Answers
The above prompts are related to the concepts of Degrees, Radians, Sines and Cosines. See the solutions below.
What are the solutions to the above prompts?
1)
(a) Cos 150 degrees
To convert 150 degrees to radians, we multiply by π/180:
150 degrees = (150π/180) radians = (5π/6) radians
We can use the unit circle and reference angle of π/6 to find the cosine of 5π/6:
cos(5π/6) = -cos(π/6) = -(√3/2) = -√3/2
Therefore, cos 150 degrees = -√3/2.
(b) Sin 240 degrees
To convert 240 degrees to radians, we multiply by π/180:
240 degrees = (240π/180) radians = (4π/3) radians
We can use the unit circle and reference angle of π/3 to find the sine of 4π/3:
sin(4π/3) = -sin(π/3) = -(√3/2) = -√3/2
Therefore, sin 240 degrees = -√3/2.
2)
To use the law of cosines, we need either a side and the two angles opposite that side, or two sides and the angle between them. In this case, we have two angles and the side opposite one of them, so we can use the law of sines to find the other side and then use the law of cosines to find the remaining side or angle.
Using the law of sines, we have:
sin A / AB = sin B / AC
where AC is the side opposite angle B. Substituting the given values, we get:
sin 52 / 26.7 = sin 70 / AC
Solving for AC, we get:
AC = sin 70 / sin 52 * 26.7 = 30.4
Now we can use the law of cosines to find the remaining side, x:
x^2 = AB^2 + AC^2 - 2ABACcos A
Substituting the given values, we get:
x^2 = 26.7^2 + 30.4^2 - 226.730.4*cos 52
Solving for x, we get:
x ≈ 22.1
Therefore, the missing side is approximately 22.1.
To find the area of the triangle, we can use the formula:
Area = (1/2) * a * b * sin C
where a and b are the lengths of the two sides, and C is the included angle. Substituting the given values, we get:
Area = (1/2) * 7 * 9 * sin 30
Using the fact that sin 30 = 1/2, we can simplify this to:
Area = (1/2) * 7 * 9 * (1/2) = 15.75
Therefore, the area of the triangle is 15.75 square units.
From the law of sines, we have:
sin A / a = sin B / b
Substituting the given values, we get:
sin 45° / (7√2) = sin B / 7
Solving for sin B, we get:
sin B = (7/7√2) * sin 45° = √2/2
Therefore, B = 45° or 135°. We can use the fact that the angles of a triangle sum to 180° to find C:
C = 180° - A - B = 90° or 0°
If C = 0°, then the triangle is degenerate and the sides a and b lie on top of each other. Therefore, we must have C = 90°.
Now we can use the Pythagorean theorem to find the remaining side:
c^2 = a^2 + b^2 - 2ab*cos C
Substituting the given values, we get:
c^2 = (7√2)^2 + 7^2 - 2(7√2)(7)*cos 90°
Solving for c, we get:
c = √(98 + 49) = √147 = 7√3
Therefore, the sides of the triangle are:
a = 7√2
b = 7
c = 7√3
Using the law of cosines to find x:
In triangle ABC with side lengths AB = 18, AC = 15, and angle A = 108 degrees, we want to find the length of side BC (denoted by x). Using the law of cosines:
x^2 = 18^2 + 15^2 - 2(18)(15)cos(108 degrees)
We can evaluate the cosine of 108 degrees using the identity cos(180 - 108) = -cos(108):
cos(108 degrees) = -cos(180 - 108 degrees) = -cos(72 degrees)
Substituting this into the equation above, we get:
x^2 = 18^2 + 15^2 - 2(18)(15)(-cos(72 degrees))
Simplifying:
x^2 = 729
Taking the square root of both sides:
x = ±27
Since x represents a length, we take the positive root:
x = 27
Therefore, the length of BC is 27 units.
Using the law of cosines to find theta:
In triangle ABC with side lengths AB = 20, BC = 12, and AC = 10, we want to find the measure of angle B (denoted by theta). Using the law of cosines:
cos(B) = (12^2 + 10^2 - 20^2) / (2(12)(10)) = -1/2
Since -1/2 is the cosine of an angle in the second quadrant, we have:
B = 180 degrees - arccos(-1/2)
Using a calculator, we find:
B ≈ 150.5 degrees
Therefore, the measure of angle B is approximately 150.5 degrees (or theta = 150.5 degrees).
