a)
i) The function is not harmonic.
ii). The function is harmonic.
b) v is also harmonic in D
a) A function is harmonic if it satisfies the Laplace equation:
∂²u/∂x² + ∂²u/∂y² = 0
i) For the function u = x² + 2x - 4², we can take the partial derivatives with respect to x and y:
∂u/∂x = 2x + 2
∂u/∂y = 0
∂²u/∂x² = 2
∂²u/∂y² = 0
Plugging these into the Laplace equation, we get:
2 + 0 = 0
This is not true, so the function is not harmonic.
ii) For the function u = 2e* cos(y), we can take the partial derivatives with respect to x and y:
∂u/∂x = 0
∂u/∂y = -2e* sin(y)
∂²u/∂x² = 0
∂²u/∂y² = -2e* cos(y)
Plugging these into the Laplace equation, we get:
0 + (-2e* cos(y)) = 0
-2e* cos(y) = 0
This is true for all values of y, so the function is harmonic.
The harmonic conjugate of a function u(x,y) is a function v(x,y) such that f(z) = u(x,y) + i*v(x,y) is analytic. To find the harmonic conjugate of u = 2e* cos(y), we can use the Cauchy-Riemann equations:
∂u/∂x = ∂v/∂y
∂u/∂y = -∂v/∂x
Plugging in the partial derivatives of u, we get:
0 = ∂v/∂y
-2e* sin(y) = -∂v/∂x
Integrating both equations with respect to x and y, we get:
v = C₁
v = 2e* cos(y) + C₂
Setting these equal to each other and solving for v, we get:
v = 2e* cos(y) + C
So the harmonic conjugate of u = 2e* cos(y) is v = 2e* cos(y) + C, where C is a constant.
b) If u is the harmonic conjugate of v in a domain D, then f(z) = u(x,y) + i*v(x,y) is analytic in D. This means that f(z) satisfies the Cauchy-Riemann equations:
∂u/∂x = ∂v/∂y
∂u/∂y = -∂v/∂x
If we take the partial derivatives of these equations with respect to x and y, we get:
∂²u/∂x² = ∂²v/∂x∂y
∂²u/∂x∂y = -∂²v/∂x²
∂²u/∂y∂x = -∂²v/∂y²
∂²u/∂y² = ∂²v/∂y∂x
Adding the first and last equations, we get:
∂²u/∂x² + ∂²u/∂y² = ∂²v/∂x∂y + ∂²v/∂y∂x
Since the mixed partial derivatives are equal, this simplifies to:
∂²u/∂x² + ∂²u/∂y² = 0
So u is harmonic in D. Similarly, we can add the second and third equations to get:
∂²v/∂x² + ∂²v/∂y² = 0
So v is also harmonic in D. Therefore, if u is the harmonic conjugate of v in a domain D, then both u and v are harmonic in D.
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Cindy bought 7/8 yard of ribbon jacob bought 4/5 the length as cindy how much ribbon did jacob buy
If Cindy bought 7/8 yards of ribbon, then the length of Ribbon that Jacob bought is 7/10 yard.
The length of ribbon which Cindy bought is = 7/8 yard;
Jacob bought 4/5 the length as Cindy,
Which means that he bought, (4/5) × (7/8) yards of ribbon,
On multiplying these two fractions,
We get,
⇒ (4/5) × (7/8) = (4×7)/(5×8) = 28/40;
On simplifying this fraction, we divide both the numerator and denominator by their greatest common factor, which is 4,
We get,
⇒ 28/40 = 7/10,
Therefore, Jacob bought 7/10 yard of ribbon.
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The length of a rectangle is represented by 6x + 5. The width of the rectangle is represented by 3x. The perimeter is 100 centimeters. Which equations represent the perimeter? Choose all the correct answers
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
simply because the perimeter means to go along every side the shape has.
I don't see any answer options. you did not provide any. I can only give you the approach of how to solve this.
so, that means for us
2(6x + 5) + 2×3x = 100
12x + 10 + 6x = 100
18x = 90
x = 90/18 = 5
Why is |x| + 2 >|x|.
|x| + 2 is always greater than |x| because |x| is always positive or zero.
What is Absolute Value of a Number?Absolute value of a number is defined as the positive value of the number. even the number is negative, the absolute value is the positive value of that number.
Consider |x| for any number x.
The possibilities of x are positive number, zero or negative number.
If x is a positive number, |x| is also the same positive number.
2 adding to |x| is also positive number.
So |x| + 2 > |x|
If x is a negative number, |x| is the positive value of that negative number.
So |x| + 2 > |x|.
If x is 0, the |x| = 0
|x| + 2 = 0 + 2 = 2 > |x| = 0
Hence in all cases, |x| + 2 > |x|.
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five students each wrote an expression to represent the perimeter of the given rectangle [3x+3x) +(4x+4x)+( 3+3)
Answer:
The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.
However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:
2(3x + 4x + 3) = 14x + 6
2(6x + 6) + 2(4x + 6) = 20x + 24
2(3x + 3) + 2(4x + 3) = 14x + 12
2(6x + 3) + 2(4x + 3) = 20x + 12
2(6x + 3x) + 2(3 + 4x) = 18x + 10
Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.
GivenG=(G;∗)is group andH≤Gand given setN(H)N(H)={g∈G∣gHg−1=H}Prove thatH◃G↔N(H)=G
we have proved that H ◃ G ↔ N(H) = G.
Given G = (G;*) is a group and H ≤ G, and given set N(H) = {g ∈ G | gHg^-1 = H}, we need to prove that H ◃ G ↔ N(H) = G.
First, let's assume that H ◃ G. This means that H is a normal subgroup of G. By definition, a normal subgroup is a subgroup that is invariant under conjugation by any element of the group. In other words, for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is exactly the condition for an element to be in N(H), so we can conclude that N(H) = G.
Now, let's assume that N(H) = G. This means that every element of G is in N(H), which means that for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is the definition of a normal subgroup, so we can conclude that H ◃ G.
Therefore, we have proved that H ◃ G ↔ N(H) = G.
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Let R4 have the Euclidean inner product. Find a unit vector with
a positive first component that is orthogonal to all three of the
following vectors. u = (1, −1, 3, 0), v = (6, 1, 0, 1),
There is no unit vector with a positive first component that is orthogonal to both u and v.
The unit vector we are looking for is (1/√14, √13/14, √15/14, -√12/14). To find this vector, we need to solve the equation 0 = u1 + v1, where u1 and v1 are the first components of u and v. From the given vectors, u1 = 1 and v1 = 6. So 0 = 1 + 6, which simplifies to -6 = 0, which is a contradiction, meaning there is no unit vector with a positive first component that is orthogonal to both u and v.
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Using the quotient and reciprocal identities again, simplify the left side. \[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\sec x+\sec x}{\csc x} \\ & =\frac{2 \sec x}{\csc x} \end{al
The simplified form of the left side of the equation is $2 \tan x$.
The left side of the equation can be simplified using the quotient and reciprocal identities. The quotient identity states that $\tan x = \frac{\sin x}{\cos x}$ and the reciprocal identity states that $\sec x = \frac{1}{\cos x}$ and $\csc x = \frac{1}{\sin x}$. By substituting these identities into the equation, we can simplify the left side:
\[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\frac{1}{\cos x}+\frac{\sin x}{\cos x} \cdot \frac{1}{\sin x}}{\frac{1}{\sin x}} \\ & =\frac{\frac{1}{\cos x}+\frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2 \cdot \frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2}{\cos x} \cdot \frac{\sin x}{1} \\ & =\frac{2 \sin x}{\cos x} \\ & =2 \tan x \end{aligned} \]
Therefore, the simplified form of the left side of the equation is $2 \tan x$.
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On average, a clothing store gets 120 customers per day. What is the probability that the store will have fewer than 12 customers in the first two hours? (Assume the store is open 12 hours each day. Round your answer to four decimal places. )
The probability that clothing store have fewer than 12 customers in first 2 hours is 0.0003.
We know that, the store is open for 12 hours and gets an average of 120 customers per day, the expected number of customers in a 2-hour period can be calculated as:
The Expected number of customers in 2 hours = 120×(2/12) = 20 customers,
We, use the Poisson distribution to find the probability of having fewer than 12 customers in the first two hours.
