Use Cauchy's residue theorem to evaluate de z(z+1)(2-3) -dz, where c is the circle |z| = 2. 5z2+2 (z1)() =

Answer:

1) -12, 2) 70

Step-by-step explanation:

Hope this helps :)

Answer:

oh someone got it already :(((( ugh

Step-by-step explanation:

ro bux

Step-by-step explanation:

Rearrange the equations to solve.

cos(-3 • pi) = -1

cos((-3pi) / 4 radians) = -0.707

cos(5 • pi) = -1

cos((5pi) / 4 radians) = -0.707

They are the same because when multiplied, they are the same value, and always will be that way. They also have the same identity if you simplify and compare the results of that equation.

The value of cos (-3π/4) and the value of cos (5π/4) are same.

Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.

The main three trigonometric ratios are sine, cosine and tangent functions.

We know that,

cos (-3π/4) = cos (3π/4)

Now,

cos (3π/4) = cos (π + π/4)

And,

cos (5π/4) = cos (π - π/4)

Now, we know that,

cos (π + x) = -cos (x) and cos (π - x) = -cos (x)

So the value of cos (π + π/4) = -cos( π/4) and cos (π - π/4) = -cos( π/4)

Hence cos (3π/4) = cos (5π/4) = -cos( π/4)

Hence both the values are same.

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The distance between the points (-7, -3) and (-3, -5) in simplest radical form is 2√5.

The distance formula used in finding the distance between two points is expressed as;

\(d = \sqrt{( x_2 - x_1 )^2 + ( y_2 - y_1)^2 }\)

Given the points in the question:

Point 1 (-7,-3)

Point 2 (-3,-5)

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1 )^2 + ( y_2 - y_1)^2 }\\\\d = \sqrt{( -3 - (-7) )^2 + ( -5 - (-3))^2 }\\\\d = \sqrt{( -3 + 7 )^2 + ( -5 + 3)^2 }\\\\d = \sqrt{( 4 )^2 + ( -2)^2 }\\\\d = \sqrt{16 + 4 }\\\\d = \sqrt{20 }\\\\d = 2\sqrt{5}\)

Therefore, the distance between the points is 2√5 .

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The average temperature on Saturday was 62.6 °F, then the actual temperature will be equal to 17 °C.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given information in the question,

The temperature on Saturday was 62.6 F

Then, the actual temperature will be,

C = 5/9(F -32)

C = 5/9(62.6 - 32)

C = 5/9(30.6)

= 17 °C

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Using a calculator, it can be found that

Rounding to three decimal places,

The standard form of the equation of the hyperbola with the given characteristics is (x - 2)² / 16 - y² / 9 = 1

To find the standard form of the equation of a hyperbola, we need the coordinates of the center and either the distance between the center and the vertices (a) or the distance between the center and the foci (c).

Given the information:

Vertices: (2, ±4)

Foci: (2, ±5)

We can see that the center of the hyperbola is at (2, 0), which is the midpoint between the vertices. The distance between the center and the vertices is 4.

Since the foci are vertically aligned with the center, the distance between the center and the foci is 5.

The standard form of the equation of a hyperbola centered at (h, k) is:

(x - h)² / a² - (y - k)² / b² = 1

Since the foci and vertices are vertically aligned, the equation becomes:

(x - 2)² / a² - (y - 0)² / b² = 1

The value of a is the distance between the center and the vertices, which is 4, so a² = 4² = 16.

The value of c is the distance between the center and the foci, which is 5.

We can use the relationship between a, b, and c in a hyperbola:

c² = a² + b²

Solving for b²:

b² = c² - a² = 5² - 4² = 25 - 16 = 9

Therefore, b² = 9.

Substituting these values into the equation, we get:

(x - 2)² / 16 - y² / 9 = 1

So, the standard form of the equation of the hyperbola with the given characteristics is:

(x - 2)² / 16 - y² / 9 = 1

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Given:

A car can travel 3.5 km on 30 litres of petrol.

To find:

The distance a car can cover if it has 50 litres of petrol in its tank.

Solution:

We have,

On 30 litres, a car can travel = 3.5 km

On 1 litre, a car can travel = \(\dfrac{3.5}{30}\) km

On 50 litres, a car can travel = \(\dfrac{3.5}{30}\times 50\) km

                                               = \(\dfrac{3.5}{3}\times 5\) km

                                               = \(\dfrac{17.5}{3}\) km

                                              \(\approx 5.83\) km

Therefore, a car can travel 5.83 km on 50 litres.

Answer:

cannot

Step-by-step explanation:

The length of NS cannot be determined because its length on the corresponding preimage (which is TK) is not given.

(a) The marginal cost C'(x) is given by C'(x) = 0.0003x^2 - 0.04x + 2.

(b) Using Leibniz's notation for the chain rule, we have dt/dC = (dx/dC) * (dt/dx).

(c) Substituting the values, when t = 4 weeks, into the expression for dt/dC, we get dt/dC = 1 / C'(x) = 1 / (0.0003x^2 - 0.04x + 2).

To find the marginal cost, we differentiate the cost function C(x) with respect to x. Taking the derivative of C(x) = 0.0001x^3 - 0.02x^2 + 2x + 400, we get C'(x) = 0.0003x^2 - 0.04x + 2.

To find dt/dC, we need to find dx/dC first. Rearranging the equation x = 1300 + 100t, we get t = (x - 1300)/100. Taking the derivative of this equation with respect to C, we get dx/dC = (dx/dt) * (dt/dC) = (dx/dt) / (dC/dx) = 1 / (dC/dx).

Therefore, the rate at which the cost is changing with respect to time t is given by dt/dC. To determine how fast costs are increasing when t = 4 weeks, we substitute x = 1300 + 100t and t = 4 into the expression for dt/dC:

dt/dC = 1 / (0.0003(1300 + 100t)^2 - 0.04(1300 + 100t) + 2).

Simplifying this expression will give us the rate of increase in dollars per week. However, the given information is incomplete, as the values for x and t are not specified.



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The given statement "If f(x)≥0, then I the area between the graph and the x-axis over [2,7]. " is true because if f(x)≥0, then the integral I is equal to the area between the graph and the x-axis over the interval [2,7].

\

When f(x)≥0, 27f(x) is also non-negative over the interval [2,7]. Therefore, the integral I is equal to the area between the graph of 27f(x) and the x-axis over the interval [2,7]. This is because the integral of a non-negative function represents the area between the graph of the function and the x-axis. Since f(x)≥0, 27f(x) is also non-negative and hence, I represents the area between the graph of 27f(x) and the x-axis.

Therefore, the given statement is true, as long as f(x) is continuous on [2,7].

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After the reflection and the translation of XYZ, the length of segment Y'Z'  is 6 units

The transformation is given as:

Both transformations are rigid transformations.

This means that the lengths YZ and Y'Z' would remain the same

The coordinates are given as:

Y = (8,3)

Z = (2,3)

Both points are on the same y coordinate.

So, the length YZ is

YZ = 8 - 2

Evaluate

YZ = 6

Hence, the length of segment Y'Z'  is 6 units

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We are asked to find the number of solutions of the equation x² ≡ 3 (mod p) where p takes different values based on the last digit of the ID number.

The quadratic congruence is valid only for some primes p and the way to approach these equations is by finding some primitive roots modulo p and some other numbers that depend on the properties of p to which the equation can be reduced. For p=59, p=61 and p=67, there are respectively 29, 30, and 20 values of x for which the congruence holds. These values can be obtained by direct substitution or by making use of the quadratic reciprocity law. Let N be the last digit or your Queens College/CUNY ID number. This statement introduces a condition that makes the values of p dependent on the last digit of the ID number. The question is asking for the number of solutions of the equation x² ≡ 3 (mod p) for three different primes p. Depending on whether N is 0, 1, 4, or 8, N is 2, 5, or 7, or N is 3, 6, or 9, we use different values of p. This shows that there is no unique solution for the quadratic congruence, but rather the number of solutions depends on the properties of the modulus p. To find the solutions for each p, we can either use direct substitution and verify for each integer from 0 to p-1 if it satisfies the congruence or we can use some techniques such as the quadratic reciprocity law and primitive roots modulo p. By using these methods, we find that there are 29, 30, and 20 solutions of the congruence for p=59, p=61, and p=67, respectively.

In conclusion, the solution of the equation x² ≡ 3 (mod p) depends on the value of p, which in turn depends on the last digit of the ID number. The different values of p for each case can be used to find the solutions of the congruence either by direct substitution or by making use of some number theory techniques. In this problem, we have used the values p=59, p=61, and p=67 to find respectively 29, 30, and 20 solutions of the quadratic congruence.

