Answer:
Step-by-step explanation:
Please, share any answer choices that were given to you.
-1 -1 -1
-1/64 is equivalent to -------- and ---------- and ---------
4^3 2^6 8^2
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
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
Tell which angles are congruent to the given angle measure.
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
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.
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
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
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.
The difference between the length and the
width of a rectangle is 5 centimeters. What is
the length (the longer side) of the rectangle, if
its perimeter is equal to 106 centimeters?
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)
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.
The distributive property of multiplication justifies which of the following statements? A 3x + 4(y – z) = 3x + 4(y) + 4(-z) B 3(x)+ 3(y) + 3(z) = 27(xyz) C 8 + (-8) = 0 D (a + b) + c = (c + a) + b
Answer:
The distributive property is used when we have to multiplicate a parenthesis:
[tex]a*(b+c) = ab+ac[/tex]
So the corrects andwer is A) 3x + 4(y-z) = 3x + 4y - 4z, because:
[tex]3x + 4(y-z) = 3x + 4*y + 4*(-z) = 3x + 4y - 4z[/tex]
B is incorrect, as [tex]3x + 3y + 3z 27\neq xyz[/tex]
C is correct, as a number plus his opposite is always 0.
D is correct, but that's the associate property as it's correct that for any three numbers of an associative set, there's another operation with verifies the equality.
Explain the order of operations you would use to evaluate (284) • 5-6+42. Then evaluate it.
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
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
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:
The Perimeter of a rectangle is 12 meters if the length of the rectangle is 5 meters what is the width
Answer:
1 meter wide
Step-by-step explanation:
5+5=10
2/2=1
Answer:
1
Step-by-step explanation:
Evaluate.
(-4)=
(-7) = 0
Please help ASAP!!
(-4)³ = (-4)(-4)(-4) = 16(-4) = - 64
(-7)² = (-7)(-7) = 49
(-)×(-) = +
(-)×(+) = -
5(6x+2)+4(5x+5)+4=50x+34
Answer:
0=0
Step-by-step explanation:
50x+34=50x+34
50x=50x
50x - 50x = 50x - 50x
0=0
Answer:
5(6x + 2)+4(5x+5)+4=50+34
multiply it then collect like terms
30x+15x+10+15+15+4=50+34
45x +54=50+34
so the 54 will cross over to the other side making it to be -54
45x=50+34-54
45x=30
the u divide both sides by 45
x= 45÷30
x=0.67
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.
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
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)=
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]
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
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.
What is 3/12 in reduced form.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
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
NED THIS AND HOW U GOT THE ANSWER find the measure of the angle greater than BFX using the figure below
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°.
Snow White is sewing stockings for the animals that visit her in the forest. When she looks around, she sees 38 legs. She knows that there are ten total animals: mice, deer, and birds. She also knows there are twice as many deer as mice. How many of each animal are there?
Answer:
B=1 M=6 D=3
Step-by-step explanation:
the equations are 4M+4D+2B=38
M+D+B=10
2D=M
step two: 4M+4D+2B=38 (multiply 2nd equation by -4)
-4M-4D-4B=-40
4M AND 4D cancels out and your left with -2B=-2 B=1
then you take the first equation and subsitute the third equation for M
step three: M+D+1 =10 (SUBSITUTE B WITH 1)
M+D=9
STEP FOUR: take the last equation (M+D=9) and subsitute 2D=M
2D+D=9
3D=9
D=3
subsitute D=3 into 2D=M so you get 2(3)=M M=6
DOUBLE CHECK USE THE SECOND EQUATION
M+D+B=1-
6+3+1=10
The required number of mice, deers, and birds are 3, 6, and 1 respectively.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Here,
Let the number of mice be x and the number of birds is y
Number of Deers = 2x
There are a total of 10 animals,
mice + deer + bird = 10
x + 2x + y = 10
3x + y = 10
y = 10 - 3x - - - - - - -(1)
Legs of mouse = 4
Legs of deers = 4
Legs of birds = 2
Total number of legs = 38
4x + 4 * 2x + 2y = 38
4x + 8x + 2y =38
12x + 2y = 38 - - - - - - - (2)
Solving equations 1 and 2
12x + 2(10 -3x ) = 38
12x + 20 - 6x = 38
6x = 18
x = 3
Put x in equation 1
y = 10 - 3 * 3
y = 1
Now,
Mice= x = 3
Deers = 2x = 2 *3 = 6
Bird = y = 1
Thus, the required number of mice, deers, and birds are 3, 6, and 1 respectively.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
What is the solution Set to 2a+6=2a+5+1
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
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.)
Answer:
10 square units
Step-by-step explanation:
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.
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.
Surface area of this figure
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
i need help with number 4
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
let f (x) =- 3x and g (x) = 2x - 1 Find the following f (x) + g (x) Pleas show steps
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]
help with math homework?
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].
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
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?
Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2∕9.6 = 21.6∕28.8?
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
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?
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]
Name the 5 ways/methods/techniques we can use to find a limit.
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 : )
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
Answer:
A
Step-by-step explanation: