Just making sure my answers are right. Please show the steps clearly. Thank you so much
Answers
Answer: See below
Step-by-step explanation:
A.
Let's split the integral into two parts, by the Sum Rule.
[tex]\int\limits {x-4x^3} \, dx[/tex] [split into 2 integrals]
[tex]\int\limits {x} \, dx -\int\limits {4x^3} \, dx[/tex] [solve integral for each part]
[tex]\frac{1}{2} x^2-x^4+C[/tex] [Remember, we need to add C for constant]
-------------------------------------------------------------------------------------------------
B.
[tex]\int\limits {\frac{1+x}{\sqrt{x} } } \, dx[/tex] [expand into 2 integrals]
[tex]\int\limits {\frac{1}{\sqrt{x} } } \, dx +\int\limits {\frac{x}{\sqrt{x} } } \, dx[/tex] [simplify second integral]
[tex]\int\limits {\frac{1}{\sqrt{x} } } \, dx +\int\limits {\sqrt{x} } \, dx[/tex] [solve integral for each part]
[tex]2\sqrt{x} +\frac{2}{3}x^3^/^2+C[/tex]
-------------------------------------------------------------------------------------------------
C.
[tex]\int\limits^4_0 {z(z^1^/^2-z^-^1^/^2)} \, dz[/tex] [distribute]
[tex]\int\limits^4_0 {z^3^/^2-z^1^/^2} \, dz[/tex] [split into 2 integrals]
[tex]\int\limits^4_0 {z^3^/^2} \, dz -\int\limits^4_0 {z^1^/^2} \, dxz[/tex] [solve integral for each part]
[tex]\frac{64}{5} -\frac{16}{3}[/tex] [solve]
[tex]\frac{112}{15}[/tex]
-------------------------------------------------------------------------------------------------
D. *Note: I can't put -1 for the interval, but know that the 1 on the bottom is supposed to be -1.
[tex]\int\limits^1_1 {(1+u)(1-u)} \, du[/tex] [expand]
[tex]\int\limits^1_1 {1-u^2} \, du[/tex] [split into 2 integrals]
[tex]\int\limits^1_1 {1} \, du-\int\limits^1_1 {u^2} \, du[/tex] [solve integral for each part]
[tex]2-\frac{2}{3}[/tex] [solve]
[tex]\frac{4}{3}[/tex]
Related Questions
I WILL GIVE THE BRAINIEST
Which of the following could be a rational number?
A. the product of two irrational numbers.
B. the sum of two irrational numbers.
C. the product of a rational number and an irrational number.
D.the sum of a rational number and an irrational number
Answers
Answer:
A.
Step-by-step explanation:
the product of two irrational numbers
Answer:
the answer is A
Step-by-step explanation:
A. the product of two irrational numbers.
I need help ASAP and I need to show my work
Answers
Answer:
Hey there!
Total students: 7+9+5+3+12=36
Students that like math: 7
7/36=19.4% of students like math.
Let me know if this helps :)
Answer:
19% (Math)
Step-by-step explanation:
7 divide by total number of students (36) X100% =19%
help with math homework?
Answers
Answer:
The range of the curve is [tex][-9,9][/tex].
Step-by-step explanation:
The domain of the curve corresponds to the values on horizontal axis (x-Axis), where the range of curve corresponds to the values on vertical axis (y-Axis). In addition, the curve is continuous in [tex](-5, 8)[/tex], so that images exists within interval.
The range of the curve is [tex][-9,9][/tex].
Tell which angles are congruent to the given angle measure.
Answers
Answer:
2, 5, & 6
Step-by-step explanation:
2, because it’s the opposite angle.
5, because it’s parallel.
6, because it’s opposite to 5.
2, 5, & 6 all equal 100°.
1, 3, 4, & 7 all equal 80°.
The angles formed that are congruent to angle measure of 100 degrees when transversal t intersects parallel lines m and n are:
<2, <5, and <6.Angle measuring 100 degrees is the given angle measure formed at the point of intersection between line m and transversal t.
Thus, angles that are congruent to 100 degrees will be equal in measure to 100 degrees.
The following are angles congruent to 100 degrees.
<2 is congruent to 100 degrees (vertically opposite angles are congruent).
<5 is congruent to 100 degrees (corresponding angles are congruent).
<6 is congruent to 100 degrees (alternate exterior angles are congruent).
Therefore, the angles formed that are congruent to angle measure of 100 degrees when transversal t intersects parallel lines m and n are:
<2, <5, and <6.Learn more here:
https://brainly.com/question/15937977
Matteo makes raspberry punch. The table shows how many parts ginger ale and raspberry juice to use for a batch. Raspberry Punch Parts Ginger Ale 2 Parts Raspberry Juice 3 Matteo decides to add one part of raspberry juice. What is the new ratio of ginger ale to raspberry juice? 2 parts ginger ale to 3 parts raspberry juice 2 parts ginger ale to 4 parts raspberry juice 3 parts ginger ale to 3 parts raspberry juice 3 parts ginger ale to 4 parts raspberry juice
Answers
Answer:
Answer: There is 1 1/2 times more juice than ginger ale; there is 2/3 as much ginger ale as there is punch.
Step-by-step explanation:
Answer:
Answer A:
Step-by-step explanation:
2 parts ginger ale to 3 parts raspberry juice.
A polygon is shown:
The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)
Answers
Answer:
10 square units
Step-by-step explanation:
let f (x) =- 3x and g (x) = 2x - 1 Find the following f (x) + g (x) Pleas show steps
Answers
Answer:
See below.
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=-3x\text{ and } g(x)=2x-1[/tex]
And we want to find f(x) + g(x).
So, substitute:
[tex]f(x)+g(x)\\=(-3x)+(2x-1)[/tex]
Combine like terms:
[tex]=(-3x+2x)+(-1)[/tex]
Simplify:
[tex]=-x-1[/tex]
So:
[tex]f(x)+g(x)=-x-1[/tex]
Explain the order of operations you would use to evaluate (284) • 5-6+42. Then evaluate it.
Answers
Answer:
1456
Step-by-step explanation:
If there are parentheses what is inside comes first, then multiplication or division, last is addition and subtraction. If you have multiple division or multiplication you go in order left to right. Once it's down to addition and subtraction you also go left to right.
First we multiply 284 * 5 = 1420
Now we go in order.
1420 - 6 + 42
1414 + 42
1414 + 42 = 1456
NED THIS AND HOW U GOT THE ANSWER find the measure of the angle greater than BFX using the figure below
Answers
Answer: 140°
Step-by-step explanation:
If you look at ∠BXF, you can see that F is at the base of the inner semi circle. Going left, you can see that it stops at 140. Now, we know that m∠BXF is 140°.
Answer:
m∠BXF = 140°
Step-by-step explanation:
The symbol "<" is "greater than." The symbol "∠" is "angle." When used as "m∠", it refers to "the measure of angle ...".
Here, you're asked for the measure of angle BXF.
You can see that it is an obtuse angle, so will have a measure greater than 90°. The protractor has two scales: one measuring angles counterclockwise, and the other measuring angles clockwise. Ray XF is aligned with the 0 on the inner (counterclockwise) scale, so the angle measure is found where ray XB crosses that scale.
Ray XB crosses the inner scale of the protractor at 140, so ...
m∠BXF = 140°.
