explanation:
Adult tickets (a) = a
Student tickets (s) = 2a
Total = 309
a + 2a = 309
3a = 309
a = 103
Answer:
103Step-by-step explanation:
Total tickets sold = 309
Let the number of adult tickets sold be x
Let the number of student tickets sold be 2x
Adult tickets + student tickets = 309
[tex]x + 2x = 309[/tex]
Collect like terms
[tex] 3x = 309[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{309}{3} [/tex]
Calculate
[tex]x = 103[/tex]
Hence, 103 adult tickets were sold.
Hope this helps..
Good luck on your assignment...
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2
Answer:
The answer is below
Step-by-step explanation:
a) y=3x-1
The standard equation of a line is given by:
y = mx + c
Where m is the slope of the line and c is the intercept on the y axis.
Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:
3 × d = -1
d = -1/3
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]
b) y=1/4 x+2
Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:
1/4 × f = -1
f = -4
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]
Evaluate the series
Answer:
the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
C) 59
Step-by-step explanation:
Recall that;
[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]
Therefore, we can evaluate the series;
[tex]\sum_{k=1}^{6}(25-k^2)[/tex]
by summing the values of the series within that interval.
the values of the series are evaluated by substituting the corresponding values of k into the equation.
[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]
So, the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
35 is 10% of what number?
Answer:
Step-by-step explanation:
If you take 10 percent of a number and get 35, then what is that number?
In other words, you know that 10 percent of a number is 35 and you want to know what that initial number is.
To solve this problem you multiply 35 by 100 and then divide the total by 10 as follows:
(35 x 100) / 10
When we put that into our calculator, we get the following answer:
350
Therefore, you can derive that 10 percent of 350 equals 35.
Write the Verbal phrases as an equation or an inequality? Use "x" as the variable?
Step-by-step explanation:
8.x×8-12=50
8x-12=50
9.1/2x>or=100
10.2 whole number5/9-x=31
Solve of the following equations for x: 3 − x = 2
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~`
3 − x = 2 =
X = 1
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you. Brainliest would be nice!
Answer: x = 1 / 1 = x.
Step-by-step explanation:
3 - x = 2
First, since you can't subtract x from 3, we find ways to subtract 2 from 3.
So, we write the 3 and attach (-) minus/negative sign to the 3 with 2. Because when a number crosses the equal sign and it is negative, it becomes positive and when it is positive, it becomes negative.
And 2 will cross the equal sign so,it will be (-) just like: -2. And -x will cross the equal sign so it will be x. Let's solve it with the steps above:
3 - x = 2
3 - 2 = x
1. = x
OR
3 - x = 2
-x = 2 - 3
-x/- = -1/-
So, negative will cancel negative.
x =1.
Please mark me as the brainliest!!
Thanks!!
The length and width of a rectangle are measured as 27 cm and 50 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
7.7cm
Step-by-step explanation:
Area of a rectangle is expressed as
A = Length × Width
A = LW
Let dL and dW be the errors in the measurements.
If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.
The area of the rectangle with error will be expressed as A = LdW + WdL
Given L = 27cm and W = 50cm
A = 27(0.1)+50(0.1)
A = 2.7+5.0
A = 7.7cm
Hence, the maximum error in the calculated area of the rectangle is 7.7cm
please help me pleaseeeeeeee
Answer:
the first blank is 2, the second one is 1
Answer:
Yellow box #1=2
Yellow box #2=1
Step-by-step explanation:
#1) 8-6=2
#2)8-7=1
The perimeter of an equilateral triangle is 15 x + 30 units. Which expression can be used to show the side length of one side of the equilateral triangle? 15 (x + 2): Each side length is x + 2 units. 30 (one-half x + 1): Each side length is One-half x + 1 units. 5 (3 x + 6): Each side length is 3 x + 10 units. 3 (5 x + 10): Each side length is 5 x + 10 units.
Answer:
Each side length is 5x + 10 units.Step-by-step explanation:
An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then
a = b = c.
The perimeter of the triangle is the sum of all the sides of the triangle.
P = a + b+ c
GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;
15 x + 30 = a + b + c
15 x + 30 = a + a + a (since all sides are equal)
15 x + 30 = 3a
3a = 15 x + 30
3a = 3(5x+10)
Dividing both sides by 3 will give;
3a/3 = 3(5x+10)/3
a = 5x+10
Hence, the length of one side of the equilateral triangle is 5x + 10 units.
Answer:
D.
Step-by-step explanation:
Edge 2020
What are the expressions for length, width, and height?
Volume = length width height
V = _____ _____ _____
For odyyseyware
Answer:
[tex]\boxed{V=lwh}[/tex]
Step-by-step explanation:
The formula for volume of a cuboid is:
[tex]V=lwh[/tex]
[tex]volume = length \times width \times height[/tex]
Answer:
V = l w h
Step-by-step explanation:
Volume of a Cuboid = Length × Width × Height
Where l = length, w = width and h = height
Trey is choosing a 2-letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are
possible?
Answer:
10
Step-by-step ex1planation:
What is the solution to the quadratic equation x2 + x - 30 = 0?
Answer:
try 3x=30 or 10
Step-by-step explanation:
At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h^2. Let v(f) be the velocity of the car t hours after 2:00 PM._________ Then By the Mean Value Theorem, there is a number c such that 0 Since v'(t) is the acceleration at time t.______ the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.
Here is the correct format for the question
At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h².Let v(f) be the velocity of the car t hours after 2:00 PM.Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex]. By the Mean Value Theorem, there is a number c such that 0 < c < [tex]\Box[/tex] with v'(c) = [tex]\Box[/tex]. Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.
Answer:
Step-by-step explanation:
From the information given :
At 2:00 PM ;
a car's speedometer v(0) = 30 mi/h
At 2:15 PM;
a car's speedometer v(1/4) = 50 mi/h
Given that:
v(f) should be the velocity of the car t hours after 2:00 PM
Then [tex]\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box[/tex] will be:
[tex]= \dfrac{50-30}{1/4 -0}[/tex]
[tex]= \dfrac{20}{1/4 }[/tex]
= 20 × 4/1
= 80 mi/h²
By the Mean value theorem; there is a number c such that :
[tex]\mathbf{0 < c< \dfrac{1}{4}}[/tex] with [tex]\mathbf{v'(c) = \dfrac{v(1/4)-v(0)}{1/4 -0}} \mathbf{ = 80 \ mi/h^2}[/tex]
By the mean value, theorem a number [tex]C[/tex] is [tex]0 < C < \frac{1}{4}[/tex].
The velocity of the car is [tex]80 \ mi/h^{2}[/tex].
Speed:Speed is defined as The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
Given that,
at 2:00 pm [tex]v(0)=30 \ mi/h[/tex]
at 2:15 pm [tex]v(1/4)=50 \ mi/h[/tex]
Then,
[tex]=\frac{v(1/4)-v(0)}{1/4-0} \\=\frac{50-30}{1/4} \\=20\times4\\=80 \ mi/h^{2}[/tex]
By the mean value theorem a number [tex]C[/tex] such that express as,
[tex]0 < C < \frac{1}{4}[/tex].
Now with,
[tex]{v}'(c)=\frac{v\left ( \frac{1}{4} \right )-v\left ( 0 \right )}{\frac{1}{4}-0} \\ =80 \ mi/h^{2}[/tex]
Learn more about the topic Speed: https://brainly.com/question/26417650
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and standard deviation 7 ml. The fill
volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL?
1.0000
0.8810
0.8413
0.9987
Answer:
0.8413
Step-by-step explanation:
Find the z score.
z = (x − μ) / σ
z = (992 − 999) / 7
z = -1
Use a chart or calculator to find the probability.
P(Z > -1)
= 1 − P(Z < -1)
= 1 − 0.1587
= 0.8413
The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct
Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined
Probability can be defined as the ratio of favorable outcomes to the total number of events.
We use Z-statistic to find out the probability,
z = (x − μ) / σ
x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1
P-value from Z-Table:
P(x<992) = 0.15866
P(x>992) = 1 - P(x<992) = 0.84134
Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134
Learn more about probability here:
brainly.com/question/14290572
#SPJ2
conditional probability. please help!
Answer:
a. 0.06
b. 0.2
Step-by-step explanation:
a. P(B given A) = P(A and B) / P(A)
0.1 = P(A and B) / 0.6
P(A and B) = 0.06
b. P(A given B) = P(A and B) / P(B)
P(A given B) = 0.06 / 0.3
P(A given B) = 0.2
helppp i will give stars,thanks and also bralienst
Answer:
21.30 dollarsis the answerStep-by-step explanation:
Total money/ number of people
63.90/3 = 21.30
If you divide by 3 then the 3 friends will get the equal amount of money.
Answer:
Step-by-step explanation:
The total amount of money is $63.90. Also, there are 3 friends.
In order to pay equally, divide $63.90 and 3 friends, so the answer would be dollars per friend
$63.90/3 friends = $21.3/friend
So the items you would drag would be:
2 $10 bills
1 $1 bill
3 $0.10 dimes
Raul and his friends each way 1/20 of a ton are standing on a truck scale . The total weight shown by the scale is 3/4 of a ton . How can I find the total number of people on the scale when Raul and his friends are weighed?