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Answer:

simplest form.

Step-by-step explanation:

The percentage decrease in the African lion population between 1975 and 2015 is 88%

To calculate the given problem

The decrease in population is:

250,000 - 30,000 = 220,000

To find the percentage decrease, we divide the decrease by the initial population:

220,000 / 250,000 = 0.88

Finally, we multiply by 100 to get the percentage:

0.88 * 100 = 88%

Therefore, the percentage decrease in the African lion population between 1975 and 2015 was 88%.

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The perpendicular bisector of a triangle is a line segment that connects a vertex to the midpoint of the opposite side, and it is perpendicular to that side.

A segment that connects a vertex of a triangle to the opposite side so that it is perpendicular to that side is called a perpendicular bisector.

In a triangle, the perpendicular bisector is a line segment that starts at a vertex and ends at the midpoint of the opposite side.

The key feature of a perpendicular bisector is that it is perpendicular, meaning it forms a right angle, with the side that it is connecting to.

This is important because it helps us divide the triangle into two smaller triangles with equal sides, which is useful in many mathematical and geometric applications.

Let's say you have a triangle with vertices A, B, and C, and side BC is opposite vertex A.

To find the perpendicular bisector of vertex A and side BC, you would need to find the midpoint of side BC and then draw a line from vertex A to the midpoint that forms a right angle with side BC.

The line that you have just drawn is the perpendicular bisector of vertex A and side BC.

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The direction of the difference between the 2 measurements.

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Answer:

The next 50 phones are working? ---> 88.3%

The next 100 phones are working? ---> 93.6%

The next 500 phones are working? ---> 98.6%

Step-by-step explanation:

I hope this helps

The correct choice is:

y= x^2 and y= 2x+3

Given equation,

x^2=2x+3

this can be used for factorization by taking all the factors in one side of the equation

x^2-2x-3=0

or, x^2-3x+x-3=0

or, x(x-3)+x(x-1)=0

or, (x-3)(x-1)=0

Therefore,

x=-1 or x= 3

The result indicates,

when we plot the equation x^2=2x+3 in graph, as a function of y=x^2-3x+x-3, the x axis will be intersected on x=-1 and x=3

Now, if we consider

y=2x+3 and y=x^2

it gives  x^2-2x-3=0 all over again, when combined.

The solution to,

x^2=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.

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The correct answer is y= \(x^{2}\) and y= 2x+3 that can be graphed to find the solution(s) to \(x^{2}\)= 2x + 3 .

The Given equation was ,

\(x^{2}\)= 2x + 3 .

this can be used for factorization by taking all the factors in one side of the equation

\(x^{2}\) - 2x - 3 =0

or, \(x^{2}\)-3x+x-3=0

x(x-3)+x(x-1)=0

(x-3)(x-1)=0

∴x=-1 or x= 3

The result indicates,

when we plot the equation \(x^{2}\)=2x+3 in graph, as a function of y=\(x^{2}\)-3x+x-3, the x axis will be intersected on x=-1 and x=3

Now, if we consider

y=2x+3 and y=x^2

it gives  \(x^{2}\)-2x-3=0 all over again, when combined.

The solution to,

\(x^{2}\)=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.

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Answer:

The solution to the inequality expression 4x−3≥(−1) is x≥12 .

Answer:

5/6

Step-by-step explanation:

(1/5)/(2/3)=(1/4)/m

(1/5)(3/2)=(1/4)(1/m)

3/10=1/4m

cross product

10*1=3*4m

10=12m

m=10/12

simplify

m=5/6

Answer:

S

Step-by-step explanation:

Segment P shows as time is increasing, distance is also increasing. Which means the cyclist is moving forward at a speed.

Segment Q shows that distance is constant but time is increasing. This means that the cyclist is at rest.

Segment R shows as time in increasing, distance is also increasing. Which means the cyclist is moving forward.

Segment S shows that as time increases, distance decreases to the t-axis [ the point where Segment P started, hence original position]. This shows the cyclist returning to the starting point

Correct answers is Segment S.

Answer:

Letter S

Step-by-step explanation:

Answer:

6 units right I believe

Step-by-step explanation:

Hey there! :)

Answer:

v = -16.

