Use the method of this example to calculate f · dr,c wheref(x, y) = 2xyi (y2 − x2)j(x2 y2)2 and c is any positively oriented simple closed curve that encloses the origin. f · dr

Answer:

Below in bold.

Step-by-step explanation:

Standard form:

-12x⁴ - 6x² + 3.

Leading Coefficient:

-12.

The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the length and y represent the width. Hence:

x + 2y = 50

x = 50 - 2y

Also:

xy = 288

(50 - 2y)y = 288

y = 9; and y = 16

x = 32; and x = 18

The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

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Answer:  1.3125 gallons

Step-by-step explanation: The machine pumps 2.1 gallons of water every 1.6 minutes. 1.6 minutes is 1.6x more than 1 minute. So, we have to divide 1.6 by 1.6. Next, we have to divide 2.1 by 1.6. We can make this a bit easier by multiplying both of them by 10 to get 21/16 which is 1.3125.

Answer:

1.3125 gallons

Step-by-step explanation:

Using the given information, we can set up a proportion;

[tex]\frac{2.1gallons}{1.6minutes} = \frac{xgallons}{1minute}[/tex]

Now, we can cross multiply to solve for x.

2.1 = 1.6x
x = 1.3125 gallons

You will need 3 cans of paint to cover the two walls

We know that 1 can will cover 200 square feet of wall.

And here we have 2 walls, let's find the total area of these walls.

wall 1 is 20ft by 8ft, then its area is:

A = 20ft*8ft = 160ft^2

wall 2 is 40t by 8 ft, then its area is:

A'  = 40ft*8ft = 320ft^2

The total area is:

160ft^2 +  320ft^2 = 480ft^2

The number of cans of paint needed is given by the quotient between the total area and the area that each can cover.

N = 480ft^2/200ft^2 = 2.4

But we can't have a 0.4 of a can, so we should round to the next whole number, which is 3.

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6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.

The boundary length of any circular shape is known as the circumference.

A scale factor is a quantity multiplier (also known as a scale). The scaling factor for x, for instance, is represented by the letter "C" in the equation y = Cx. The factor would be 5 if y = 5x were the equation.

After scale factor 2 is applied, 6.4 cm must be the gasket's needed circumference.

It includes a rubber gasket with a 3.2 cm circumference. The circumference of the gasket has must be calculated after scaling up by factor 2.

Here,

3.2 cm is the gasket's circumference.

The circumference changed upon scale factor 2 dilatation.

Dilated gasket circumference: 2 * 3.2 = 6.4 cm

As a result, 6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.

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Answer:

6.4cm

Step-by-step explanation:

I Just Took the Test.

Answer:

8.5/12 m

Step-by-step explanation:

1. calculate the metres above the ground

2. therefore, 8.5 out of the total 12 metres are above ground

hope this helps :)

The mean, median, and mode of the 5 number 5, 7, 8, a, b. are equal so

the possibilities of a+b is 20.

The" mean" is the" average" you are used to, where you add up all the figures and also divide by the number of figures.

The" median" is the" middle" value in the list of figures. To know the median, your figures have to be listed in numerical order from lowest to largest, so you may have to rewrite your list before you can find the median.

The" mode" is the value that occurs utmost often. However, also there's no mode for the list, If no number in the list is repeated.

Given numbers are: 5, 7, 8, a, b

Total number =5

Then,

The mean = (5+7+8+a+b) / 5

Mean=(20+a+b) / 5          ------------------ (1)

Median=middle value in the list of figures

Median=8                  ------------------(2)

According to the question ,mean and median  are equal

Compare equation (1) and (2),

we get

= (20+a+b) / 5=8  20+a+b

=40a+b=20

there is no repetition of any number, so no mode is there

hence, all the possibilities of a+b is 20.

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==========================================================

Reason:

The only even prime number is 2. The other primes are odd.

The list of the first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

A prime is any number that has factors of 1 and itself, and nothing else.

For instance, 13 is prime because 1 and 13 are the only factors.

-----------

As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).

So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.

So we reduce the list of choices to 1, 3, 7, 9 for the units digit.

Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.

-----------

Let's try to build some primes.

Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.

On the other hand, 31 is prime since only 1 and 31 are factors.

The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.

Cross 1 and 4 off the list.

The next odd number is 3 which is our units digit. The value 23 is prime.

So far we have 41 and 23 as our two primes.

Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.

The number 67 is prime for similar reasoning mentioned earlier.

------------

We have these primes: 41, 23, 67

The next number either 58 or 85 isn't prime

This is one way to show an example of why we're only able to get 3 primes out of this.

The largest pyramid's surface area is roughly 159.31 [tex]ft^2[/tex].

A hexagonal pyramid is one that has six isosceles triangles that meet at a point, each of which is supported by a hexagonal foundation. It is self-dual, just as any pyramid. It possesses C6v symmetry when the base of a right hexagonal pyramid is a regular hexagon.

A pyramid is a solid,

Additionally, the ratio of two solids' surfaces when they are comparable is equal to the square of the similarity scale factor.

The similarity scale factor in this instance

                 = (Hight of the larger pyramid)/(Height of smaller pyramid)

                  =15/6

Due to the aforementioned characteristic,

                  = (15/6)^2

Given that the smaller pyramid's surface area is 25.49 [tex]ft^2[/tex],

(The surface of larger pyramid)/(25.49) = 225/36

The surface of larger pyramid = (25.49*225)/36

                                                   = 5735.25/36

                                                   =  159.3125 ft^2      

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Answer:

34 L

Step-by-step explanation:

there are four 100 km(s) in 400 km

so

8.5 * 4 is what you need to do to find your answer

8.5 * 4 = 34

34 L is your answer

The cubic meters of water did the hull of the titanic have to displace to stay afloat is known to be about 52,310 tons that is 51843.918 m³ of water.

The RMS Titanic is known to be a ship that is said to be owned by the White Star Line.

This is known to be the biggest British passenger liner that was said to have  sank when it was on its maiden voyage in the year 1912 in the North Atlantic Ocean.

Note that it sank because it was said to have hit an iceberg on Sunday, 14 April 1912.

The Titanic was said to be about 46,328 gross register tons and was known to have displaced about 52,310 tons of water.

So, 1 ton (displacement) ≈ 0.99109 cubic meters (m³)

Therefore, 52,310 tons

= 52,310 × 0.99109 m³

≈ 51843.918 m³

Therefore, The cubic meters of water did the hull of the titanic have to displace to stay afloat is known to be about 52,310 tons that is 51843.918 m³ of water.

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▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]

▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

» [tex] \tt{For \: \: y,}[/tex]

[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]

[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]

» [tex] \tt{At \: \: x = 2,}[/tex]

[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]

[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]

[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]

[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]

The surface area of the rectangular prism is 3668.94 m²

From the question, we are to determine the surface area of the rectangular prism

Surface area of a rectangular prism is given by the formula,

Surface area = 2(lw + lh + wh)

Where l is the length

w is the width

and h is the height

From the given diagram,

l = 35.7 m

w = 25.5 m

h = 15.1 m

Putting the parameters into the formula, we get

Surface area = 2(35.7×25.5 + 35.7×15.1 + 25.5×15.1)

Surface area = 2(910.35 + 539.07 + 385.05)

Surface area = 2(1834.47)

Surface area = 3668.94 m²

Hence, the surface area of the rectangular prism is 3668.94 m²

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Answer:

The y-intercept is (0, 0).

Step-by-step explanation:

The y-intercept is where the line passes through the y-axis.

Please see attachment.

Hope this helps!

The equation of the hyperbola on which the ship is positioned is x²/2025-y²/4375=1

Given that radio stations, A and B are 160 kilometers apart and the signal from B arrives 0.0003 seconds before the signal from A and the signal travels 300,000 kilometers per second.

The distance between radio station A and B are d=160 km.

The time is t=0.0003s.

The speed of the signal travel is v=300000 km/s.

Consider both radio stations A and B lie at foci on the x-axis.

The origin lies at the midpoint between the stations.

The distance of one of the stations from the origin is,

c=d/2

c=160km/2

c=80km

The centre of the hyperbola lies at (0,0), so both stations lie at coordinates points of (-80,0) and (80,0).

The expression for the difference in distance is,

I=vt

I=300000×0.0003

I=90km

The semi-major axis of the hyperbola is,

a=I/2

a=90km/2

a=45km

The expression for the semi-minor axis of the hyperbola is,

b²=c²-a²

b²=(80)²-(45)²

b²=6400-2025

b²=4375

The expression for the hyperbola on which the ship is positioned,

x²/a²-y²/b²=1

x²/(45)²-y²/4375=1

x²/2025-y²/4375=1

Hence, the equation of hyperbola on which the ship is positioned for radio stations, A and B are 160 kilometers apart and signal from B arrives 0.0003 seconds before the signal from A is x²/2025-y²/4375=1.

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Answer:

 29.9 cm³

Step-by-step explanation:

You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.

The volume of a cone is given by ...

  V = 1/3πr²h

The volume of the cone of interest is ...

  V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³

1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...

  1/3(89.797 cm³) ≈ 29.9 cm³

They sloshed out about 29.9 cm³ before they drank the water.

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Answer:The number of pennies on square 64 is greater than the pennies on 63 squares  since 64 is already greater 63 that when 63 gets bigger 64 will also get bigger so it will always be greater than 63

Step-by-step explanation:

Answer:

Step-by-step explanation:

greater than

the sum between negative 4 and 13, this can be tought as:

The expression is just the sum:

-4 + 13

So we have the sum between negative 4 and 13, this can be tought as:

Now, none of the written options (a, b, and c) depict any of this, so I assume that the correct option is the one that you did not write, which is option D.