Let Y be a random variable. In a population, mu Subscript Upper Y Baseline equals 65μY=65 and sigma Subscript Upper Y Superscript 2 Baseline equals 49σ2Y=49. Use the central limit theorem to answer the following questions. (Note: any intermediate results should be rounded to four decimal places)
In a random sample of size n = 69, find Pr(Y <68) =
In a random sample of size n = 124, find Pr (68< Y <69)=
In a random sample of size n = 196, find Pr (Y >66)=
Answers
Answer:
a. [tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]
b. [tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]
c. [tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]
Step-by-step explanation:
Given that ;
Let Y be a random variable In a population, where:
mean [tex]\mu_y[/tex] = 65
[tex]\sigma^2_y[/tex] = 49
standard deviation σ = [tex]\sqrt{49}[/tex] = 7
The objective is to determine the following :
In a random sample of size n = 69, find Pr(Y <68) =
Using the Central limit theorem
[tex]P(\overline x < 68) = \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{68 - \mu }{\dfrac{\sigma}{\sqrt{n}}} } \end {pmatrix}[/tex]
[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{68 - 65 }{\dfrac{7}{\sqrt{69}}} } \end {pmatrix}[/tex]
[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{3 }{\dfrac{7}{8.3066}} } \end {pmatrix}[/tex]
[tex]P(\overline x < 68) = (Z < 3.5599 )[/tex]
From the z tables:
[tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]
In a random sample of size n = 124, find Pr (68< Y <69)=
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{ 69 - \mu}{\dfrac{\sigma}{\sqrt{n}}} \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- 65}{\dfrac{7}{\sqrt{124}}} < Z < \dfrac{ 69 - 65}{\dfrac{7}{\sqrt{124}}} \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{3}{\dfrac{7}{11.1355}} < Z < \dfrac{ 4}{\dfrac{7}{11.1355}} \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} 4.7724 < Z < 6.3631 \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P( Z < 6.3631 ) - P ( Z < 4.7724 )[/tex]
From z tables
[tex]P(68 < \overline x < 69 ) = 0.9999 - 0.9999[/tex]
[tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]
In a random sample of size n = 196, find Pr (Y >66)=
[tex]P ( \overline x > 66 ) = P ( \dfrac{\overline x -\mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{66 -\mu }{\dfrac{\sigma}{\sqrt{n}}})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{66 - 65 }{\dfrac{7}{\sqrt{196}}})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{1 }{\dfrac{7}{14}})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{14 }{7})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z>2)[/tex]
[tex]P ( \overline x > 66 ) = 1 - P ( Z<2)[/tex]
from z tables
[tex]P ( \overline x > 66 ) = 1 - 0.9773[/tex]
[tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]
A family is planning a three-week vacation for which they will drive across the country. They have a van that gets 12 miles per gallon, and they have a sedan that gets 36 miles per gallon. How much more will they pay for gasoline if they take the van? (Assume that the family will drive 2500 miles and that gas costs $2.50 a gallon. Round your answers to the nearest cent.)
Answers
Answer:
The family will pay 34722 cents more if they take the van
Step-by-step explanation:
Given
Van = 12 miles per gallon
Sedan = 36 miles per gallon
Distance = 2500 miles
Gas = $2.50 per gallon
First, we need to determine the number of gallons that'll be used by both vehicles
This is done by dividing total distance by number of miles per gallon
[tex]Van = \frac{2500}{12} \ gallon[/tex]
[tex]Sedan = \frac{2500}{36}\ gallon[/tex]
Next, is to multiply this by the cost of gas per gallon;
This gives the total spendable amount on both vehicles
[tex]Van = \frac{2500}{12} * \$2.50[/tex]
[tex]Van = \frac{\$6250}{12}[/tex]
[tex]Van = \$520.833[/tex]
[tex]Sedan = \frac{2500}{36}* \$2.50[/tex]
[tex]Sedan = \frac{\$6250}{36}[/tex]
[tex]Sedan = \$173.611[/tex]
Next is to get the difference between these amounts
[tex]Difference = \$520.833 - \$173.611[/tex]
[tex]Difference = \$347.222[/tex]
Multiply by 100 to convert to cents
[tex]Difference = 347.222 * 100 cents[/tex]
[tex]Difference = 34722.2 \ cents[/tex]
[tex]Difference = 34722\ cents[/tex] (Approximated)
Hence;
The family will pay 34722 cents more if they take the van
What is the solution Set to 2a+6=2a+5+1
Answers
Answer:
6=6
True for all a
Step-by-step explanation:
[tex]2a+6=2a+5+1\\\mathrm{Subtract\:}2a\mathrm{\:from\:both\:sides}\\\mathrm{Simplify}\\6=5+1\\\mathrm{Simplify\:}5+1:\quad 6\\\\6 = 6[/tex]
Answer:
infinite solutions
Step-by-step explanation:
2a+6=2a+5+1
Combine like terms
2a+6 = 2a+6
Subtract 2a from each side
6 =6
Since this is always true, we have infinite solutions
What is the number in standard form? 5.708 • 10^-8 Drag the answer into the box to match the number. 100 POINTS!!! HELP ME!!!
Answers
Answer:
.00000005708 is your answer. If it's asking you to solve the problem, 49.08
Answer:
[tex]\Huge \boxed{0.00000005708}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]5.708 \cdot 10^{-8}[/tex]
Solving for exponent and evaluating:
[tex]\displaystyle 5.708 \cdot \frac{1}{10^8 }[/tex]
[tex]\displaystyle \frac{5.708}{10^8 }[/tex]
[tex]\Rightarrow \ \displaystyle \frac{5.708}{100000000}[/tex]
The decimal place moves 8 units to the left side.
[tex]\Rightarrow \ 0.00000005708[/tex]
[tex]\rule[225]{225}{2}[/tex]
A triangle has vertices at F (8, 3), G (3, 5), and H (1, 7). What are the coordinates of each vertex if the triangle is rotated 180° about the origin counterclockwise?
Question 1 options:
F ¢(8, 3), G¢(-3, 5), H ¢(-1, -7)
F ¢(8, -3), G ¢(3, -5), H ¢(1, -7)
F ¢(-8, 3), G¢(-3, 5), H ¢(-1, 7)
F ¢(-8, -3), G ¢(-3, -5), H ¢(-1, -7)
Answers
Answer: F (-8, -3), G (-3, -5) and H (-1, -7)
Step-by-step explanation:
A rotation of 180° around the origin is equivalent to a reflection over the x-axis, and then another reflection over the y-axis.
Then, if we have a point (x, y) and we do a rotation of 180°, the point will transform into (-x, -y)
Then if at the start the vertices of the triangle are:
F (8, 3), G (3, 5), and H (1, 7).
After a rotation of 180°, the vertices will be:
F (-8, -3), G (-3, -5) and H (-1, -7)
The correct option is the last one.
Surface area of this figure
Answers
Answer:
23
Step-by-step explanation:
you add 10m(h) plus 8m(w) plus 15m(l)
Answer:
523.1m²
Step-by-step explanation:
Triangle: 1/2bh=1/2(4)(10)=20x2=40 each
Bottom Rectangle: 15x8=120
Side Rectangles: Since the side is a hypotenuse of a right triangle, it’s the square root of 10²+4²=√116=10.77. 10.77x15=161.55
So the total surface area would be 40+40+120+161.55+161.55=523.1m²
The Perimeter of a rectangle is 12 meters if the length of the rectangle is 5 meters what is the width
Answers
Answer:
1 meter wide
Step-by-step explanation:
5+5=10
2/2=1
Answer:
1
Step-by-step explanation:
Andre says that x is 7 becuase he can move the two 1s with the x to the other side. True or false
I will mark you brainiest
Answers
Answer:
False!
Step-by-step explanation:It is not possible.
Answer:
False
Step-by-step explanation: there is no possible way
plz brainliest
Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2∕9.6 = 21.6∕28.8?
Answers
Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2 ∕ 9.6 = 21.6 ∕ 28.8?
a. 7.2 ⋅ 9.6 = 21.6 ⋅ 28.8
b. 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2
c. 7.2 ⋅ 21.6 = 28.8 ⋅ 9.6
d. 7.2 ⋅ 28.8 = 21.6 ⋅ 28.8
Answer:
b. 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2
Step-by-step explanation:
When a proportion say a/b = c/d is given, the outer terms are called the extremes while the inner/middle terms are called the means.
In the case of a / b = c / d,
the outer terms are a and d
the inner terms are b and c
Often times, we find the cross products of the proportion to test whether the two ratios in the proportion are equal. To do that, we find the product of the extremes and equate it to the product of the means.
In the case of a / b = c / d,
the cross products are a x d and b x c
So if a x d = b x c, then a/b = c/d is a true proportion.
Now to the question;
Given proportion: 7.2 / 9.6 = 21.6 / 28.8
Extremes = 7.2 and 28.8
Means = 9.6 and 21.6
The correct multiplication of the means and extremes is therefore
9.6 x 21.6 = 7.2 x 28.8
or
9.6 · 21.6 = 7.2 · 28.8
i need help with number 4
Answers
Answer:
x = 9, AR = 25 , AM = 40
Step-by-step explanation:
Since AM = AR + RM and AM also = 7x-23
7x - 23 = (2x + 7) + 15
7x - 23 = 2x + 22
+23 +23
7x = 2x + 45
-2x -2x
5x = 45
x = 9
Now plug x = 9 into 2x + 7 to find AR
AR = 2x + 7
= 2 (9) + 7
= 18 + 7
AR = 25
Now to find AM plug x = 9 into 7x - 23
AM = 7x - 23
= 7 (9) - 23
= 63 - 23
AM = 40
To double check, we already know that RM = 15, so add AR + RM to find AM
AM = 25 + 15
AM = 40
Answer:
9 = x
AR = 25
AM = 40
Step-by-step explanation:
AR + RM = AM
2x+7 +15 = 7x - 23
Combine like terms
2x+22 = 7x -23
Subtract 2x from each side
2x+22 -2x = 7x-2x -23
22 = 5x - 23
Add 23 to each side
22+23 = 5x-23+23
45 = 5x
Divide each side by 5
45/5 = 5x/5
9 = x
AR = 2x+7 = 2*9 +7 = 18+7 = 25
AM = 7x-23 = 7*9 -23 = 63-23 = 40
What is 3/12 in reduced form.
Answers
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
To simplify a number, you have to find the greatest common factor (of the numerator and the denominator) and divide each number by the greatest common factor.
The greatest common factor of 3 and 12 is 3.
Now divide each 3 and 12 by 3.
3 ÷ 3 = 1
12 ÷ 3 = 4
Now the numerator is 1 and the denominator is 4.
3/12 in reduced form is 1/4.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Answer:
3/12 in reduced form is 1/4
Step-by-step explanation:
find GCF for 3 and 12 which is 3 . step 2 divide numerator and denominator by GCd which is 3 and rewrite the fraction = (3/3) / (12/3) which equals 1/4. Thus 1/4 is the simplified fraction for 3/12 your welcome
17. x^2 + 2x + 1
O A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
O B. This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
C. This polynomial could be factored only by using the perfect squares method.
O D. This polynomial could be factored only by using the difference of squares method.
E. This polynomial could be factored by using grouping or the perfect squares methods.
O F. This polynomial cannot be factored by any of the methods used in this lesson.
Answers
Answer:
E. This polynomial could be factored by using grouping or the perfect squares methods.
Step-by-step explanation:
x^2 + 2x + 1
There is no greatest common factor
This is a perfect square
a^2 + 2ab+ b^2 = ( x+1)^2
We can factor this by grouping
x^2 + 2x + 1
(x^2 +x) + (x+1)
x( x+1) + x+1
Factor out x+1
( x+1) ( x+1)
This is not the difference of squares since there is no subtraction
the cube of the sum of 4 and 9 times x divided by the product of 5 times x and the difference of x and 1
Answers
Answer:
Step-by-step explanation:
(4 + 9x)^3 represents "the cube of the sum of 4 and 9 times x"
and if we divide by "the product of 5 times x and the difference of x and 1," we get
(4 + 9x)^3
-----------------------
5x(x - 1)
What exactly do you need to know, or to do?