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Related Questions
What is the answer to
7 + 60 / (3x5)
Answers
= 11
Step-by-step explanation:
To solve this problem, we need to follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, we have to perform the multiplication in the denominator:
7 + 60 / 15
Then, we can simplify the division:
7 + 4
Finally, we can add:
11
Therefore, the answer is 11.
To show the working:
7 + 60 / (3x5) = 7 + 60 / 15 (multiply 3x5 to get 15)
= 7 + 4 (divide 60 by 15)
= 11 (add 7 and 4)
Use the graph to answer the question.
graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at 8 comma 5, 10 comma 1, 14 comma 1, 12 comma 5
Determine the translation used to create the image.
7 units to the right
7 units to the left
3 units to the right
3 units to the left
Answers
A sphere has a radius of 4 in choose true or false for each statement
Answers
The true statements are (a) A sphere with half the radius has 1/8 of the volume and (c) A sphere with 3 times the radius has 27 times the volume
Finding the true statements from the radius and volumeGiven that the radius of the sphere is represented as
Radius, r = 4 inches
The formula of the volume of the sphere is represented as
V = 4/3πr³
For the transformed volume, we have
V₂ = 4/3πR³
Where
R = kr and k is the scale factor
So, we have
V₂ = 4/3π(kr)³
V₂ = 4/3πr³k³
This gives
V₂ = Vk³
Testing the statements, we have
(a) A sphere with half the radius has 1/8 of the volume
V₂ = V(1/2)³
Evaluate
V₂ = 1/8V
So, the statement is true
(b) A sphere with twice the radius has 6 times the volume
V₂ = V(2)³
Evaluate
V₂ = 8V
So, the statement is false
(c) A sphere with 3 times the radius has 27 times the volume
V₂ = V(3)³
Evaluate
V₂ = 27V
So, the statement is true
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Complete question
A sphere has a radius of 4 inches.
Choose True or False for each statement.
(a) A sphere with half the radius has 1/8 of the volume
(b) A sphere with twice the radius has 6 times the volume
(c) A sphere with 3 times the radius has 27 times the volume
How much money will be in the savings account after 13 years if I start with $4200, the annual interest rate is 5.2%, and it's compounded quarterly?
In the Show Your Work box, must have the following:
- 1 pt- Formula used
- 1 pt- Variables and what they stand for
- 3 pts- Full solving process
In the answer box, ONLY the amount (round to a whole number)!
Answers
The accrued value of the account in 14 years is $4967.89
Determining the accrued value of the account in 13 yearsFrom the question, we have the following parameters that can be used in our computation:
You invest 4200 in an account5.2% interest compounded quarterlyUsing the above as a guide, we have the following:
Amount = P * (1 + 0.25r)ᵗ
Where
P = Principal = 4200
r = Rate = 5.2% = 0.052
t = time = 13
Substitute the known values in the above equation, so, we have the following representation
Amount = 4200 * (1 + 0.25 * 0.052)¹³
Evaluate
Amount = 4967.89
Hence, the amount is 4967.89
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Is (-5, 3) a solution to this system of equations?
y = X-6
y = -2x - 7
yes
no
Answers
Answer:
No
Step-by-step explanation:
to determine if (- 5, 3 ) is a solution substitute the x- coordinate into both equations and if the value of y is equal to the y- coordinate then the point is a solution to the system.
y = x - 6 = - 5 - 6 = - 11 ≠ 3
y = - 2x - 7 = - 2(- 5) - 7 = 10 - 7 = 3
since both equations are not satisfied , then
(- 5, 3 ) is not a solution to the system
ayuda porfavor
necesito resolver esto es simplificarlo no resolverlo ayuda pls
Answers
The Simplification of the algebraic expression gives:
a. -2/3x² - (4/15)xy + (11/4)y²
b. -(12/7)x³ + (20/9)y
How to simplify algebraic expressions?Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression
a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
To simplify this, add or subtract like terms. That is:
(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
= (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y² + (3/4)y²
= -2/3x² - (4/15)xy + (11/4)y²
b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y
To simplify this, add or subtract like terms. That is:
(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y
= -(12/7)x³ + (20/9)y
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If XZ ⊥ WY, XE = 4, and WY = 7, what is the perimeter of WXYZ, rounded to the nearest tenth?