The Poisson distribution is given by : P(X = k) = (e^(-λ) × λ^k)/k! ;
where X = random variable (the number of customers), λ = expected value of X (in this case, λ = 20), k = number of customers we want to calculate the probability for, and k! is the factorial of k.
To find the probability of having fewer than 12 customers in the first 2 hours, we need to calculate the probability for k = 0, 1, 2, ..., 11 and add up the probabilities.
So, we have,
⇒ P(X < 12) = e⁻²⁰×(20⁰/0!) + e⁻²⁰×(20¹/1!) + ... + e⁻²⁰×(20¹¹/11!);
On solving, We get,
⇒ P(X < 12) = 0.0003,
Therefore, the required probability is 0.0003.
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Which graph models function m?
x- 0 1 2 3 4 5
m(x)- -9 -4 -1 0 -1 -4
A ferry traveled
1
6
6
1
start fraction, 1, divided by, 6, end fraction of the distance between two ports in
3
7
7
3
start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.
At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The ferry travels at constant rate is 7/18 miles/hour
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
As per the data given in the question we have to find the ferry travels at a constant rate.
As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.
Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours
Hence, Rate of Ferry is equal to distance travelled over time taken.
Rate of ferry = 1/6 ÷ 3/7
Now we calculate it.
Rate of ferry = 1/6 × 7 / 3 miles/hour
Rate of Ferry = 7/18 miles/hour
Hence, The ferry travels at constant rate is, 7/18 miles/hour.
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About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected.
1) Mean:
2) Standard Deviation:
3) What is the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%?
About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected. The mean is 0.71. Standard Deviation is 0.043. The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.
1) Mean:
The mean of a proportion is simply the proportion itself, so the mean is 0.71.
2) Standard Deviation:
The standard deviation of a proportion is given by the formula:
σ = √(p(1-p)/n)
where p is the proportion, and n is the sample size. Plugging in the values given in the question:
σ = √(0.71(1-0.71)/110)
σ = 0.043
3) To find this probability, we need to use the normal distribution. We will use the z-score formula:
z = (x - μ) / σ
where x is the proportion we are interested in (0.8), μ is the mean (0.71), and σ is the standard deviation (0.043). Plugging in the values:
z = (0.8 - 0.71) / 0.043
z = 2.09
Using a z-table, we find that the probability of getting a z-score greater than 2.09 is 0.0183. So the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.
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HELPPP!!!!
What should be reason 2 in the following proof?
The reason that should be used to complete statement 2 "∠2 and ∠3 are supplementary" is linear pair postulate.
What is the linear pair theorem?In Mathematics, the linear pair theorem is sometimes referred to as linear pair postulate and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.
This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.
According to the linear pair theorem, we have the following supplementary angles:
∠2 + ∠3 = 180°
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the data is given for 62 students in certain class regarding their mathematics marks out of 100.take the classes 0-10,10-20..and prepare frequency distribution table and cumulative frequency table more than or equal to type 55,60,81,90,45,65,45,52,30,85,20,10,75,95,09,20,25,39,45,50,78,70,46,64,42,58,31,82,27,11,78,97,07,22,27,36,35,40,75,80,47,69,48,59,32,83,23,17,77,45,05,23,37,38,35,25,46,57,68,45,47,49.from the prepared table answer the following question 1.
The frequency and cumulative frequency distribution tables for the given data are below in the solution part.
What is the cumulative frequency of the data?Cumulative frequency is used to calculate the number of observations in a data collection that is above (or below) a specific value.
The data is provided for 62 students in a certain class in terms of their maths marks out of 100.
55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
The frequency distribution table for the given data is as follows:
Class Frequency
(Marks obtained) (No. of students)
0 - 10 4
10 - 20 3
20 - 30 8
30 - 40 9
40 - 50 13
50 - 60 6
60 - 70 5
70 - 80 6
80 - 90 5
90 - 100 3
N = 62
The cumulative frequency table more than or equal to the type for the given data is as follows:
Class Frequency Cumulative frequency
(Marks obtained) (No. of students)
0 - 10 4 62
10 - 20 3 58
20 - 30 8 55
30 - 40 9 47
40 - 50 13 38
50 - 60 6 25
60 - 70 5 19
70 - 80 6 14
80 - 90 5 8
90 - 100 3 3
N = 62
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Friends
Jennifer and Jose are planning to meet at the
playground. Jennifer is already there, but her
friend Jose needs to take the shortest
path possible on his e-bike. Jose has two ways
he can go:
Option 1: he can follow the roads getting to the
park- first heading south 3 miles, then heading
west 4 miles.
Option2: he can get there by cutting through
some open fields and riding directly to the park.
Draw a diagram to illustrate the two options.
Apply Pythagorean Theorem to find the total
distance for option 2 and make a
recommendation. Explain which option is
shorter any by how much
The shortest distance Jose can ride to park is 5 miles.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, Jose can follow the roads getting to the park- first heading south 3 miles, then heading west 4 miles.
Let the shortest root Jose can choose be x miles.
By using Pythagoras theorem, we get
x²=3²+4²
x²=9+16
x²=25
x= 5 miles
Therefore, the shortest distance is 5 miles.
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What term refers to the achievements that will take a person awhile to meet? A. backwards goals B. short-term goals C. long-term goals D. visualization
Answer:
C is the answer
7. What are the coordinates of the intersection point? Does this match your answer from question 4? (2 points: 1 point each question)
8. Answer the original questions. (2 points: 1 point each question)
a) How long is each individual act?
b) How long is each group act?
9. Discussion.
Discuss the reasonableness of your answers. (2 points: 1 point for each part)
a) Is the answer you found reasonable? Does it seem like enough time?
b) Would a negative solution such as (–5, –10) be acceptable in this situation? Why or why not?
No, a negative solution such as (-5, -10) would not be acceptable in this situation.
What is coordinates?Coordinates are a set of values that indicate a position on a two-dimensional grid. The most common type of coordinates are known as Cartesian coordinates, which have an x-axis and a y-axis. Coordinates can also be used to describe points in three-dimensional space, such as a latitude and longitude on a map. Coordinates are used by scientists, engineers, and navigators to pinpoint exact locations and make calculations.
This is because a negative solution would imply that the acts were running for a negative amount of time, which is impossible. Additionally, the intersection point of the two equations should be a point of equilibrium where both acts are running for the same amount of time. A negative solution would indicate that one of the acts is running for more time than the other, which defeats the purpose of the equations. Therefore, a negative solution would not be an acceptable answer for this situation.
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can you help me find the equation of the line
Answer:
[tex]y=\frac{2}{3}x+1[/tex]
Step-by-step explanation:
Slope-Intercept Line Equation:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
From the graph, we can see that the y-intercept is (0, 1). This means that the equation is currently:
[tex]y=mx+1[/tex]
To find the slope, we can use a point on the line to replace the x and y variables. The point that we use cannot have x equal to zero. If we use the x-intercept [tex](-1.5, 0)[/tex], the new equation will be:
[tex]0=m(-1.5)+1[/tex]
Then, we must find m:
[tex]0=m(-1.5)+1[/tex]
[tex]-1=m(-1.5)[/tex]
[tex]\frac{-1}{-1.5}=m[/tex]
[tex]m=\frac{2}{3}[/tex]
Now we can find the equation of the line:
[tex]y=\frac{2}{3}x+1[/tex]
Magnus needed to put 6 gallons 3quarts of gas into his boat on Monday and twice as much on Saturday if he had 19 gallon jug of gas available did he have enough gas for both days.
Therefore , the solution of the given problem of unitary method comes out to be he only had a 19 gallon jug of petroleum, which was insufficient for both days.
Describe the unitary method.To finish the job using the unitary method, multiply the subsets measures taken from this microsecond section by two. In a nutshell, when a wanted thing is present, the characterized by a variable group but also colour groups are both eliminated from the unit technique. For instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
Magnus had to fill up his skiff with 6 gallons and 3 quarts of gas on Monday. We can observe that 1 quart is equivalent to 0.25 gallons to express this in decimal form:
=> 6 gallons 3 quarts = 6 + 3/4 = 6.75 gallons
Magnus used 6.75 litres of fuel on Monday as a result.
He required twice as much petrol on Saturday as he did on Monday:
=> 13.5 gallons from
=> 2 (6.75" gallons).
So on Saturday, he consumed 13.5 litres of fuel.
Overall, he employed:
=> 6.75 gallons + 13.5 gallons = 20.25 gallons
He only had a 19 gallon jug of petroleum, which was insufficient for both days.
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The table represents a quadratic function C(t).
t C(t)
−2 7
−1 4
0 3
1 4
2 7
What is the equation of C(t)?
C(t) = −(x − 3)2
C(t) = (x − 3)2
C(t) = −x2 + 3
C(t) = x2 + 3
The value for the quadratic equation is C(t) = t² + 3.
What is vertex?When two lines or rays intersect and cross at one endpoint or vertex, a vertex angle is created. This angle, which is expressed in degrees, is occasionally confused with face angle. Two intersecting lines at the corner of a 2D object, such a polygon, generate a vertex angle. In 3D forms, however, multiple angles are conceivable since there are more than two lines.
The standard form of the quadratic function is given as:
C(t) = at² + bt + c
Using different values of t from the table we have:
a(-2)² + b(-2) + c = 7
a(-1)² + b(-1) + c = 4
a(0)² + b(0) + c = 3
Simplifying the equations we have:
4a - 2b + c = 7
a - b + c = 4
c = 3
Substituting the value of c = 3 in equation 2:
a - b = 1
Further solving the equation for a and b we have:
a = 1
b = 0
Hence, the equation for the quadratic equation is C(t) = t² + 3.
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Maria drops a stone from the top of a building. The stone falls 2. 0 meters in the 1st second. If it has fallen 149 meters by the 50th second. How many meters would the stone have fallen after 10 seconds?
If the stone dropped by Maria falls 2 meter in 1st second, then the stone would have fallen 30 meter after 10 seconds.
The distance that the stone falls in the first second is = 2 meters;
The distance that the stone falls in the 50th second is = 149 meters;
So, the rate of fall of the stone can be calculated as:
⇒ (149 - 2)/(50 - 1);
⇒ 147/49;
⇒ 3.
So , the stone is falling at the rate of 3 meter per second,
The distance fall by the stone after 10 second can be calculated as :
⇒ 10×3
⇒ 30 meter.
Therefore, After 10 seconds the stone would have fallen 30 meter.
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Write a quadratic function f whose zeros are -2 and 9 .
To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).
How to find the quadratic function of f?A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:
f(x)= (x+2) (x-9)Expanding the product, we have:f(x)= x²-7x-18So the quadratic function whose zeros are -2 and 9 is:
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What is the domain and range of y = log(-x + 3) - 1?
Answer:
The argument of the logarithmic function should be greater than zero.
Thus, for y = log(-x + 3) - 1 to be real-valued, we need:
-x + 3 > 0
or
x < 3
So, the domain of the function is all real numbers less than 3.
To find the range, let's consider the behavior of the logarithmic function.
As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.
As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.
Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.
Step-by-step explanation:
Suppose vector d = vector a - vector b where vector vector a has components ax = 4, ay = 5 and vector vector b has components bx = -4, by = -4
The vector representing D = A - B has following values,
1. x- component of vector D = 9 and y- component of vector D = 9.
2. Magnitude and direction of vector D is equal to 12.73 and 45° above the positive x-axis.
Here, Vector D= A-B __(1)
Components of vector A are,
Ax=5
Ay=5
Components of vector B are,
Bx= -4,
By= -4
1. Subtract the x- and y-components of vector B from vector A, respectively by substituting in (1) we get,
Dx = Ax - Bx
= 5 - (-4)
= 5 + 4
= 9
Dy = Ay - By
= 5 - (-4)
= 5 + 4
= 9
2. Magnitude of vector D, use the Pythagorean theorem,
|D| = √(Dx² + Dy²)
= √(9² + 9²)
= √(162)
≈ 12.73
Direction of vector D, use trigonometry.
Angle θ represents vector D makes angle with positive x-axis is ,
θ = tan⁻¹(Dy / Dx)
= tan⁻¹(9 / 9)
= tan⁻¹(1)
= 45°
Therefore, required value of the vectors are,
1. x- and y-components of vector D are 9 and 9, respectively.
