Answer: ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA = 5/3
Step-by-step explanation:
Given that;
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)
Green's Theorem is given as;
∫c (P(x,y)dx + Q(x,y)dy) = ∫∫ₐ { (-β/βy) P(x,y) + (β/βy) Q(x,y) } dA
Now our P(x,y) = 3y + 7e^(√x) and our Q(x,y) = 8x + 5 cos (y²)
Since we know this, therefore; we substitute
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ { (-β/βy) (3y + 7e^(√x)) + (β/βy) (8x + 5 cos (y²)) } dA
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ ( 8-3) dA
∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA
from the question, our region is defined by a lower bound: y = x² and an upper bound of y = √x
going from x = 0 to x = 1
Now calculating ∫∫ₐ 5dA by means of the description of the region, we say;
∫∫ₐ 5dA = 5¹∫₀ ₓ²∫^(√x) dydx
∫∫ₐ 5dA = 5¹∫₀ (y)∧(y-√x) ∨(y-x²) dx
∫∫ₐ 5dA = 5¹∫₀ (√x-x²) dx
∫∫ₐ 5dA = 5 [ ((x^(3/2))/(3/2)) - x³/3]¹₀ NOW since ∫[f(x)]ⁿ dx = ([f(x)]ⁿ⁺¹ / n+1) + C
then
∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3) - ((0^(3/2))/(3/2)) - 0³ / 3) ]
∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3)
∫∫ₐ 5dA = 5/3
Therefore ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA = 5/3
In this exercise we have to use green's theorem to calculate the values of the curve through the integers, so we will find that:
[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]
First, the integral given in this exercise corresponds to:
[tex]\int\limits_C {((3y+7e{\sqrt{x}} dx) + (8x+5cos(y^2)) } \, dy[/tex]
Green's Theorem is given as;
[tex]\int\limits_C {(P(x,y)dx + Q(x,y)dy)} \, = \int\limits \int\limits_a { (-\beta/ \beta_y) P(x,y) + (\beta/ \beta_y) Q(x,y) } dA \,[/tex]
Now our:
[tex]P(x,y) = 3y + 7e^{(\sqrt{x} )} \\ Q(x,y) = 8x + 5 cos (y^2)[/tex]
Since we know this, therefore; we substitute:
[tex]\int\limits_C {((3y + 7e^{(\sqrt{x} )} dx + (8x + 5 cos (y^2)) dy)} = \int\limits \int\limits_a {(-\beta / \beta_y) (3y + 7e^{(\sqrt{x} )} + (\beta / \beta_y) (8x + 5 cos (y^2))} \, dA\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {( 8-3) dA}\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {5 dA}\\[/tex]
From the question, our region is defined by:
lower bound: [tex]y = x^2[/tex] upper bound: [tex]y = \sqrt{x}[/tex]
Now calculating by means of the description of the region, we say;
[tex]\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 \int\limits^{\sqrt{x} }_{x^2} {x^2} \, dydx\\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {y^{\sqrt{x} } \, dx \\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {{\sqrt{x} -x^2} \, dx\\\int\limits \int\limits_a {5} \, dA = 5 [ ((x^{3/2})/(3/2)) - x^3/3][/tex]
Knowing the formula:
[tex]\int\limits {[f(x)]^n} \, dx = ([f(x)]^{n+1} / n+1) + C[/tex]
Applying the values in the presented formula we find that:
[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]
See more about Green's Theorem at brainly.com/question/15062695
In the problem below, what is the SECOND operation that should be performed:
42 - (28 + 7) + 111
Answer:
Add -28 and -7 (2nd operation)
Step-by-step explanation:
42-(28+7)+111
Step 1: Remove the brackets
42-28-7-11
Step 2: Add 42 and 111( 1st operation ) you can also rewrite to avoid confusion
42+111-28-7
= 153-28-7
Step 3: Add -28 and -7 (2nd operation)
153-28-7
=153-35
Step 4 : Subtract
153-35
=118
Solve for non extraneous solution and show work/check please help i need help asap! Please no fake answers ___ 1√x+2+2=6
Answer:
x=14
Step-by-step explanation:
1[tex]\sqrt{x+2}[/tex] +2 = 6 --------------- put nums on 1 side
1[tex]\sqrt{x+2}[/tex] = 4 -------------------by the way, 1
[tex]\sqrt{x+2}[/tex] =4 ------------- square both sides
x+2 = 16 --------------- subtract 2 from both sides
x = 14
68. What property of real numbers would simplify the following expression: 4+7(x-1) ?
Answer:
7x - 3
hoped i helped
The final expression after applying the distributive property is 7x-3
What Is Distributive Property?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given here: The expression as 4+7(x-1)
The distributive property tells us how to solve expressions in the form of a(b + c).
Now applying distributive property and solving for like terms we get :
4+7(x-1) =4+7x-7
=7x-3
Thus the distributive property rule of real numbers is used to simplify the given expression.
Hence, The final expression after applying the distributive property is 7x-3
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Suppose you are going to graph the data in the table below. What data should be represented on each axis, and what would be the appropriate increments? (2 points) Reporting periods Sales Jan.–Mar., 2010 $100,000 Apr.–Jun., 2010 $55,000 Jul.–Sep., 2010 $45,000 Oct.–Dec., 2010 $110,000 Jan.–Mar., 2011 $330,000 Apr.–Jun., 2011 $800,000 Jul.–Sep., 2011 $242,000 Oct.–Dec., 2011 $150,000
Answer:
Is b
Step-by-step explanation:
Tom can type 120 words in 3 minutes. What is the ratio of words typed to minutes? Question 2 options: A. 1 : 117 B. 1 : 40 C. 40 : 1 D. 117 : 1
Answer:
C
Step-by-step explanation:
Since he writes 120 words in 3 minutes, we know that Tom will write 120 / 3 = 40 words in 1 minute, therefore the ratio is 40 : 1. It's not 1 : 40 because the question is asking for the ratio of words typed to minutes, not minutes to words typed.
My question got deleted so I'll post these into two separate
posts 100 POINTS!
Convert 1 million seconds to years. (Round to 3 decimal places.)
If your teacher is 50 years old, what is their age in seconds?
Convert 46 inches to miles (there are 12 inches in one foot). Round 6 decimal places.
Answer:
see below
Step-by-step explanation:
1 million
1,000,000 seconds * 1 hour/ 3600 seconds * 1 day/ 24 hours * 1 year / 365 days
.031709792 years
Rounding to 3 decimal places
.032 years
50 years * 365 days/ 1 year * 24 hours/ 1 day * 3600 second / 1 hour
1577000000 seconds
46 inches * 1 ft/ 12 inches * 1 mile/5280 ft
0.000726 miles
Convert the following angle to decimal degrees.
a=274° 33' 23"
Answer:
274.556 degrees to the nearest thousandth.
Step-by-step explanation:
33 ' = 33/60 = 0.55 degrees.
23" = 23/60 minutes
= 23/60 / 60 = 0.00639 degrees
So the answer is 274 + 0.55 + 0.00639 degrees
=
274.55639 degrees.
List the following from least to greatest. |71|, |3|, |94|, |-46|
Answer:
Hey there!
From least to greatest, we have |3|, |-46|, |71|, and |94|
Let me know if this helps :)
tyler brought 7/12 pound of trail mix on a camping trip. he ate 4/12 pound of the trail mix. how much trail mix is left
Answer:
Tyler had 7/12 pound of trail mix
He ate 4/12 of it i.e
7/12-4/12=7-4/12
3/12=1/4
He has 1/4 of trial mix left
Solve 3х - х + 2 = 12.
a. -5
b. 4
c. 7
d. 5
Answer:
3x-x+2=12
2x+2=12
2x = 10
x=5
Answer:
d
Step-by-step explanation:
Given
3x - x + 2 = 12, that is
2x + 2 = 12 ( subtract 2 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
Two angles that have the same initial and terminal sides are ---Select--- .
They are called coterminal angles.
Answer:
It's coterminal
Step-by-step explanation:
Same initial
QUSTUN 5
1 2 3 4 5 6
>
>
Dwayne is trying to find the fraction represented by the repeating decimal 0.5. He completes the three
steps shown:
1) Let x = 0.5
2) 10x = 5.5
3)
10x =
5.5
-X =
9x = 5
0.5
What is the purpose of Step 3?
It removes the repeating part of the decimal from the equation.
o It shows that 0.5 is an irrational number.
It puts the fraction in lowest terms.
It shows that 0.5 is a terminating decimal.
Answer:
It removes the repeating part of the decimal from the equation.
Step-by-step explanation:
Described here is the process of converting the repeating decimal fraction into fraction in the form of p/q
1) --------------
x = 0.5555552) --------------
10x = 5.5555553) --------------
10 x - x = 5.555555 - 0.5555559x = 5x = 5/9So the purpose of step 3 here is to remove the repeating part of the decimal from the equation
Correct option is the first one.
Assuming that workers' salaries in your company are uniformly distributed between $15,000 and $40,000 per year, find the probability that a randomly chosen worker earns an annual salary between $20,000 and $35,000.
Answer:
The probability is [tex]P(\$20,000 < X < \$35,000) = 0.6[/tex]
Step-by-step explanation:
From the question we are told that
Workers' salaries in your company are uniformly distributed between $15,000 and $40,000 per year
Generally the probability that a randomly chosen worker earns an annual salary between $20,000 and $35,000 is mathematically represented as
[tex]P(\$20,000 < X \$35,000) = \frac{ 35000 - 20000}{ 40000 - 150000}[/tex]
=> [tex]P(\$20,000 < X < \$35,000) = 0.6[/tex]
Using the uniform distribution, it is found that there is a 0.6 = 60% probability that a randomly chosen worker earns an annual salary between $20,000 and $35,000.
An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
In this problem, uniformly distributed between $15,000 and $40,000, hence [tex]a = 15, b = 40[/tex].
The desired probability is:
[tex]P(20 \leq X \leq 35) = \frac{35 - 20}{40 - 15} = 0.6[/tex]
0.6 = 60% probability that a randomly chosen worker earns an annual salary between $20,000 and $35,000.
A similar problem is given at https://brainly.com/question/13547683
According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled. What is the probability percentage that 121 or more Americans in the survey are afraid to fly
Answer:
0.137.
Step-by-step explanation:
Given that
Sample size = 1100
Afraid to fly = 10 %
Mean = n x p
Mean = 1100 x 0.1 = 110
Variance = n p q
Variance = 1100 x 0.1 x 0.9 = 99
Standard deviation = [tex]\sqrt{n\times p\times q}[/tex]
S.D.=[tex]\sqrt{1100\times 0.1\times 0.9}[/tex]
S.D.=9.94
By using Normal distribution
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
[tex]Z=\dfrac{121-110}{9.94}[/tex]
Z=1.16
[tex]P(X>121)=P(Z>1.16)=1-0.8643\\P(X>121)=0.137\\[/tex]
Thus the answer will be 0.137.
Solve 64^x = 16^(x−1). (1 point) Select one: a. x = −2 b. x = −1 c. x = negative 1 over 4 d. x = negative 1 over 3
Answer:
a. x = -2
Step-by-step explanation:
64ˣ = 16⁽ˣ⁻¹)
64 = 4³
16 = 4²
4³⁽ˣ⁾ = 4²⁽ˣ⁻¹)
4³ˣ = 4²ˣ⁻²
3x = 2x - 2
x = -2
Answer:
[tex]\huge \boxed{x=-2}[/tex]
Step-by-step explanation:
64^x = 16^(x-1)
Rewrite the bases with base of 4.
(4^3)^x = (4^2)^(x-1)
Multiply exponents.
4^(3x) = 4^(2(x-1))
Cancel same bases.
3x = 2(x-1)
Expand brackets.
3x = 2x - 2
Subtract 2x from both sides.
x = -2
Solve for x: 2/3=8/x+6
Answer:
x = 6
Step-by-step explanation:
2/3=8/x+6
Using cross products
2 * (x+6) = 3*8
2(x+6) = 24
Divide by 2
x+6 =12
Subtract 6
x = 6
Use the coordinate plane to plot the point (3, 6). Then complete the statements that explain how to plot the point. Start at the ____ Move 3 units ____ Move 6 units ____ Plot a point ____
Answer:
Use the coordinate plane to plot the point (3, 6). Then complete the statements that explain how to plot the point. Start at the origin. Move 3 units right Move 6 units up Plot a point there.
Step-by-step explanation:
To plot the point, start at the origin. Move 3 units right and Move 6 units upwards to plot a point (3 6).
What is a coordinate plane ?A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.
The given point is (3, 6).
The coordinate plane to plot the point (3, 6) is shown below.
To plot the graph of point (3, 6) on coordinate plane,
Start at the origin. Move 3 units right and Move 6 units upwards to plot a point (3 6).
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Given the original number n. Multiply the number by 9. Add 99. Divide this sum by 9. Subtract the original number, n, from the quotient.
Answer:
11
Step-by-step explanation:
Hello,
Given the original number n.
[tex]\large \boxed{n}[/tex]
Multiply the number by 9.
[tex]\large \boxed{9n}[/tex]
Add 99.
[tex]\large \boxed{9n+99}[/tex]
Divide this sum by 9.
[tex]\large \boxed{\dfrac{9n+99}{9}=n+11}[/tex]
Subtract the original number, n, from the quotient.
[tex]\large \boxed{n+11-n=11}[/tex]
Thank you.
A plan traveled for a total of 2,773 miles over the course of 8 hours. Heading south, the plan traveled at an average speed of 344 miles per hour and heading west. It traveled at an average speed of 351 miles per hour. For how many hours was the plane heading south?
Answer:
5 hours
Step-by-step explanation:
Let s and w represent hours spent traveling south and west, respectively. The problem statement tells us ...
s + w = 8 . . . . . . total trip time
344s + 351w = 2773 . . . . total mileage (using d = s·t)
By Cramer's rule, we can find the value of s as ...
s = (1(2773) -351(8))/(1(344) -351(1)) = -35/-7 = 5
The plane was heading south for 5 hours.
_____
Comment on Cramer's rule
For the equations ...
ax +by = c
dx +ey = f
The solution for x can be found to be ...
x = (bf-ec)/(bd-ea)
Similarly, the solution for y is ...
y = (cd-fa)/(bd-ea)
Is a temperature of 35 degrees Fahrenheit as cold as a temperature of -35 degrees Fahrenheit?
Answer:
Step-by-step explanation:
Definitely not. -35 degrees is far below freezing (+32 degrees). On the other hand, +35 degrees is very warm indeed.
No, the temperature of 35 degrees Fahrenheit is not as cold as a temperature of -35 degrees Fahrenheit.
We have temperature in degrees Fahrenheit.
We have to investigate - " Is a temperature of 35 degrees Fahrenheit as cold as a temperature of -35 degrees Fahrenheit ".
What is the formula to convert Fahrenheit to degrees Celsius ?The formula is -
(°F − 32) × 5/9 = °C
According to the question -
Assume that -
A = 35°F = 1667 °C
B = -35°F = -37.2222 °C
The temperature 35°F represents very very high temperature (hot) whereas the temperature -35°F represents very very low temperature (cold).
Hence, No, the temperature of 35 degrees Fahrenheit is not as cold as a temperature of -35 degrees Fahrenheit.
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what number goes on top
I'm not sure what you're really talking about.
But I think you are talking about fractions.
In fractions there are two places
The number that goes on the top is numerator.
If 3a +5b =10 and 5a +3b =30 what is the average of a and b?
Hello, please consider the following.
[tex]3a+5b + 5a + 3b = 8(a+b)=10+30=40\\\\a+b=\dfrac{40}{8}=5[/tex]
And the average is
[tex]\dfrac{a+b}{2}\boxed{=\dfrac{5}{2}}[/tex]
Thank you.
GRIDDED RESPONSE Mark got 18 out of 25
questions correct on his science test. What percent
of the questions did he get correct?
he got 0.08 percent questions correct
Answer:
72%
Step-by-step explanation:
A percentage is a number out of 100. For example, 32/100 is 32%. What you want to do with percentages is multiply the denominator of a fraction so it becomes 100 and multiply that same number to the numerator. Sort of like a ratio!
If Mark got 18/25, we can multiply 25 by 4 to get 100 as the denominator.
Since you multiplied the denominator by 4, you have to multiply the numerator by 4 as well.
18 times 4= 72. So the numerator is 72 and the denominator is 100. The fraction is 72/100, which is 72% since it is out of 100.
Given that 2^x = 7, find the value of 4^{x-1}.
Answer:
[tex] {4}^{x - 1} = \frac{49}{4} [/tex]
Step-by-step explanation:
My work is in the attachment but I essentially used a hefty bit of Algebraic manipulation to turn 2^x into 4^(x-1) and then isolating that bit.
Comment if you have any questions.
Answer:
49/4
Step-by-step explanation:
4^x-1 = (2^x)^2/4 = 7^2/4 = 49/4
given that cos 60°= sin 30°= 1/2 and cos 30°= sin 60°= √3/2, evaluate tan 60°-1/ 1- tan 30°
Answer:
answer is on the sheet photo
7 1/8 + 7 1/13= Give my answer as a mixed number
Answer:
[see below]
Step-by-step explanation:
[tex]7(1/8)+7(1/13)\\\\\text{Add Whole Numbers: }\\\\7 + 7 = 14\\\\\text {Add fractions: }\\\\ (1/8)+(1/13)\\\\LCM (8, 13): 104\\\\(13/104)+(8/104)\\\\(21/104)\\\\\\\text{Combine: }\\\\14 + (21/104)\\\\\boxed{14\frac{21}{104}}[/tex]
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed {14\frac{35}{104}}[/tex]
Step 1 : Solving the fraction parts.
[tex]\frac{71}{8} + \frac{71}{13} = ?[/tex]
Find the LCD of 71/8 and 71/13 and rewrite to solve with the equivalent fractions.
LCD = 104
[tex]\frac{923}{104} + \frac{568}{104} = \frac{1491}{104}[/tex]
Simplifying the fraction part, 1491/104,
[tex]\frac{1491}{104} = 14\frac{35}{104}[/tex]
____________________
Solution by Formulas
____________________
Using the given fractions
[tex]\frac{71}{8} + \frac{71}{13}[/tex]
Applying the fractions formula for addition,
[tex]= \frac{(71 . 13) + ( 71 . 8 ) }{8 . 13}[/tex]
[tex]= \frac{923 . 568}{104}[/tex]
[tex]= \frac{1491}{104}[/tex]
Simplifying 1491/104, the answer is:
[tex]\boxed {14\frac{35}{104}}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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Have a great day/night!
❀*May*❀
Suppose you start with a full tank of gas (18 gallons) in your truck. After driving 6 hours, you now have 8 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is your truck using gas
Step-by-step explanation:
y is the number of gallons left in the tank.
x is the number of hours you have been driving
Rate of consumption of gas
= (18 - y / x)
= 5 / 3 gallon per hour
= 6.309 L / hr
The rate at which your truck is using gas is 5/3 gallons per hour.
What is rate at which your truck is using gas?The rate at which your truck is using gas is calculated as follows;
Given that after 6 hours of driving, you have 8 gallons left in the tank, we can set up the following equation using the two given data points:
(Initial gallons - Remaining gallons) / (Initial time - Time elapsed) = (Change in gallons) / (Change in time)
The equation becomes;
Rate = (18 gallons - 8 gallons) / (6 hours - 0 hours)
Rate = (18 - 8) / 6
Simplifying this equation, we get:
Rate = 10 / 6
Rate = 5 / 3
Therefore, the rate at which your truck is using gas is 5/3 gallons per hour.
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The sales tax in your city is 8.8% an item costs $63 before tax how much tax would you pay on that item
Answer:
68.67
Step-by-step explanation:
Round 8.8% to 9%.
multiply 63.00*0.09=68.67
Answer:
$5.54
Step-by-step explanation:
how i found it out
63×.088=5.54
Which scenario is best represented by the graph
Answer:
A taxi travels at a constant speed of 50 miles per hour.
Hope this helps!
What is the solution to X-7 less than or equal to -4
Answer:
x ≤ 3
we have to transpose -7 from left to right