Evaluate the line integral of the vector field u =-yi + xj counterclockwise around a triangle with vertices (0,0),(L,0) and (0,L)

Answer:

D

Step-by-step explanation:

They didn't provide the number for one of the faces btw..

13) The scientific notation is        1.4354125 * 10⁸. 14) The scientific notation is        1.4354125 * 10⁻¹. 15) The scientific notation is 22366.0992. 16) The scientific notation is 1.55 * 10¹⁰.

Let's solve the given expressions and write the answers in scientific notation:

13) \((6.125*10^3) * (2.345*10^4)\)

To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:

\((6.125 * 2.345) * (10^3 * 10^4) = 14.354125 * 10^(3 + 4) = 14.354125 * 10^7 = 1.4354125 * 10^8\)

\(= 1.4354125 * 10^8\)

14) \((6.1258*10^3) * (2.345*10^{-4})\)

To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:

\((6.125 * 2.345) * (10^3 * 10^{-4}) = 14.354125 * 10^{3 - 4} = 14.354125 * 10^{-1} = 1.43541258* 10^{-1}\)

\(= 1.4354125 * 10^{-1}\)

15) \(3700.13 * (6.04*10^4)\)

To multiply a decimal number and a number in scientific notation, we simply multiply the decimal by the coefficient of the scientific notation:

3700.13 × 6.04 = 22366.0992

Since the answer does not need to be expressed in scientific notation, the result is 22366.0992.

= 22366.0992

16) \((6.2*10^4) / (0.4*10^{-5})\)

To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:

\((6.2 / 0.4) * (10^4 / 10^{-5}) \\= 15.5 * 10^{4 - (-5}) \\= 15.5 * 10^9 \\= 1.55 * 10^{10}\\= 1.55 * 10^{10}\)

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Answer:

It's 12/5 . When u divide the BC by AB ie. tanC becomes 12/5 .......Try it hope it helps!

Answer:

see explanation

Step-by-step explanation:

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{24}{10}\) = \(\frac{12}{5}\)

Answer:

D: {-4, -1, 4}

R: {0, 2}

Step-by-step explanation:

The domain of a relationship is the possible values of x. On the other hand, the range is the possible values of y. To write out the domain and range of a discrete relationship simply write the given x and y values. The x values are -4, -1, and 4. Set notation is written least to greatest and uses brackets, so the domain is {-4, -1, 4}. Do the same for the range and remember that numbers should not repeat in set notation. This gives you {0, 2}.

Answer:

Step-by-step explanation:

let the rate of travel of bicycle=x m/h

rate of travel of motor scooter=2x+2

time taken by motor scooter to travel 12 mi=12/(2x+2) hrs.

time taken by bicycle to travel 5 mi=5/x

as time is same

\(\frac{12}{2x+2}=5/x\\12x=5(2x+2)\\12x=10x+10\\12x-10x=10\\2x=10\\x=10/2=5\\rate~ of~ travel~ of~bicycle=5 m/h\\rate~ of~ travel~ of~ motor~ scooter=2x+2=2 \times 5+2=12 ~m/h\)

Step-by-step explanation:

9 b^2 c  = a     divide both sides of the equation by 9c

b^2 = a / (9c)    now take the sqrt of both sides

b = ± sqrt ( a/(9c) ) =   ± 1/3 sqrt ( a/c)  <====I do not see the correct answer posted....    perhaps one of the choices was transcribed incorrectly....

Answer:

8

Step-by-step explanation:

5x - 2y

5 ( 2 ) - 2 ( 1 )

10 - 2

8

Answer:

B.

Step-by-step explanation:

Because I know... trust me.

Answer:

By the Pythagorean theorem, the diagonal length (d) of the square is

 d² = 7² + 7²

 d = √98 ≈ 9.8995

Since the diameter of the circle (11 cm) is greater than the diagonal length of the square (9.9 cm), you know the square will fit into the circle without touching.

Step-by-step explanation:

Answer:

what is the question ?

Step-by-step explanation:

Answer: c

Step-by-step explanation:

Answer:

=0.017+0.00025

=0.01725

=1.725×10^-2

=C

As per the given statement Since consumption cannot be negative, the optimal consumption amount of ham for Mandy is 0 (±5%).

To find Mandy's optimal consumption amount of ham, we need to maximize her utility subject to her budget constraint.

Given:

U = 131(Cheese) + 32(Ham)

Price of Ham (PH) = $76 per pound

Price of Cheese (PC) = $24 per pound

Income (I) = $2489

Let x represent the amount of ham consumed. The budget constraint equation is:

PH * x + PC * (I - x) = I

Substituting the given values, we have:

76x + 24(2489 - x) = 2489

Simplifying the equation:

76x + 59736 - 24x = 2489

52x = 2489 - 59736

52x = -57247

x = -57247 / 52

x ≈ -1101.29

Since consumption cannot be negative, the optimal consumption amount of ham for Mandy is 0 (±5%).

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Mandy's optimal consumption amount of ham is within a range of \($0 \pm 5\%$\)

To determine Mandy's optimal consumption amount of ham, we need to find the quantity of ham that maximizes her utility given her budget constraint.

Let \($H$\) be the quantity of ham consumed in pounds. The price of ham is \(\$76\) per pound. Mandy's income is \(\$2489\), and her utility function is given by \($U = 131C + 32H$\), where \($C$\) represents the quantity of cheese consumed in pounds.

We can set up Mandy's budget constraint as follows:

\(\[76H + 24C = 2489\]\)

To find the optimal consumption amount of ham, we can solve this equation for \($H$\). Rearranging the equation, we have:

\(\[H = \frac{2489 - 24C}{76}\]\)

Substituting the given values, we have:

\(\[H = \frac{2489 - 24C}{76}\]\)

To calculate the optimal consumption amount of ham, we can substitute different values for \($C$\) and solve for \($H$\). The optimal value will be within a range of \($0 \pm 5\%$\) due to the uncertainty in the problem statement.

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Answer:

I guess d is the answer . cause the sum of a number (a number added to something) represented by a variable is added to twelve

The simplified form of the algebraic expression is \(\frac{23}{10} p+\frac{6}{5} r\) .

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Given expression is of the form:

\(\frac{3}{5} (\frac{1}{2}p+2r )+2p\)

Now we will use the distributive property to expand the algebraic expression:

\(or, (\frac{3}{5} \times\frac{1}{2}p+\frac{3}{5} \times2r) +2p\\\\or,\frac{3}{10}p+\frac{6}{5} r+2p\\ \\or,\frac{3+20}{10} p+\frac{6}{5} r\\\\or,\frac{23}{10} p+\frac{6}{5} r\)

Hence the simplified algebraic expression is  \(\frac{23}{10} p+\frac{6}{5} r\) .

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The values of all sub-parts have been obtained.

(a). The radian measure of angle A is 6 radians.

(b). The radian measure of angle B is 3 radians.

(c). The radian measure of angle C is 2 radians.

What is relation between radian and degree?

A circle's whole angle is 360 degrees and two radians. This serves as the foundation for converting angles' measurements between different units. This means that a circle contains an angle whose radian measure is 2 and whose central degree measure is 360. This can be written as:

2π radian = 360° or

π radian = 180°

(a). Evaluate the radian measure of angle A:

Near to 360° and radians measure whole number, so we get,

A = 6 radian {1 radian = 57.296°}.

(b). Evaluate the radian measure of angle B:

Near to 180°, and radian measure whole number, so we get,

B = 3 radian

(c). Evaluate the radian measure of angle C:

Near to 90 and radian measure whole number, so we get,

C = 2 radian.

Hence, the values of all sub-parts have been obtained.

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g(x+a)−g(x) for the following function g(x)=−x^2 −6x  g(x+a) - g(x) = -2ax - a^2 - 6a - 6x

To determine g(x+a) - g(x) for the function g(x) = -x^2 - 6x, we substitute x+a into the function and then subtract g(x):

g(x+a) - g(x) = [-(x+a)^2 - 6(x+a)] - [-(x^2 - 6x)]

Expanding the expressions inside the brackets:

= [-(x^2 + 2ax + a^2) - 6x - 6a] - [-(x^2 - 6x)]

Now distribute the negative sign inside the first bracket:

= -x^2 - 2ax - a^2 - 6x - 6a + x^2 - 6x

Simplifying the expression:

= -2ax - a^2 - 6a - 6x

So, g(x+a) - g(x) = -2ax - a^2 - 6a - 6x

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The volume of a container is found to be 38.5 in³. Its volume in units of cm³ will be 630.902 cm³.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

To create a formula to convert 38.49 in³ to cm³, we start with the fact that 1 inch is 2.54 centimetres, which means that you multiply inches by 2.54 to get centimetres. We can therefore make the following equation:

inches × 2.54 = centimeters

(inches × 2.54)³ = centimeters³

inches³ × 16.387064 = centimeters³

in³ × 16.387064 = cm³

Now that we have the in³ to cm³ formula, we can calculate and convert 38.5 in³ to cm³. Here is 38.5 in³ converted to cm³, along with the math and the formula:

= in³ × 16.387064

= 38.5 × 16.387064

= 630.902 cm³

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Answer:

CN75A if this is college format ; A2B3 if this is lower grade format (1st to 5th)

86 to 75 if this is middle school format; R1H7 if this is for high school format; V12315 and if you are at any other school in anywhere out of North America this would be your format.

Step-by-step explanation:

I know this is right I am a expert at all types of math.

The maximum and minimum values of f(x,y,z) = 2xyz are \(\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }\)

The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function.

f(x,y,z)=2xyz

Computation:

Differentiating the given equation up to second order

\(\begin{gathered}f_x=2yz\Rightarrow 2yz=0 either y=0 or z=0\\f_y=0\Rightarrow 2xz=0 either x=0 or z=0\\f_z=0\Rightarrow 2xy=0 either x=0 or y=0\end{gathered}\)

So, the critical point is (0,0,0)

Now, using the Lagrange's on the boundary,

\(\begin{gathered}g(x,y,z)=x^2+y^2+z^2-1=0\\g_x=2x\\g_y=2y\\g_z=2z\end{gathered}\)

\(So, \bigtriangledown f=\lambda \bigtriangledown g\left < 5yz,5xz,5xy \right > =\lambda \left < 2x,2y,2z )\)

By solving we get,

\(x^2=y^2=z^2\) then,

\(\begin{gathered}x^2+y^2+z^2=1\\3z^2=1\\z=\pm \frac{1}{\sqrt{3} } \\y=\pm \frac{1}{\sqrt{3} } \\\\x=\pm \frac{1}{\sqrt{3} } \\\end{gathered} x 2+y 2+z 2=13z 2=1z=± 31\)

\(So, the critical points are (0,0,0),(\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } )and (\frac{-1}{\sqrt{3} }, \frac{-1}{\sqrt{3} },\frac{-1}{\sqrt{3} })\)

So, by substituting the critical points we get,

\(\begin{gathered}f(0,0,0)=0\\f(\frac{1}{\sqrt{3} }, \frac{1}{\sqrt{3} },\frac{1}{\sqrt{3} })=2(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })\\=\frac{2}{3\sqrt{3} } \\f(-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} })=2(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })\\=-\frac{2}{3\sqrt{3} }\end{gathered}\)

Hence the maximum and minimum values of f(x,y,z) are \(\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }\)

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Answer:

D = 60.25m

Step-by-step explanation:

Answer:

Slope = 8.000/2.000 = 4.000

 x-intercept = 10/4 = 5/2 = 2.50000

 y-intercept = -10/1 = -10.00000

Step-by-step explanation:

y= mx + b is the slope intercept form of a line where m is the slope and b is the y intercept.

Step  1  :   Equation of a Straight Line

Step 2: Graph of a Straight Line

Step 3: Calculate the Y-Intercept

Step 4: Calculate the X-Intercept

Step 5: Calculate the Slope

Hope this helps.

Since the 3 pack cost $6.75 this means that:

each bottle of juice cost $2.25.

Step-by-step explanation:

a diagram is necessary. please provide a diagram.

Answer:

Hello! answers:

Question 13: 12

Question 14: 18

Question 15: 15

Hope that helps!

For question 13 I found the answer by doing 6 ÷ 2 and 6 ÷ 2 = 3 so I know that 4 will be enlarged by 3 so 4 × 3 = 12 so 12 is the answer for 13

For question 14 I found the answer by using 1 of the sides so I did 24 ÷ 16 and 24 ÷ 16 = 1.5 and 1.5 × 12 = 18 so the answer is 18

For question 15 I did the same thing!

25 ÷ 20 = 1.25 and 1.25 × 12 = 15 so 15 is the answer Hope that helps!

Answer:

-16/45

Step-by-step explanation:

8/15*-2/3= -16/45

Answer:

8/15 times -2/3 =-0.35555555555

Answer:

58°

Step-by-step explanation:

x and the angle adjacent to x are supplementary, so the angle adjacent to x measures 180 - x.

180 - x = (1/2)(100 + 144)

180 - x = 122

58 = x

Center = (3,-4)   Radius = 5

This equation is already in standard form so you just have to pull out the h and k values which in this case are 3&4, just remember to flip the signs so it'll be 3&-4. Just square the right side and that is the radius, in this case 5

The slope of the given equation of the straight line is - 5/4.

We know that the direction of a line is defined by its slope. The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.

Here the equation of the line is

y = - (5/4)x - 1.

At x = 0, y = -(5/4) × 0 - 1 = -1

and at x = 4, y = -(5/4) × 4 - 1 = - 5 - 1 = -6

Now the slope = (-6 - (-1))/(4 - 0) = (-6 + 1)/4 = - 5/4

Therefore the slope of the given equation of the straight line is - 5/4.

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The distance traveled by a passenger on each rotation of the Ferris wheel is 1635.2 feet.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

The expression is given in the question as:

⇒ 3.14d

The circumference of the Ferris wheel can be determined by multiplying the diameter, d, by (3.14).

Thus, the circumference of the Ferris wheel is:

⇒ 3.14 × 520 = 1635.2 feet.

Since the Ferris wheel makes one full rotation in one ride, the distance traveled by a passenger on each rotation of the Ferris wheel is 1635.2 feet.

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