2. Magnitude of vector D is 12.73, and direction is 45° above the positive x-axis.
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The above question is incomplete , the complete question is:
Suppose D= A-B where vector A has components Ax=5, and Ay=5 and vector B has components Bx= -4, By= -4.
1. What are the x- and y- components of vector D?
2. What are the magnitude and direction of vector D?
In the triangle shown below AB=BC=10
and AC=12.
To
A) 0.4
B) 0.6
C) 0.8
D) 1.2
10
B
12
What is the value of sin ?
10
#
0
point
The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.
What is Pythagorean theorem?
The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.
The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.
The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.
The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.
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. Line y = 2x + 1 is
transformed by a dilation
with a scale factor of 2 and centered at (3, 5). Is
the image the same line or a parallel line? How do
you know?
You are planning a vacation. The hotel you are going to stay at charges $135 per night. This can be represented by the function p(x) = 135x. The car rental company charges a $45 insurance fee plus $79 per day. This can be represented by the function p(x) = 45 + 79x. Formulate a function to represent the total charges for your hotel and car rental.
A,) p(x) = 259x
B,) p(x) = 135(79x + 45)
C,) p(x) = 45 + 214x
D,) p(x) = 45(135x + 79x)
The function to represent the total charges for your hotel and car rental is C,) p(x) = 45 + 214x
What is the equation?In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.
Given that hotel, you are going to stay at charge $135 per night. It can be represented by the function p(x) = 135x.
Also, car rental company charges a $45 insurance fee plus $79 per day.
It can be represented by the function p(x) = 45 + 79x.
Daily rental fee = $135 per night,
Write the equation for the total fees
p(x) = 45 + 214x
Thus, x represents the number of days.
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Please please help will mark BRAINLIEST due tomorrow,!!!!! PLEASE PLEASE THANK YOU (PICTURE ATTACHED)
The solution for the inequality in this problem is problem is given as follows:
v ≤ 81.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality is given as follows:
5v/9 ≤ 45.
v ≤ 45 x 9/5
v ≤ 9 x 9
v ≤ 81.
Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.
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245% of what number is 49
Answer: 20
Step-by-step explanation:
49 ÷ 245 %
convert the percentage to decimals
49 ÷ 2.455
calculate the product or quotient
20
Please give me brainliest
Answer:20
Step-by-step explanation:
Let's denote the number we are looking for as "x".
We can set up the equation:
245% of x = 49
We can convert 245% to the decimal form by dividing by 100:
2.45 * x = 49
To solve for x, we can divide both sides of the equation by 2.45:
x = 49 / 2.45
x = 20
Therefore, 245% of 20 is equal to 49.
3) The height of a ball above the ground t seconds after it is thrown is h(t) = 20 + 32t - 16t².
a) How long will it take for the ball to hit the ground?
b) How long does it take to reach its maximum height?
c) What is the ball's maximum height?
d) If the ball was thrown from a height of 30 feet what would the equation be?
Answer:It will hit the ground when 84 - 16t^2 = 0
Step-by-step explanation:
16t^2 = 84
t^2 = 5.25
t = 2.29
The following illustrates an application of optimization using parabolas.
A study found that the cost C per pupil of operating a high school in a certain country depends on the number n of students enrolled. The cost is given by
C = 70,000 − 500n + n2 dollars per pupil.
What enrollment produces the minimum cost per pupil?
n = students
The minimum cost per pupil is $7,500 when 250 students are enrolled.
To find the minimum cost per pupil, we need to find the vertex of the parabola C = 70,000 − 500n + n². The vertex of a parabola in the form y = ax² + bx + c is given by the formula x = -b/2a. In this case, a = 1, b = -500, and c = 70,000.
Plugging these values into the formula, we get:
x = -(-500)/2(1) = 500/2 = 250
So the minimum cost per pupil occurs when n = 250 students are enrolled.
To find the minimum cost, we can plug n = 250 back into the equation for C:
C = 70,000 − 500(250) + (250)² = 70,000 - 125,000 + 62,500 = 7,500
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