Answer:
15 people
Step-by-step explanation:
since Raul and his friends each weigh 1/20 ton,
and the total weight reads 3/4 ton
The total number pf people on the scale will be:
The total weight of Raul and his friends divided by their individual weight
==> (3/4 ton) ÷ (1/20 ton)
= 3/4 X 20/1 = 15 people
Answer:
I can find the total number of people by dividing the total weight by the weight of one person.
This is the plato answer, I hope this is the answer youre looking for! :))
g Suppose that twenty different hypothesis tests for whether jellybeans cause acne are conducted. In order that the probability of one or more type I error between these should be at most 0.05, at most what significance level should be used for each of them?
Answer:
The level of significance to be used is α = 0.0025
Step-by-step explanation:
Here, we are interested in calculating the the level of significance which at most must be used for each of the hypothesis test
We proceed as follows;
P(type 1 error) = α
From the question, n = number of hypotheses = 20
P( of one or more type one error) ≤ 0.05
1- P(no type one error) ≤ 0.05
Hence;
1- (1-α)^20 ≤ 0.05
(1-α)^20 ≥ 0.95
1- α ≥ 0.997438621223
α ≤ 0.00256
Thus α = 0.0025
The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other?
Answer:
The beryllium atom; 1.99 times larger.
Step-by-step explanation:
The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.
(1.12 * 10^-10) / (5.6 * 10^-11)
= (1.112 / 5.6) * (10^-10 + 11)
= 0.1985714286 * 10
= 1.985714286 * 10^0
So, the beryllium atom is about 1.99 times larger than the other.
Hope this helps!
Currently Shawn pays $550 per month to rent his apartment. Next year his rent will increase by 13.5% from what he currently pays . a) find the amount that shawn's rent will increase . b) what will be shawn's new monthly rent?. c) If you divide your answer from (b) by shawn's original rent of $550, what is the decimal result? do you see any connection to part (a)?
a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.
b) Simply do 550+74.25 to get that his new rent is $624.25.
c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.
Hope it helps <3
Answer:
A. $74.25
B. $624.25
C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.
Step-by-step explanation:
If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.
[tex]1+0.135=1.135[/tex]
[tex]550\cdot1.135=624.25[/tex]
This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.
[tex]624.25-550=74.25[/tex]
Now, for part C, let's divide 624.25 by 550.
[tex]624.25\div550 = 1.135[/tex]
If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.
Hope this helped!
The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on 10 values for the data sets where y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary: Coefficients: Estimate Std. Error t value Pr(> |t|) (Intercept) −90.020 16.702 −5.390 0.000 Length 0.701 0.044 15.798 0.000 Using this information, compute a 95% confidence interval for the slope.
Answer: { 0.5995, 0.8025 }
Step-by-step explanation:
Given that
Estimates Std. Error t value Pr(>/t/)
Intercept: -90.020 16.702 -5.390 0.000
length : 0.701 0.044 15.798 0.000
Now using the given information to compute a 95% confidence interval for the slope:
We use the formula
β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁
So we know that number of values (n) = 10
therefore error of degree of freedom df = n -2 = (10-2) = 8
Level of significance α ( 1 - 0.95 ) = 0.05
so tₐ/₂, ₙ₋₂ = t ₍₀.₀₅/₂, ₁₀₋₂
t ₀.₀₂₅, ₈ = 2.306 (critical value)
From the given table ( regression analysis output)
slope regression β₁ = 0.701
The standard error of the slope is Sβ₁ = 0.044
Let “the maximum size of salmonids consumed by a northern squaw fish” be the response variable and “squawfish length” be the explanatory variable.
The 95% confidence interval for the slope of the regression is:
β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁ = 0.701 ± 2.306 (0.044)
= 0.701 ± 0.101464
= { 0.701 - 0.101464, 0.701 + 0.101464 }
= { 0.599536, 0.802464 } ≈ {0.5995, 0.8025 }
The confidence interval of the slope is (0.599, 0.803)
The sample size is given as:
[tex]\mathbf{n = 10}[/tex]
The confidence interval is given as:
[tex]\mathbf{CI = 95\%}[/tex]
Start by calculating the degrees of freedom
[tex]\mathbf{df = n - 2}[/tex]
So, we have:
[tex]\mathbf{df = 10 - 2}[/tex]
[tex]\mathbf{df = 8}[/tex]
The level of significance is calculated as:
[tex]\mathbf{\alpha = 1 - CI}[/tex]
So, we have:
[tex]\mathbf{\alpha = 1 - 95\%}[/tex]
[tex]\mathbf{\alpha = 0.05}[/tex]
The critical value at 0.05 level of significance and 8 degrees of freedom is:
[tex]\mathbf{t_{\alpha} =2.306}[/tex]
The confidence interval of the slope is then calculated as:
[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]
From the question, we have:
[tex]\mathbf{S\beta_1 = 0.044}[/tex] --- standard error of the slope
[tex]\mathbf{\beta_1 = 0.701}[/tex] -- the slope
So, the equation becomes
[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]
[tex]\mathbf{CI = 0.701 \pm 2.306 \times 0.044}[/tex]
[tex]\mathbf{CI = 0.701 \pm 0.102}[/tex]
Split
[tex]\mathbf{CI = (0.701 - 0.102,0.701 + 0.102)}[/tex]
[tex]\mathbf{CI = (0.599,0.803)}[/tex]
Hence, the confidence interval of the slope is (0.599, 0.803)
Read more about confidence intervals at:
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Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a major. Event B: Randomly select a major who is years old. These events ▼ are are not mutually exclusive, since ▼ every male biology major is 20 years old. it is not possible to select a male biology major who is 20 years old. all biology majors are male. it is possible to select a male biology major who is 20 years old. no biology majors are male. not every male biology major is 20 years old. not all biology majors are male.
Answer:
Event B is mutually exclusive
Step-by-step explanation:
The mutually exclusive events are one which cannot happen together. The observation is made regarding male biology age. It is not possible that all male biology are 20 years old. There can male biology who are less than or greater than 20 years of age. The can not be all together 20 years old. The event is then considered as mutually exclusive.
Given that r = ( 7, 3, 9) and v = ( 3, 7, -9), evaluate r + v
a. (-21,-21,81)
b. (10,10,0)
c. (21,21,-81)
d. (-10,-10,0)
Answer:
b. (10,10,0)
Step-by-step explanation:
r+v can be evaluated if the vectors/matrices have the same dimensions.
These do. They are both 1 by 3 vectors.
Just add first to first in each.
Just add second to second in each.
Just add third to third in each.
Example:
(5,-5,6)+(1,2,3)
=(5+1,-5+2,6+3)
=(6,-3,9)
Done!
In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).
r+v
=(7,3,9)+(3,7,-9)
=(7+3,3+7,9+-9)
=(10,10,0)
Done!
Solve equation :
A=Bt+c for t
Answer:
( A -c) /B =t
Step-by-step explanation:
A=Bt+c
Subtract c from each side
A-c=Bt+c-c
A -c = Bt
Divide each side by B
( A -c) /B = Bt/B
( A -c) /B =t
Answer:
Hey there!
A=Bt+c
A-c=Bt
t=(a-c)/B
Hope this helps :)
What the answer fast now
Answer:
45°
Step-by-step explanation:
This is a special 6 - 6 - 6√2 right triangle with angle measures 45° - 45° - 90°
Answer: m∠R = 45°
Step-by-step explanation:
[tex]6^{2}\ +\ 6^{2} = 72[/tex]
[tex]\frac{\left(6\right)}{\sqrt{72}}=0.7071067812[/tex]
[tex]\sin^{-1}\left(\frac{\left(6\right)}{\sqrt{72}}\right)= 45[/tex]
pls help me help me
Answer:
A
Step-by-step explanation:
For an inequality to have a shaded area above the graph, the variable has to be on the left side of a greater than sign, or a greater than or equal to sign.
A is the only option with one of these signs, so it is the correct answer.
What is the value of x
Answer:
x=7
Step-by-step explanation:
What is the total of 49 1/4+3 3/8
Answer:
52 5/8
Step-by-step explanation:
To add fractions, you have to make sure both fractions have a common denominator.
As you can see, the fractions have different denominators, so to make both denominators 8, we have to multiply 1/4 by two, which gives us 2/8.
Then, we just add like normal!
49 2/8+ 3 3/8 = 52 5/8!
Hope this helped! :)
The equations x + 5 y = 10, 3 x minus y = 1, x minus 5 y = 10, and 3 x + y = 1 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, negative 1) and (1, 2). Blue line goes through (0, 1) and (1, negative 2). Pink line goes through (0, 2), and (2, 1.5). Orange line goes through (negative 2, negative 2.5) and (2, negative 1.5). Which is the approximate solution for the system of equations x + 5 y = 10 and 3 x + y = 1? (–0.3, 2.1) (–0.3, –2.1) (0.9, –1.8) (0.9, 1.8)
Answer:
A: (–0.3, 2.1)
Answer:a
Step-by-step explanation:
Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.)F(x, y) = y cos(x) − xy sin(x), xy + x cos(x) , C is the triangle from (0, 0) to (0, 8) to (2, 0) to (0, 0)
Notice that C has a clockwise orientation. By Green's theorem, we have
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
where D is the triangule region with C as its boundary, given by the set
[tex]D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}[/tex]
So we have
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx[/tex]
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}[/tex]