Answers
The perimeter of the rhombus is approximately 7.6 units.
XZ is perpendicular to WY and XE is 4,
Since WXYZ is a rhombus because only the diagonal of the rhombus and square bisect each other at 90°
By the Pythagorean theorem, we have:
XE² = XY² + EY²
4² = XY² + (7/2)²
XY = 1.9
So the perimeter of WXYZ is 4(XY), rounded to the nearest tenth:
4(1.9) ≈ 7.6 units.
Therefore, the perimeter of the rhombus is approximately 7.6 units.
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Solve 3/8 + n = 7/8
giving away 10 points for this
Answers
7/8 - 3/8 = 4/8
n = 4/8 or 1/2
If full employment is $2000, how large is the recessionary or inflationary gap?
Answers
Answer:
inflationary expenditure gap of $500
Step-by-step explanation:
At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.
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In July 1964, an elderly woman was mugged in Costa Mesa, California. In the vicinity of the crime a tall, bearded man sat waiting in a yellow car. Shortly after the crime was committed, a young, tall woman, wearing her blond hair in a ponytail, was seen running from the scene of the crime and getting into the car, which sped off. The police broadcast a description of the suspected muggers. Soon afterward, a couple fitting the description was arrested and convicted of the crime. Although the evidence in the case was largely circumstantial, the two people arrested were nonetheless convicted of the crime. The prosecutor based his entire case on basic probability theory, showing the unlikeness of another couple being in that area while having all the same characteristics that the elderly woman described. The following probabilities were used. Characteristic Assumed probability Drives yellow car 1 out of 12 Man over 6 feet tall 1 out of 10 Man wearing tennis shoes 1 out of 4 Man with beard 1 out of 11 Woman with blond hair 1 out of 3 Woman with hair in a ponytail 1 out of 13 Woman over 6 feet tall 1 out of 100 Compute the probability of another couple being in that area with the same characteristics. Would you use the addition or multiplication rule? Why? Are the characteristics independent or dependent? How are the computations affected by the assumption of independence or dependence? Should any court case be based solely on probabilities? Would you convict the couple who was arrested even if there were no eyewitnesses? Comment on why in today’s justice system no person can be convicted solely on the results of probabilities. In actuality, aren’t most court cases based on uncalculated probabilities?
Answers
No, any court case should not be based solely on probabilities as probability does not imply certainty.
How to solveCompute the probability of another couple being in that area with the same characteristics
CHARACTERISTIC ASSUMED PROBABILITY
Drives a yellow car 1 out of 12
Man over 6 feet tall 1 /10
Man wearing tennis shoes 1/4
Man with beard 1/11
Woman with blond hair 1/3
Woman with hair in a ponytail 1 /13
Women over 6 feet tall 1/100
We will use the multiplication rule as all the characteristics should be present in the couple.
The probability of another couple being in that area with the same characteristics is given as
P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800
The characteristics dependent on the sum of the probabilities is not equal to 1.
The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).
No, any court case should not be based solely on probabilities as probability does not imply certainty.
No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.
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Question 9: Use the function f(t) = -16t^2 + 60t + 16 to answer Part A, B, & C. Part B: identify the line of symmetry vertex of the parabola ( give exact decimal answers )
Answers
The line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).
What is a function?A function is a mathematical concept that relates an input value (or values) to an output value (or values) according to a specific rule or set of rules. It can be thought of as a machine that takes in one or more inputs and produces a corresponding output. Functions are often represented using function notation, such as f(x) or g(t), where the variable in the parentheses (x or t) represents the input and the value of the function (f(x) or g(t)) represents the output.