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The equation which shows the commutative property of addition is (A) 4+3=3+4.

So,

The commutative property for addition states that, a + b = b + a .

Where a, b is any number.

The above condition is satisfied by the equation

Therefore, the equation which shows the commutative property of addition is (A) 4+3=3+4.

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The correct question is given below:

Which equation shows the commutative property of addition?

A. 4+3=3+4

B. 1(3)=3

C. (2+7)+12=2+(7+12)

D. 4+0=4

Answer:

5B; 7B; 1,024; see answer

Step-by-step explanation:

5.

We can see from the table that

a1 = 5

a2= 5·2 = 10

a3= 5·2·2 = 5·2² = 20

a4 = 5·2·2·2 = 5·2³ = 40

...

[tex]a_{n} = 5*2^{n-1}[/tex]

7.

Is given that the filter removes 90% of contaminated air

after run 1 :

100% air

90% contamination removed for 100% air

100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%

10% is still contaminated air

after run 2:

10% air

90% contamination removed for 10% air

10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%

1% is still contaminated air

after run 3:

1% air

90% contamination removed for 1% air

1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%

.1% is still contaminated air

11.

Figure 1 = 1 piece

Figure 2 = 4 pieces

Figure 3 = 4² = 16

...

[tex]Figure 6 = 4^{(6-1)} = 4^{5} = 1024[/tex]

12.

[tex](c+d)^{6} \\[/tex]

-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1

-we start with c to the lowest power 0 and d to the highest power 6  and end with  d to the lowest power 0 and c to the highest power 6

[tex](c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}[/tex]

-we simplify to have the final answer:

[tex](c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}[/tex]

Answer:1/2 of the teapot

Step-by-step explanation: Since 1/3 of the teapot is equal to 2/3 of the container, 1/3 of the container is equal to half of 1/3 of the teapot. We know that 1/3 divided by 2 equals 1/6, so 1/6 of the teapot is equal to 1/3 of the container. There are 3-thirds in a whole so we have to multiply 1/6 by 3. This equals 3/6 or 1/2.

The equation for function g is given by using translational ideas:

g(x) = 7x/3 + 1.

According to operations like multiplication or sum/subtraction either in its definition or in its domain, a translation is represented by a change in the function graph. Examples include shifting to the left or right or up or down, compressing or stretching vertically or horizontally, and reflecting over the x- or y-axis.

Given that f(x) exists, obtaining f is equal to compressing horizontally by a factor of a. (ax).

The function in this issue is as follows:

f(x) = 7x + 1.

We have the following for a horizontal compression of 1/3:

g(x) = f(1/3x) = 7x/3 + 1.

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The slope of this linear equation that models the data indicate: B. the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (5 - 5.5)/(10 - 5)

Slope = -0.5/5

Slope = -0.1.

In conclusion, we can infer and logically deduce that the slope of this linear equation that models the data indicate the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute.

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A substance is tested and has a Ph of 7.0. It would be a weak acid.

The correct option is (c) a weak acid .

What is the nature of substance if the pH is less than 7?

What is pH?

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Answer:

x = -1, x = -2 , x= 2

Step-by-step explanation:

First we factorise this cubic function :

(x+1)(x+2)(x-2) = 0

Using the law a×b×0 = 0

We know that to find the zeros we have to set each bracket equal to 0 :

x+1 = 0    OR   x+2 = 0    OR   x-2 = 0  

x = -1                x = -2               x = 2

Hope this helped and have a good day

The critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

For given question,

We need to find the critical values for a 2-tailed sign test for 13-coin flips.

We have been given an alpha level of 0.05 that is 5%

⇒ α = 0.05

We know that in hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

These are the points on the distribution which have the same probability as your test statistic, equal to the significance level α.

The critical values are assumed to be at least as extreme at those critical values.

Now we find 1 - α

⇒ 1 - α = 1 - 0.05

⇒ 1 - α = 0.95

Because it is a two-tailed test, we are going to divide 0.95 by 2.

⇒ 0.95/2 = 0.475

Now we look in the z-table to find out cutoff points.

For the area of 0.475, the critical values is ± 1.96 .

Therefore, the critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

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The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

An equation is an expression that shows the relationship between two numbers and variables.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let f(t) represents the number of subscribers and t represents the time in months. Hence:

[tex]f(t) = 250(1.4)^t[/tex]

a = 250, b = 1.4

The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

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Answer: 250,      1 month,      and    1.4

Answer:

Ten thousands place

Step-by-step explanation:

84 530 216

Frm here u can see that the 3 is in the ten thousands place