The reference angles are in the first, second, third, and fourth is 78°, 102°, 258°, and 282° respectively.
What is the reference angle?the angle between the terminal side of the angle and the x-axis.
For the first quadrant:
The reference angle = 258 - 180 = 78°
For the second quadrant:
= 180 - 78 = 102°
For the third quadrant:
= 78 + 180
= 258°
For the fourth quadrant:
= 360- 78
= 282°
Thus, the reference angles are in the first, second, third, and fourth is 78°, 102°, 258°, and 282° respectively.
Learn more about the reference angle here:
brainly.com/question/16210309
#SPJ2
Solve system of equations given below using both inverse matrix (if possible) and reduced row echelon forms. (20 Points each)
a) xy + 2x_2 + 2x_3 = 1
x_1 - 2x_2 + 2x_3 = - 3
3x_1 - x_2 + 5x_3 = 7
b) x_1 + 2x_2 + 2x_3 + 5x_4 = 0
x_1 - 2x_2 + 2x_3 - 4x_4 = 0
3x_1 - x_2 + 5x_3 + 2x_4 = 0
3x_1, -2x_2 + 6x_3 - 3x_4 = 0.
The solution to the system of equations is: x1 = 1/2, x2 = 9/4, x3 = 1, x4 = 0
a) Solving the system of equations using inverse matrix:
Let's write the system of equations in matrix form: AX = B
The coefficient matrix A is:
A = [[y, 2, 2], [1, -2, 2], [3, -1, 5]]
The variable matrix X is:
X = [[x], [y], [z]]
The constant matrix B is:
B = [[1], [-3], [7]]
To solve for X, we need to find the inverse of matrix A (if it exists):
Calculate the determinant of matrix A: |A|
|A| = y((-2)(5) - (-1)(2)) - 2((1)(5) - (3)(2)) + 2((1)(-1) - (3)(-2))
= -9y + 4
Check if |A| is non-zero. If |A| ≠ 0, then the inverse of A exists.
Since |A| = -9y + 4, it can only be zero if y = 4/9.
If y ≠ 4/9, then |A| ≠ 0, and we can proceed to find the inverse of A.
Calculate the matrix of minors of A: Minors(A)
Minors(A) = [[(-2)(5) - (-1)(2), (1)(5) - (3)(2), (1)(-1) - (3)(-2)],
[(2)(5) - (2)(2), (3)(5) - (3)(2), (3)(-1) - (3)(-2)],
[(2)(-1) - (2)(-2), (3)(-1) - (1)(2), (3)(-2) - (1)(-1)]]
= [[-8, -1, -1],
[6, 9, -3],
[2, -1, -5]]
Calculate the matrix of cofactors of A: Cofactors(A)
Cofactors(A) = [[(-1)^1(-8), (-1)^2(-1), (-1)^3(-1)],
[(-1)^2(6), (-1)^3(9), (-1)^4(-3)],
[(-1)^3(2), (-1)^4(-1), (-1)^5(-5)]]
= [[-8, 1, -1],
[6, -9, 3],
[-2, 1, -5]]
Calculate the adjugate of A: Adj(A) = Transpose(Cofactors(A))
Adj(A) = [[-8, 6, -2],
[1, -9, 1],
[-1, 3, -5]]
Calculate the inverse of A: A^(-1) = Adj(A)/|A|
A^(-1) = [[(-8)/(9y - 4), 6/(9y - 4), (-2)/(9y - 4)],
[1/(9y - 4), (-9)/(9y - 4), 1/(9y - 4)],
[(-1)/(9y - 4), 3/(9y - 4), (-5)/(9y - 4)]]
Multiply A^(-1) by B to find X:
X = A^(-1) * B
= [[(-8)/(9y - 4), 6/(9y - 4), (-2)/(9y - 4)],
[1/(9y - 4), (-9)/(9y - 4), 1/(9y - 4)],
[(-1)/(9y - 4), 3/(9y - 4), (-5)/(9y - 4)]] * [[1], [-3], [7]]
Simplifying the multiplication will give the solution for X in terms of y.
b) Solving the system of equations using reduced row echelon form:
Let's write the system of equations in augmented matrix form [A | B]:
The augmented matrix [A | B] is:
[1, 2, 2, 5 | 0]
[1, -2, 2, -4 | 0]
[3, -1, 5, 2 | 0]
[3, -2, 6, -3 | 0]
Using Gaussian elimination and row operations, we can transform the augmented matrix to reduced row echelon form.