According to the given information:To identify the line of symmetry and vertex of the parabola given by the function [tex]f(t) = -16t^2 + 60t + 16[/tex], we need to use the formula:
t = -b/2a
where "a" is the coefficient of the [tex]t^2[/tex] term (-16 in this case) and "b" is the coefficient of the t term (60 in this case).
Part A: Identify the line of symmetry of the parabola.
Using the formula above, we get:
t = -60 / 2(-16) = 1.875
So the line of symmetry of the parabola is t = 1.875.
Part B: Identify the vertex of the parabola.
To find the vertex, we need to substitute the value we found for t into the original function:
[tex]f(1.875) = -16(1.875)^2 + 60(1.875) + 16 = 77[/tex]
So the vertex of the parabola is (1.875, 77).
Therefore, the line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).
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solve for f
f/40 = 10/f
Answers
Answer:
Step-by-step explanation:
To solve for f, we can cross-multiply the equation:
f/40 = 10/f
Multiplying both sides by 40f gives:
f^2 = 400
Taking the square root of both sides yields:
f = ±20
Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:
f = 20
f = 20
Step-by-Step Explanation:
Starting with:
f/40 = 10/f
We can simplify by multiplying both sides by f:
f/40 * f = 10/f * f
f^2 / 40 = 10
Multiplying both sides by 40:
f^2 = 400
Taking the square root of both sides, remembering to consider both the positive and negative roots:
f = ±20
So the two possible solutions are f = 20 or f = -20.
Pattern A starts at 1 and uses the rule add 5." Pattern B starts at 28 and uses the rule "subtract 4."
What are the next four terms in each pattern?
Enter your answers in the boxes.
Answers
For the pattern A, the terms are 6, 11, 16 and 21
For the pattern B, the terms are 24, 20, 16, 12
How to determine the termsTo determine the consecutive terms of the sequence, we need to take note of the rule of each.
From the information given, we have that;
For the Pattern A
Each term is the previous term plus 5
This is represented as;
Pattern A = a + 5,
The first term = 1
Second term = 1 + 5 = 6
Third term = 6 + 5 = 11
Fourth term = 11 + 5 = 16
Fifth term = 16 + 5 = 21
For Pattern B = a - 4
Second term = 28 - 4 = 24
Third term = 24 - 4 = 20
Fourth term = 20 -4 = 16
Fifth term = 16 - 4 = 12
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(cscx+sexc)/(sinx + cosx) = cotx + tanx
Answers
It is true. The trigonometric identity [tex]\frac{cscx+secx}{sinx + cosx}[/tex] = cotx + tanx
How do we verify or prove that the trigonometric identity (cscx+secx)/(sinx + cosx) = cotx + tanx?To verify that (cscx+secx)/(sinx + cosx) = cotx + tanx
csc = [tex]\frac{1}{sin}[/tex] and Sec = [tex]\frac{1}{cos}[/tex]
If we insert the values, it would be
[tex]\frac{ 1/sinx + 1/cosx}{sinx + cosx}[/tex]
= [tex]\frac{cosx + sinx}{sinx * cosx}[/tex] ÷ ([tex]\frac{1}{sinx + cosx}[/tex])
= [tex]\frac{1}{sinx * cosx}[/tex]
[tex]\frac{Sin^2 x + Cos^2x}{Sin x Cos x}[/tex] = [tex]\frac{Sin^2x}{SinxCosx}[/tex] + [tex]\frac{Cos^2x}{SinxCosx}[/tex]
= cotx + Tanx
Mind you
cotx = [tex]\frac{1}{tanx}[/tex] = [tex]\frac{cosx}{sinx}[/tex]
tanx = [tex]\frac{sinx}{cosx}[/tex]
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7x³+5x² - 2 = [?]
X = -1
Answers
Use the form |x – b | ≤ c or |x – b | ≥ c to write an absolute value inequality that has the solution set x ≤ –9 or x ≥ –5
what is the answer?
Answers
The inequality |x + 7| ≥ 2 has the solution set x ≤ –9 or x ≥ –5, as required.
Writing an absolute value inequalityWe can write an absolute value inequality with the given solution set as follows:
|x + 7| ≥ 2
Here's how we arrived at this inequality:
First, we find the midpoint of the given solution set:
midpoint = (-9 + (-5)) / 2 = -7
Next, we find the distance from the midpoint to each endpoint of the solution set:
distance to -9 = |-7 - (-9)| = 2
distance to -5 = |-7 - (-5)| = 2
The maximum distance is 2, so we use c = 2 in the inequality.
Since the midpoint is to the left of both endpoints, we use the form |x - b| ≥ c.
Plugging in b = -7 and c = 2, we get:
|x + 7| ≥ 2
This inequality has the solution set x ≤ –9 or x ≥ –5, as required.
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12. Mr. Wright is five times as old as
his daughter, Lilly. Lilly is twice
as old as her brother, Micah. If
Micah is 3 years old, how old is
Mr. Wright?
Answers
Based on the given data, the age of Mr. Wright currently is 30 years
Calculating Mr. Wright's age
If Micah is 3 years old, then Lilly is twice as old, which means that
Lilly is 2 * 3 = 6 years old.
Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:
5 * 6 = 30 years old.
Therefore, Mr. Wright is 30 years old.
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Which values should be added
Answers
The missing values of h(x) to show it is a linear function are:
X=1, h(x)=3
X=3, h(x)=17
X=5, h(X)=31
So, the correct answer is (c)
What is linear function?A linear function is a mathematical relationship between two variables that produces a straight line when plotted on a graph, with a constant rate of change between them.
What is function?A function is a mathematical rule that assigns each input value to a unique output value. It can be represented graphically, algebraically, or with a table of values.
According to the given information:
To prove that h(x) is a linear function, we need to show that the difference in h(x) values between any two points is proportional to the difference in their corresponding x values.
Using the given values in the table, we can calculate the differences in h(x) values and x values:
Δh(x) = h(x) - h(x-1)
Δx = x - (x-1) = 1
Δh(x=1) = h(x=1) - h(x=0) = ? - (-4) = ?
Δh(x=3) = h(x=3) - h(x=2) = ? - 10 = ?
Δh(x=5) = h(x=5) - h(x=4) = ? - 24 = ?
If h(x) is a linear function, then the ratio of Δh(x) to Δx should be the same for all pairs of consecutive x values. We can use the given values of Δh(x=2) and Δx=1 to calculate this ratio:
Δh(x=2)/Δx = (10 - (-4))/2 = 7
We can now use this ratio to find the missing values of h(x):
Δh(x=1)/Δx = ?/1 = 7
Δh(x=3)/Δx = ?/1 = 7
Δh(x=5)/Δx = ?/1 = 7
?/1 = 7 => ? = 7
Therefore, the missing values of h(x) are:
X=1, h(x)=3
X=3, h(x)=17
X=5, h(X)=31
So, the correct answer is (c)
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A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.
Assume the rate of change is linear and complete the table.
Answers
The complete table is
Time (mins) 0 1 2 3 4 5 6 7 8 9 10
Amount of air (ft³) 40 36 32 28 24 20 16 12 8 4 0
What is the Rate of change :
The rate of change refers to the speed at which a quantity is changing with respect to time or some other variable.
It is a measure of how quickly or slowly a quantity is increasing or decreasing, and it is often represented as the slope of a graph or function. To fill the table we need to know the rate of change per minute in the air. Using the rate of change we can fill the table as follows
Here we have
A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.
To complete the table, calculate the rate of change of the amount of air in the scuba tank.
We know that the scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive, so we can use this information to find the rate of change:
Rate of change = (final amount - initial amount) / time
Rate of change = (0 - 40) / 10 = -4 ft³/min
The negative sign indicates that the amount of air in the scuba tank is decreasing over time, which makes sense since the diver is using up the air during the dive.
Using this rate of change, we can complete the table as follows:
For 1 min = 40 ft³ - 4 ft³ = 36 ft³
For 2 min = 36 ft³ - 4 ft³ = 32 ft³
For 3 min = 32 ft³ - 4 ft³ = 28 ft³
Similarly, we can fill the table as given below
Therefore
The complete table is
Time (mins) 0 1 2 3 4 5 6 7 8 9 10
Amount of air (ft³) 40 36 32 28 24 20 16 12 8 4 0
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The volume of a rectangular prism is 5058
50
5
8
cubic inches.
The dimensions are given below.
What is the missing value in the table?
Answers
The missing value in the table include the following: B. 4 1/2 in.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;
50 5/8 = 5 × W × 2 1/4
Width, W = 4 1/2 inches.
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Complete Question:
The volume of a rectangular prism is 50 5/8 cubic inches.
The dimensions are given below.
What is the missing value in the table?
Length Width Height
5 in. 214 in.
A. 79in.
B. 412in.
C. 134in.
D. 1018in.
find slope and y intercept of -5x = 8 - y
Answers
Starting with -5x = 8 - y, we can add y to both sides to get:
-5x + y = 8
Next, we can add 5x to both sides to isolate y:
y = 5x + 8
Now we can see that the equation is in slope-intercept form, where the slope is 5 and the y-intercept is 8.
Therefore, the slope of the equation -5x = 8 - y is 5 and the y-intercept is 8.
The First National Bank pays 8 1/2%?interest per year compounded annually . City Bank pays 8.25 % terest per year compounded daily . In 5 years , what is the difference in the amounts of interest aid on $ 500 by the two banks ? Which bank gave more interest ?
Answers
City Bank paid more interest than First National Bank over the 5-year period.
What is compound interest?
Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods.
We can use the formula for compound interest to calculate the amounts of interest earned by the two banks over 5 years:
Amount of interest with First National Bank = [tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]
where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.
Amount of interest with First National Bank
=[tex]$500\left(1 + \frac{0.085}{1}\right)^{1\times 5} - 500$[/tex]
= $235.15 (rounded to two decimal places)
Amount of interest with City Bank =[tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]
where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year (365 in this case, since interest is compounded daily), and t is the number of years.
Amount of interest with City Bank
=[tex]$500\left(1 + \frac{0.0825}{365}\right)^{365\times 5} - 500$[/tex]
= $240.45 (rounded to two decimal places)
The difference in the amounts of interest paid by the two banks is:
$240.45 - $235.15 = $5.30
Therefore, City Bank paid more interest than First National Bank over the 5-year period.
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Given a continuous-time system with the input-output relation:
[tex]y(t) = T\left\{x(t) \right\} = x^2(t)[/tex]
Determine whether this system is:
- Linear
- Time-invariant
Answers
The given input-output relation is a nonlinear function of the input signal x(t), since it involves squaring the signal at every point in time. A linear system must satisfy the property of superposition, which states that the output to a linear combination of inputs must be the same as the linear combination of the outputs to each individual input.
To determine whether the system is time-invariant, we need to check if a time shift in the input signal produces the same time shift in the output signal. That is, if: [tex]y(t) = T{x(t)}[/tex] for all values of t. Then we want to check [tex]y(t - τ) = T{x(t - τ)}[/tex] for all values of [tex]τ[/tex] and [tex]t[/tex].
We shall the consider the case where [tex]τ > 0[/tex], then we have:
[tex]y(t - τ) = (x(t - τ))^2[/tex]
[tex]T{x(t - τ)} = (x(t - τ))^2[/tex]
Since [tex]y(t - τ) = T{x(t - τ)}[/tex], we can conclude that the given system is time-invariant.
Therefore, the given system is nonlinear but time-invariant.
anyone know this answer cus I don’t
Answers
Answer: 13 units
Step-by-step explanation:
If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.
Find the perimeter and the area of the figure. Round answers to the nearest tenth.
Composite shape formed by a rectangle and two semicircles. Each semicircle has a diameter of 15 feet and is aligned with the length of the rectangle. The rectangle has a width of 4 feet.
perimeter: about
ft
area: about
ft²
Answers
The answer of the given question based on the circle and rectangle is , the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².
What is Perimeter?Perimeter is a measurement of the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is often measured in units of length, such as centimeters, meters, or feet.
To find the perimeter and area of the composite shape formed by a rectangle and two semicircles, we can break it down into its individual components and then add them up.
First, let's find the perimeter. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The perimeter can be calculated as:
Perimeter = 2 × (semicircle circumference) + rectangle perimeter
The circumference of circle is by the formula 2πr, where r is the radius. Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the circumference of each semicircle is:
C = 2πr = 2π(7.5) = 15π feet
The perimeter of the rectangle is simply the sum of its four sides, which is:
P = 2(length + width) = 2(15 + 4) = 38 feet
Putting it all together, we have:
Perimeter = 2 × 15π + 38 ≈ 83.8 feet
Now let's find the area. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The area can be calculated as:
Area = (semicircle area) + rectangle area
The area of a circle is given by the formula πr². Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the area of each semicircle is:
A = (1/2)πr² = (1/2)π(7.5)² = 44.18 feet²
The area of the rectangle is simply its length multiplied by its width, which is:
A = length × width = 15 × 4 = 60 feet²
Putting it all together, we have:
Area = 2 × 44.18 + 60 = 148.4feet²
Therefore, the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².
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6.1: Fill in the Box
For each expression, what value would need to be in the box in order for the expression to
be a perfect square trinomial?
10. x² + 10x + __
11. x²-16x + __
12. x² + 40x+ __
13. x2+5x+ __
Fill the blanks fr
Answers
(10) The value that will make the equation a perfect square is 25.
(11) The value that will make the equation a perfect square is 64.
(12) The value that will make the equation a perfect square is 400.
(13) The value that will make the equation a perfect square is 6.25.
What is the required value for a perfect square?To make a perfect square trinomial of the form x² + bx + c, we need to add (b/2)² to both sides.
the perfect square is calculated as;
x² + 10x + __
b = 10,
(b/2)² = 25
the perfect square is calculated as;
x² - 16x + __
b = -16
(b/2)² = 64
the perfect square is calculated as;
x² + 40x + __
b = 40
(b/2)² = 400
the perfect square is calculated as;
x² + 5x + __
b = 5
(b/2)² = 6.25
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*HELP!!* MULTIPLE CHOICE!!
Consider the graph of the function f(x)=log2 x, what are the features of function g if g(x)=-f(x)-1
Answers
The features of function g if g(x) = -f(x)-1 include the following:
B. domain of (0, ∞).
C. vertical asymptote of x = 0.
D. x-intercept at (1/2, 0).
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following key features:
Domain = (0, ∞)
Range = (-∞, ∞).
vertical asymptote, x = 0.
x-intercept = (1/2, 0).
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What 4×4/3 in its simplest form
Answers
To start, we will change the whole number 4 into a fraction. Because when multiplying fractions, you will multiply the numerator and denominator across. So 4 = 4/1.
(4/1)(4/3)
Now multiply the numerators and denominators across:
16/3
That’s your answer in improper fraction form, or 5 1/3 in mixed number, or 5.333… in decimal form.
Hope this helped!
Answer:
5 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{4}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{3}[/tex]
You can re-write [tex]\frac{16}{3}[/tex] as
[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] I wrote it like this because every [tex]\frac{3}{3}[/tex] is equal to 1.
1 + 1 + 1 + 1 + 1 + [tex]\frac{1}{3}[/tex] = 5[tex]\frac{1}{3}[/tex]
Helping in the name of Jesus.
Mary can mow Mrs. Greenway’s lawn in 45 minutes. Mary’s little brother takes twice as long to do the same lawn. How long will it take them if they each have a mower and they work together?
Answers
Answer:
30 minutes
Step-by-step explanation:
1/45 m + 1/90 m = 1
2/9 m + 1/90 m = 1
3/90 m = 1 Multiply both sides by 90/3
90/3 x 3/90 m = 1 x 90/3
m = 90/3
m = 30
Helping in the name of Jesus.
Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?
Answers
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
what is angle ?Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.
given
The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.
The information provided in the problem can then be used to create an equation as follows:
m∠A = 5(m∠B + 7.2°)
Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:
180 - m∠B = 5(m∠B + 7.2°)
The right side is being widened:
180 - m∠B = 5m∠B + 36
Simplifying and putting all the mB words to one side:
6m∠B = 144
m∠B = 24
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
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