A ladder leans against the side of a house. The angle of elevation of the ladder is 65, and the top of the ladder is 13 from the ground. Find the length of the ladder. Round your answer to the nearest tenth.
Answers
Answer:
SOHCAHTOA.
we have to use SOH(Sin) here because the theta is 65° and the opposite is 13 while the hypotenuse is x.
which is Sin 65°=13/x.
xSin65°=13.
0.906307787x=13.
x=13/0.9063=14.34403619~14.
Write an equation that represents the perimeter of the rectangle. The length of a rectangle is 4 feet less than twice its width, while the perimeter is 15.
Answers
Answer:
Equation: 7.5 = ((2b-4) + b)length = 3.6667 ftwidth = 3.8333 ftStep-by-step explanation:
perimeter = 2(length+width)
then:
15 = 2(a+b)
a = 2b - 4
a = length
b = width
solve:
15/2 = (a+b)
7.5 = ((2b-4) + b) ⇒ Equation that represents the perimeter of the
rectangle)
7.5 = 3b -4
7.5+4 = 3b
11.5 = 3b
b = 11.5/3
b = 3.8333
a = 2b - 4
a = 2*3.8333 - 4
a = 3.6667
Check:
15 = 2(3.8333 + 3.6667)
15 = 2*7.5
Solve the equation 6x + 2x - 5= 19
Answers
Answer:
x = 3
Step-by-step explanation:
6x + 2x - 5= 19
8x -5 = 19
8x = 24
x = 3
Answer:
x = 3
Step-by-step explanation:
6x + 2x - 5 = 19
Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, combine like terms:
(6x + 2x) - 5 = 19
(8x) - 5 = 19
Next, isolate the variable, x. First, add 5 to both sides:
8x - 5 (+5) = 19 (+5)
8x = 19 + 5
8x = 24
Next, divide 8 from both sides:
(8x)/8 = (24)/8
x = 24/8
x = 3
3 is your answer for x.
~
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c? One-half c plus 1 equals 6 One-half c minus 1 equals 6 One-half c plus 6 equals 1 One-half c minus 6 equals 1
Answers
Answer:
The equation used to solve Carey's hourly rate is:
1 + (c/2) = 6
Step-by-step explanation:
Answer:
The equation used to solve Carey's hourly rate is:
1 + (c/2) = 6
Step-by-step explanation:
edg2020
Plz Help!!!!!!!!!
15. Men need to intake between 2200 and 2800 calories daily. Women need 600 fewer calories than this. Write and solve an inequality to discover how many calories women should be taking in per day.
A. 2200 x < 2800
B. 2200 > x < 2800
C. 600 < x < 1200
D. 1600 < x < 2800
E. 1600 < x < 2200
F. 2800 < x < 3200
Answers
Answer:
A
Step-by-step explanation:
Lines L and M are parallel.
L
3/4
2/5
1/6
38° 7
-M
Find : m_3
belongs in the green box. [?]
?
o
Entor
Answers
Step-by-step explanation:
Hey, there!
Let's simply solve it.
As there is given that L and M are parallel. Use all the condition or properties of parallel lines.
Here use:
vertically opposite angle. coointerior angles sum is 180°.Now,
angle 6= 38° { Vertically opposite angle}.
angle 6 + angle 5 = 180° { as sum of coointerior angles are equal to 180°}
38°+angle 5 = 180°
or, angke 5 = 180°-38°
Therefore, angle 5 = 142°
Now, angle 3 = angle 5 { Vertically opposite angle}
Therefore, the measure of angle 3 is 142°.
[tex]hope \: it \: helps...[/tex]
Answer: 142
Step-by-step explanation:
Name the 5 ways/methods/techniques we can use to find a limit.
Answers
Answer:
you have four techniques to choose from: plugging in the x value, factoring, rationalizing the numerator, and finding the lowest common denominator.
hope that helps : )
Use Stokes' Theorem to evaluate
∫
C
F � dr
where F(x, y, z) = x2yi + 1/3x3j + xyk and C is the curve of intersection of the hyperbolic paraboloid z = y2 ? x2
and the cylinder x2 + y2 = 1 oriented counterclockwise as viewed from above.
Find parametric equations for C,Let x and y be in terms of t where
0 ? t ? 2?
Answers
Answer:
[tex]\int_C F . dr = \pi[/tex]
[tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]
Step-by-step explanation:
Given that:
[tex]F(x,y,z) = x^2yi + \dfrac{1}{3}x^3j +xyk[/tex]
Here C is the curve of intersection of the hyperbolic parabolic [tex]z = y^2 - x^2[/tex] and the cylinder [tex]x^2 +y^2 =1[/tex]
Using Stokes' Theorem
[tex]\int_C F . dr =\int \int \limits_s \ curl \ F. \ds[/tex]
From above ;
S = the region under the surface [tex]z = y^2 -x^2[/tex] and above the circle [tex]x^2+y^2 =1[/tex]
Suppose, we consider [tex]f(x,y,z) =z-y^2+x^2[/tex]
therefore, S will be the level curve of f(x,y,z) = 0
Recall that:
[tex]\bigtriangledown f (x,y,z)[/tex] is always normal to the surface S at the point (x,y,z).
∴
This implies that the unit vector [tex]n = \dfrac{\bigtriangledown f}{|| \bigtriangledown ||}[/tex]
So [tex]\bigtriangledown f = <2x, -2y,1 >[/tex]
Also, [tex]|| \bigtriangledown f ||= \sqrt{4x^2+4y^2+1}[/tex]
Similarly ;
[tex]curl \ F = \begin {vmatrix} \begin{array} {ccc}{\dfrac{\partial }{\partial x} }&{\dfrac{\partial }{\partial y} }& {\dfrac{\partial }{\partial z} }\\ \\ x^2y& \dfrac{1}{3}x^3&xy \end {array} \end{vmatrix}[/tex]
[tex]curl \ F = \langle x ,-y,0 \rangle[/tex]
Then:
[tex]\int \int_s curl \ F .ds = \int \int_s curl \ F .nds[/tex]
[tex]\int \int_s curl \ F .ds = \iint_D curl \ F \dfrac{\bigtriangledown f}{ || \bigtriangledown f||} \sqrt{ (\dfrac{\partial z}{\partial x }^2) + \dfrac{\partial z}{\partial x }^2)+1 } \ dA[/tex]
[tex]\int \int_s curl \ F .ds = \iint_D \dfrac{\langle x,-y,0 \rangle * \langle 2x,-2y,1 \rangle }{\sqrt{4x^2 +4y^2 +1 }} \times \sqrt{4x^2 +4y^2 +1 }\ dA[/tex]
[tex]\int \int_s curl \ F .ds = \iint_D (2x^2 + 2y^2) \ dA[/tex]
[tex]\int \int_s curl \ F .ds = 2 \iint_D (x^2 + y^2) \ dA[/tex]
[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]
converting the integral to polar coordinates
This implies that:
[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]
⇒ [tex]\int_C F . dr = 2(\theta) ^{2 \pi} _{0} \begin {pmatrix} \dfrac{r^4}{4}^ \end {pmatrix}^1_0[/tex]
[tex]\int_C F . dr = 2(2 \pi) (\dfrac{1}{4})[/tex]
[tex]\int_C F . dr =(4 \pi) (\dfrac{1}{4})[/tex]
[tex]\int_C F . dr = \pi[/tex]
Therefore, the value of [tex]\int_C F . dr = \pi[/tex]
The parametric equations for the curve of intersection of the hyperbolic paraboloid can be expressed as the equations of the plane and cylinder in parametric form . i.e
[tex]z = y^2 - x^2 \ such \ that:\ x=x , y=y , z = y^2 - x^2[/tex]
[tex]x^2 +y^2 =1 \ such \ that \ : x = cos \ t , y= sin \ t, z = z, 0 \leq t \leq 2 \pi[/tex]
Set them equal now,
the Parametric equation of [tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]