Step-by-step explanation:

Given:

-2 = 2 + v/4

Subtract 2 from both sides:

-2 -2 = 2 - 2 + v/4

-4 = v/4

Multiply both sides by 4:

-4 · 4 = v/4 · 4

-16 = v

The y-intercept is (0, 4).

An alternate method to find the x-intercepts is to factor the quadratic equation.

The vertex is (-2, 0).

The graph of the equation is illustrated below.

One of the most common types of equations is a quadratic equation, which is an equation of the form ax² + bx + c = 0. In this case, we have the equation x² + 4x + 4 = 0, and we need to find the x-intercepts.

To find the x-intercepts, we can use the quadratic formula, which is given by:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 4, and c = 4, so we can substitute these values into the formula:

x = (-4 ± √(4² - 4(1)(4))) / 2(1) x = (-4 ± √(0)) / 2 x = -2

Therefore, the x-intercept is -2. We can check this by plugging in x = -2 into the equation and verifying that it equals zero:

(-2)² + 4(-2) + 4 = 0

In this case, we can see that the equation can be factored as:

(x + 2)² = 0

Taking the square root of both sides, we get:

x + 2 = 0

x = -2

This gives us the same x-intercept as before.

To find the vertex of the parabola represented by the equation, we can use the formula:

x = -b / 2a

and then substitute this value of x into the equation to find the y-coordinate of the vertex. In this case, we have:

x = -4 / 2(1) x = -2

Substituting x = -2 into the equation, we get:

(-2)² + 4(-2) + 4 = 0

Since the coefficient of x² is positive (i.e., a = 1 > 0), the parabola opens upwards and the vertex is a minimum.

To graph the parabola, we can plot the vertex at (-2, 0) and use the x-intercept we found earlier at (-2, 0). Since the equation is symmetric about the vertical line through the vertex, we know that there is another point on the graph that is the same distance from the vertex but on the other side of the line. Therefore, we can plot the point (-3, 0) as well. We can also find the y-intercept by setting x = 0 in the equation:

0² + 4(0) + 4 = 4

Using this information, we can sketch the parabola by connecting the points (-3, 0), (-2, 0), and (0, 4), and noting that the parabola is symmetric about the line x = -2.

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Answer:

Horizontal compression by a factor of 2 followed by a vertical shift by positive 3

Step-by-step explanation:

a*f(k(x-d))+c

k=2

c=3

Answer:

radius is 14

Step-by-step explanation:

C = 2πr

28π = 2πr (you can divide the π from each side to eliminate them)

28 = 2r

28/2 = r

14 = r

The tangential and normal components of the acceleration when s = 10 m is 40 m/s^2 and 8 m/s^2 respectively.

In the given question, a car is travelling along the road with a speed of 2s m/s, where s is in meters.

We have to determine the tangential and normal components of the acceleration when s = 10 m.

Speed (v) = 2s  

Motion is circular so, Radius of circle = 50m

Tangential acceleration = dv/dt

Tangential acceleration = d(2s) / dt

Tangential acceleration = 2(ds)/dt

Tangential acceleration = 2v

Tangential acceleration = 2(2s)

Tangential Acceleration = 4s

As given s = 10 m

Tangential acceleration = 4 x 10

Tangential acceleration  = 40 m/s^2

Normal acceleration = v^2/ r

Normal acceleration = 4s^2/r

Normal acceleration = {4 x 10^2}/50

Normal acceleration = {4 x 100}/50

Normal acceleration = 400/50

Normal acceleration = 8 m/s^2

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The complete question is:

A car is travelling along the road with a speed of 2s m/s, where s is in meters. Determine the tangential and normal components of the acceleration when s = 10 m. Treat the car as a particle

The equation of the line graphed is y = x + 6

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The number of downloads of Starship than Flurry include the following: A. 1.5 million.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached below, we can logically deduce the following parameters and key features:

Next, we would calculate the difference between the downloads in the  3rd quarter for Starship and Flurry as follows;

Difference = 3 million downloads - 1.5 million downloads.

Difference = 1.5 million downloads.

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Answer: The answer is 10

Step-by-step explanation:

The centroid of any triangle has the following property:
The distance between the centroid and one of the extremities is two times longer than the distance between the opposite side.  
In this case AG = 20 should be twice the distance then GK.
If 20 is twice the distance then that distance that we are  searching for is:
20/2 = 10