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4 years ago

Give one positive and one negative coterminal angle for 135°

Mathematics

1 answer:

8_murik_8 [283]4 years ago

6 0

Answer:

495°, -225°

Step-by-step explanation:

You add and subtract 360° to 135° to get your positve and negative coterminal angle.

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Evaluate the line integral by the two following methods. xy dx + x2 dy C is counterclockwise around the rectangle with vertices

Airida [17]

Answer:

25/2

Step-by-step explanation:

Recall that for a parametrized differentiable curve C = (x(t), y(t)) with the parameter t varying on some interval [a, b]

$\large \displaystyle\int_{C}[P(x,y)dx+Q(x,y)dy]=\displaystyle\int_{a}^{b}[P(x(t),y(t))x'(t)+Q(x(t),y(t))y'(t)]dt$

Where P, Q are scalar functions

We want to compute

$\large \displaystyle\int_{C}P(x,y)dx+Q(x,y)dy=\displaystyle\int_{C}xydx+x^2dy$

Where C is the rectangle with vertices (0, 0), (5, 0), (5, 1), (0, 1) going counterclockwise.

a) Directly

Let us break down C into 4 paths $\large C_1,C_2,C_3,C_4$ which represents the sides of the rectangle.

$\large C_1$ is the line segment from (0,0) to (5,0)

$\large C_2$ is the line segment from (5,0) to (5,1)

$\large C_3$ is the line segment from (5,1) to (0,1)

$\large C_4$ is the line segment from (0,1) to (0,0)

Then

$\large \displaystyle\int_{C}=\displaystyle\int_{C_1}+\displaystyle\int_{C_2}+\displaystyle\int_{C_3}+\displaystyle\int_{C_4}$

Given 2 points P, Q we can always parametrize the line segment from P to Q with

r(t) = tQ + (1-t)P for 0≤ t≤ 1

Let us compute the first integral. We parametrize $\large C_1$ as

r(t) = t(5,0)+(1-t)(0,0) = (5t, 0) for 0≤ t≤ 1 and

r'(t) = (5,0) so

$\large \displaystyle\int_{C_1}xydx+x^2dy=0$

Now the second integral. We parametrize $\large C_2$ as

r(t) = t(5,1)+(1-t)(5,0) = (5 , t) for 0≤ t≤ 1 and

r'(t) = (0,1) so

$\large \displaystyle\int_{C_2}xydx+x^2dy=\displaystyle\int_{0}^{1}25dt=25$

The third integral. We parametrize $\large C_3$ as

r(t) = t(0,1)+(1-t)(5,1) = (5-5t, 1) for 0≤ t≤ 1 and

r'(t) = (-5,0) so

$\large \displaystyle\int_{C_3}xydx+x^2dy=\displaystyle\int_{0}^{1}(5-5t)(-5)dt=-25\displaystyle\int_{0}^{1}dt+25\displaystyle\int_{0}^{1}tdt=\\\\=-25+25/2=-25/2$

The fourth integral. We parametrize $\large C_4$ as

r(t) = t(0,0)+(1-t)(0,1) = (0, 1-t) for 0≤ t≤ 1 and

r'(t) = (0,-1) so

$\large \displaystyle\int_{C_4}xydx+x^2dy=0$

$\large \displaystyle\int_{C}xydx+x^2dy=25-25/2=25/2$

Now, let us compute the value using Green's theorem.

According with this theorem

$\large \displaystyle\int_{C}Pdx+Qdy=\displaystyle\iint_{A}(\displaystyle\frac{\partial Q}{\partial x}-\displaystyle\frac{\partial P}{\partial y})dydx$

where A is the interior of the rectangle.

so A={(x,y) | 0≤ x≤ 5, 0≤ y≤ 1}

We have

$\large \displaystyle\frac{\partial Q}{\partial x}=2x\\\\\displaystyle\frac{\partial P}{\partial y}=x$

$\large \displaystyle\iint_{A}(\displaystyle\frac{\partial Q}{\partial x}-\displaystyle\frac{\partial P}{\partial y})dydx=\displaystyle\int_{0}^{5}\displaystyle\int_{0}^{1}xdydx=\displaystyle\int_{0}^{5}xdx\displaystyle\int_{0}^{1}dy=25/2$

3 0

4 years ago

Identify all sets to which the number belongs.

ra1l [238]

Option B

-0.249851765 is a irrational number

<em><u>Solution:</u></em>

Given number is -0.249851765

We have to classify the number

Let us first understand about irrational, real, whole, integer and rational numbers

<h3><u>Integers:</u></h3>

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043

Every integer can be expressed as a decimal, but most numbers that can be expressed as a decimal are not integers. If all the digits after the decimal point are zeroes, the number is an integer. If there are any non-zero digits after the decimal point, the number is not an integer.

Thus -0.249851765 has non zero digits after decimal point. So it is not a integer

<h3><u>Whole numbers:</u></h3>

Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."

But the given number -0.249851765 is negative number. So it is not a whole number

<h3><u>Natural numbers:</u></h3>

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.

A decimal is a natural number if it is non-negative and the only digits after its decimal points are zero

So the given number -0.249851765 is a negative number and so it is not a natural number

<h3><u>Rational numbers:</u></h3>

A rational number is a number that can be expressed as a fraction (ratio) in the form $\frac{p}{q}$ where p and q are integers and q is not zero.

The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another.

When a rational number fraction is divided to form a decimal value, it becomes a terminating or repeating decimal.

So -0.249851765 is not a rational number

<h3><u>Irrational number:</u></h3>

An irrational number is real number that cannot be expressed as a ratio of two integers.

When an irrational number is expressed in decimal form, it goes on forever without repeating

So the given number -0.249851765 is irrational number

We can conclude that:

-0.249851765 is a irrational number, So Option B is correct

3 0

3 years ago

Idk how to answer this question

Naya [18.7K]

Answer:

It's z^11

Step-by-step explanation:

To multiply exponents with the same base (z), you add the exponents so in this case you add 5 and 6 to get z^11

5 0

4 years ago

Read 2 more answers

A rectangle has a length of 4 cm, a width

Blizzard [7]

19 is the answer to this question

4 0

3 years ago

A local little league has a total of 65 players of 20% or left handed how many left-handed players are there

sladkih [1.3K]

Number of players=85
percent of left handed players=20%
85*20/100=
simplify that:
85*1/5=
simplify again:
85*5= 17
17 players are left handed.
Hope that helps!!
Have a wonderful day!!

5 0

4 years ago