Performing row operations:
R2 = R2 - R1
[1, 2, 2, 5 | 0]
[0, -4, 0, -9 | 0]
[3, -1, 5, 2 | 0]
[3, -2, 6, -3 | 0]
R3 = R3 - 3R1
[1, 2, 2, 5 | 0]
[0, -4, 0, -9 | 0]
[0, -7, -1, -13 | 0]
[3, -2, 6, -3 | 0]
R4 = R4 - 3R1
[1, 2, 2, 5 | 0]
[0, -4, 0, -9 | 0]
[0, -7, -1, -13 | 0]
[0, -8, 0, -18 | 0]
R2 = (-1/4)R2
[1, 2, 2, 5 | 0]
[0, 1, 0, 9/4 | 0]
[0, -7, -1, -13 | 0]
[0, -8, 0, -18 | 0]
R3 = R3 + 7R2
[1, 2, 2, 5 | 0]
[0, 1, 0, 9/4 | 0]
[0, 0, -1, -1 | 0]
[0, -8, 0, -18 | 0]
R4 = R4 + 8R2
[1, 2, 2, 5 | 0]
[0, 1, 0, 9/4 | 0]
[0, 0, -1, -1 | 0]
[0, 0, 0, -6 | 0]
R4 = (-1/6)R4
[1, 2, 2, 5 | 0]
[0, 1, 0, 9/4 | 0]
[0, 0, -1, -1 | 0]
[0, 0, 0, 1 | 0]
R1 = R1 - 2R2 - 2R3
[1, 0, 0, 1/2 | 0]
[0, 1, 0, 9/4 | 0]
[0, 0, -1, -1 | 0]
[0, 0, 0, 1 | 0]
R3 = -R3
[1, 0, 0, 1/2 | 0]
[0, 1, 0, 9/4 | 0]
[0, 0, 1, 1 | 0]
[0, 0, 0, 1 | 0]
The reduced row echelon form of the augmented matrix is obtained.
From the reduced row echelon form, we can write the system of equations:
x1 = 1/2
x2 = 9/4
x3 = 1
x4 = 0
To learn more about matrix
https://brainly.com/question/28180105
#SPJ11
Find the value of x. Also with explanation please
Answer:
x+90°+130°=360°
x+220°=360°
x=360°-220°
x=140°
We can write logs into the form A logs + Blog, y where A = and B = Write A and B as integers or reduced fractions.
The logarithmic expression can be written in the form Alog(s) + Blog(y), where A and B are integers or reduced fractions.
To express a logarithmic expression in the form Alog(s) + Blog(y), we need to understand the properties of logarithms and simplify the given expression.
The generic logarithmic expression can be written as log(b)(x), where b is the base and x is the argument. To write it in the desired form, we aim to express it as a combination of logarithmic terms with the same base.
First, let's consider an example expression: log(a)(x). We can rewrite it as (1/log(x))(log(a)(x)). Here, A = 1/log(x) and B = log(a)(x). Notice that A is the reciprocal of the logarithm of the base.
Similarly, for the expression log(b)(y), we can rewrite it as (1/log(y))(log(b)(y)). In this case, A = 1/log(y) and B = log(b)(y).
So, in general, for a logarithmic expression log(b)(x), we can express it as Alog(s) + Blog(y), where A = 1/log(x) and B = log(b)(x). These coefficients A and B can be integers or reduced fractions, depending on the specific values of the logarithmic expression and the chosen base.
Learn more about logarithmic expression here:
https://brainly.com/question/29194783
#SPJ11
Use the decimal grid to write the percent and fraction equivalents.
0.53
Answer:
53%
53/100
Step-by-step explanation:
Test test the daim that the proportion of children from the low income group that did well on the test is different than the proportion of the high income group. Test at the 0.05 significance level. We are given that 24 of 40 children in the low income group did well, and 12 of 35 did in the high income group. If we use L to denote the low income group and H to denote the high income group, identify the correct alternative hypothesis.
The correct alternative hypothesis is:
Ha: The proportion of children from the low-income group that did well on the test is not equal to the proportion of the high-income group who did well on the test.
The alternative hypothesis is what the researcher wants to test.
It is the opposite of the null hypothesis.
In other words, if the null hypothesis is rejected, the alternative hypothesis is accepted.
The null hypothesis (H0) states that there is no significant difference between the proportions of children from the low income group and the high income group who did well on the test.
The alternative hypothesis (Ha) states that there is a significant difference between the proportions of children from the low income group and the high income group who did well on the test.
Therefore, the correct alternative hypothesis is:
Ha: The proportion of children from the low-income group that did well on the test is not equal to the proportion of the high-income group who did well on the test.
To know more about proportion, visit :
https://brainly.com/question/1496357
#SPJ11
encontre as raízes quadradas dos números:
a)²√625
b)²√100
c)²√81
Answer:
a.) 25, b.)10, c.)9
Step-by-step explanation:
a.) 25x25=625
b.)10x10=100
c.) 9x9=81
9 Marty conducted a survey in his first period class to determine student preferences for music. Out of 25 students, 14 like hip-hop music best. There are 300 students in Marty's school. Based on the survey, how many students in the school like hip- hop music best? A. 50 students B. 132 students C. 168 students D. 261 students
Answer:
C
Step-by-step explanation:
14/25=0.56 0.56x300=168
Based on the survey,
168 students like hip-hop music.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
Marty conducted a survey in his first period class to determine student preferences for music.
Out of 25 students, 14 like hip-hop music best.
That means, the ratio is 14/25 = 0.56.
There are 300 students in Marty's school.
Based on the survey,
the number of students = 300 x 0.56 = 168 students like hip-hop music.
Therefore, 168 students like hip-hop music.
To learn more about the ratio;
https://brainly.com/question/13419413
#SPJ6
Find the area of the shape shown below.
3
3
units?
Answer:
find the answer of the rectangle (7×3=21)
than find the area if one triangle and do 7/2 to get base then multiply 1/2base×height. because there are two triangles add the area to itself then add it to the area of the rectangle. the two triangles shoukd equal 21 together and 21 plus 21 equals 42.
Step-by-step explanation:
im sorry if this is incorrect but it should be right
Find the area of the figure.
HELP PLZZ
Answer:
159.25 ft²
I hope this helps! :)
Step-by-step explanation:
Formulas:
For the Rectangle... bh = a
For the Semicircle... 1/2 × πr²
Step 1:
Solve the area for the rectangle:
bh = a
10 × 12 = 120
a = 120 ft²
Step 2:
Solve the Area for the Semicircle:
1/2 × πr²
1/2 × 3.14 = 1.57
Radius = Diameter ÷ 2
10 ÷ 2 = 5
Radius = 5
1.57 × 5²
1.57 × 5 × 5
= 39.25 ft²
Step 3:
Add the two areas together:
120 + 39.25 = 159.25 ft²
How many turns must an ideal solenoid 10 cm long have if it is to generate a magnetic field of 1.5 mT when a current of 1.0 A passes through it?
a) 3.5
b) 1.8
c) 2.2
d) 0.50
e) 2.8
1.8 turns must an ideal solenoid should have if it is to generate a magnetic field of 1.5 mT when a current of 1.0 A passes through it
To calculate the number of turns required for an ideal solenoid, we can use the formula for the magnetic field inside a solenoid: B = μ₀ * n * I, where B is the magnetic field, μ₀ is the permeability of free space (constant), n is the number of turns per unit length, and I is the current.
Rearranging the formula, we have n = B / (μ₀ * I).
Given B = 1.5 mT (or 1.5 x 10⁻³ T) and I = 1.0 A, and knowing that μ₀ is a constant, we can substitute these values into the formula to find n.
n = (1.5 x 10⁻³) / (4π x 10⁻⁷ * 1.0) ≈ 1.19 x 10⁴ turns/m.
Since the solenoid is 10 cm (0.1 m) long, we can multiply n by the length to find the total number of turns:
Total turns = (1.19 x 10⁴ turns/m) * 0.1 m ≈ 1.19 x 10³ turns.
Rounding to the nearest whole number, the closest option is (b) 1.8.
Learn more about Magnetic Field:
https://brainly.com/question/31838837
#SPJ4
Show that the eigenvalue problem (4.75-4.77) has no negative eigenvalues. Hint: Use an energy argument-multiply the ODE by y and integrate from p=0 to r=R; use integration by parts and use the boundedness at r = 0 to get the boundary term to vanish.
The eigenvalue problem (4.75-4.77) has no negative eigenvalues.
In the eigenvalue problem (4.75-4.77), we aim to show that there are no negative eigenvalues. To do this, we employ an energy argument.
First, we multiply the ordinary differential equation (ODE) by the eigenfunction y and integrate from p=0 to r=R. By applying integration by parts, we manipulate the resulting equation to obtain a boundary term. Utilizing the boundedness at r=0, we can show that this boundary term vanishes.
Consequently, this implies that there are no negative eigenvalues in the given eigenvalue problem.
By employing this energy argument and carefully considering the properties of the ODE, we can confidently conclude the absence of negative eigenvalues.
Learn more about eigenvalue
brainly.com/question/14415841
#SPJ11
class 9 help who are clever will get a brainlist
The mean score of a competency test is 64, with a standard deviation of 4. Between what two values do about 99.7% of the values lie? (Assume the data set has a bell-shaped distribution.) Between 56 and 72 Between 60 and 68 O Between 52 and 76 Between 48 and 80
In a dataset with a bell-shaped distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Given a mean score of 64 and a standard deviation of 4 on a competency test, we can determine the range within which about 99.7% of the values will fall. The correct range is between 56 and 72.
To calculate the range, we need to consider three standard deviations above and below the mean. Three standard deviations from the mean account for approximately 99.7% of the data in a bell-shaped distribution.
Lower limit: Mean - (3 * Standard Deviation)
= 64 - (3 * 4)
= 64 - 12
= 52
Upper limit: Mean + (3 * Standard Deviation)
= 64 + (3 * 4)
= 64 + 12
= 76
Therefore, about 99.7% of the values lie between 52 and 76.
Learn more about standard deviation here: brainly.com/question/29115611
#SPJ11
Can someone please help me answer this question asap thank you
Colby made a scale model of the Washington Monument. The monument has an actual height of 554 feet. Colby’s model used a scale in which 1 inch represents 100 feet. What is the height in inches of Colby’s model?
Answer:
500043004030405.3
Step-by-step explanation:
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second.
a. 7:8 and 49:64
b. 8:9 and 49:64
c. 8:9 and 64:81
d. 7:8 and 64:81
The correct answer is: c. 8:9 and 64:81. The ratio of the areas of the first figure to the second figure is 64:81. This means that the area of the second figure is larger by a factor of 81/64 compared to the first figure.
When two figures are similar, their corresponding sides are proportional. This means that the ratio of the perimeters is equal to the ratio of the corresponding side lengths. Additionally, the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
In this case, the ratio of the perimeters of the first figure to the second figure is 8:9. This means that the perimeter of the second figure is larger by a factor of 9/8 compared to the first figure.
The ratio of the areas of the first figure to the second figure is 64:81. This means that the area of the second figure is larger by a factor of 81/64 compared to the first figure.
Therefore, the correct answer is c. 8:9 and 64:81.
To know more about ratio of the areas, click here: brainly.com/question/29254296
#SPJ11
11 - x when x= -4 how do you solve this
Answer:
15 is the answer
Step-by-step explanation:
We know that x = -4, so substitute x for -4 in the problem
11 - (-4)
2 negative signs make a positive sign
11 + 4
=15
Answer:
Hi! The answer to your question is [tex]15[/tex]
How to solve is whenever there is an x, replace it with a -4 so the problem would be set up like this 11-(-4) and at that point you can just solve it in a calculator
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!!☁
Hope this helps!!
- Brooklynn Deka
a - 2/3 = 3/5 how much is a?
Answer:
19/15
Step-by-step explanation: In order to solve for A add 2/3 to both sides of the equation to get A alone and 2/3 + 3/5 is equal to 10/15 + 9/15 which means the answer is 19/15.
you make a scale drawing of a banner for school dance .you use a scale of 1 inch ,2 feet what is the actual width of the banner HELP ASAP!!!!
Answer:
6.5
Step-by-step explanation:
you take the sides all added up (which was 13in) and divided it by two
Answer: the answer is 18. Trust me. I know what I’m doing lol
Step-by-step explanation:
can someone please help me out its important please.
Which of the following scatterplots do not show a clear relationship and would not have a trend line?
Answer:
B
Step-by-step explanation:
The graph does not form a obvious line and therefore is the answer.
Answer:
The answer is B i got it right.
Step-by-step explanation:
Andy has $ 200 to buy a new TV . One- forth of that money came from his grandmother and he saved the rest . How much money did Andy save?
Answer:
$150
Step-by-step explanation:
200/4=50
200-50=150
8 ft
Find the area of the figure.
Answer:
Area of a rectangle is length multiplied by the width. In this case, length is equal to width. So, Area is 8 ft * 8 ft which is 64 ft2.
calculate the double integral ∫∫r(10x 10y 100)da where r is the region: 0≤x≤5,0≤y≤5
The solution of the double integral ∫∫r(10x+10y+100)dA is found to be 5937.5.
To calculate the double integral ∫∫r(10x+10y+100)dA over the region r: 0 ≤ x ≤ 5, 0 ≤ y ≤ 5, we can integrate with respect to x first and then with respect to y. Let's start by integrating with respect to x,
∫∫r(10x+10y+100) dA = ∫[0,5] ∫[0,5] (10x+10y+100)dxdy
Integrating with respect to x, we treat y as a constant,
= ∫[0,5] [(10x²/2) + 10xy + 100x] dx dy
Next, we integrate the expression [(10x²/2) + 10xy + 100x] with respect to x over the range [0,5],
= ∫[0,5] [(10x²/2) + 10xy + 100x] dx dy
= [5x³/3 + 5xy²/2 + 50x²] evaluated from x=0 to x=5 dy
= [(5(5)³/3 + 5(5)y²/2 + 50(5)²) - (5(0)³/3 + 5(0)y²/2 + 50(0)²)] dy
= [(125/3 + 125y²/2 + 250) - 0] dy
= (125/3 + 125y²/2 + 250) dy
Now, we integrate the expression (125/3 + 125y/2 + 250) with respect to y over the range [0,5],
= ∫[0,5] (125/3 + 125y²/2 + 250) dy
= [(125/3)y + (125/6)y³ + 250y] evaluated from y=0 to y=5
= [(125/3)(5) + (125/6)(5³) + 250(5)] - [(125/3)(0) + (125/6)(0³) + 250(0)]
= [625/3 + (125/6)(125) + 1250] - [0 + 0 + 0]
= 625/3 + 125/6 * 125 + 1250
= 625/3 + 15625/6 + 1250
= 2083.33 + 2604.17 + 1250
= 5937.5
Therefore, the double integral ∫∫r(10x+10y+100)dA over the region r: 0 ≤ x ≤ 5, 0 ≤ y ≤ 5 is equal to 5937.5.
To know more about double integral, visit,
https://brainly.com/question/27360126
#SPJ4
My friend Yoy purchased some rews for $3 each and some jooghs for
$5 each. The total cost was about $60. Altogether, he purchased 18
items.
Write a system of equations, in standard form, to model the
relationship between Yoy's rews (x) and jooghs (y).
Answer:
x+Y =x68 i thinkStep-by-step explanation:
Answer:
86
Step-by-step explanation:
Example 1
Make a graph for the table in the Opening Exercise.
Example 2
Use the graph to determine which variable is the independent variable and which is the dependent variable. Then state the relationship between the quantities represented by the variables
Are the following true or false? Justify your answers briefly. a) Let f, g (0, [infinity]) → R. If limx→[infinity] (fg)(x) exists and is finite then so are both limx→[infinity] f(x) and limx→[infinity] g(x). b) Let {n} and {n} be sequences such that n < yn for all n € N. If → x and Yny, then x
False. The limit of f(x) as x approaches infinity does not exist (it approaches zero), and the limit of g(x) as x approaches infinity is infinite. Therefore, the statement is false.
False. The statement is not necessarily true. The existence of the limit of the product (fg)(x) as x approaches infinity does not guarantee the existence of the limits of f(x) and g(x) individually.
Counterexamples can be found by considering functions that approach zero at different rates. For instance, let f(x) = 1/x and g(x) = x. As x approaches infinity, the product (fg)(x) = x/x = 1 approaches 1, which is finite. However, the limit of f(x) as x approaches infinity does not exist (it approaches zero), and the limit of g(x) as x approaches infinity is infinite. Therefore, the statement is false.
For instance, let f(x) = 1/x and g(x) = x. As x approaches infinity, the product (fg)(x) = x/x = 1 approaches 1, which is finite.
Learn more about function here:
https://brainly.com/question/31062578
#SPJ11
ok so i thought i knew what i was doing but then i didn't know what i was doin-
4(8x - 3) - 6 = 5 + 2x
WHATS THE SOLUTION???
Answer:
x = 23/30
Step-by-step explanation:
4(8x - 3) - 6 = 5 + 2x
32x - 12 - 6 = 5 + 2x
32x - 18 = 5 + 2x
32x - 2x = 5 + 18
30x = 23
x = 23/30
Answer:
30x=14
Step by Step Explanation:
32x-9=5+2x
32x-2x=30x
30x-9=5
5+9 is 14
30x=14
Do dilations always produce congruent figures
Answer:
No, sometimes it can just produce a similar image .
Can I get brainliest?
Step-by-step explanation:
will give 20 brainly PLEASE NEED HELP NOW
plz put the answer as simple as a b c or d
Answer:
1. A
2. C
Step-by-step explanation: