To sketch the graphs, square the y-values of sin(x) and cos(x) to get f^2(x) and g^2(x), respectively. Then, add the squared y-values of f(x) and g(x) to get f^2(x)+g^2(x). Plot the points obtained for each function and sketch the graphs.
Explanation:a) To sketch the graph of f^2, we need to square every y-value of the function f(x)=sin(x). This means finding the square of the sine of each angle. For example, f^2(0)=sin^2(0)=0^2=0. By repeating this process for multiple angles, we can plot the points and sketch the graph.
b) Similarly, to sketch the graph of g^2, we need to square every y-value of the function g(x)=cos(x). This means finding the square of the cosine of each angle. For example, g^2(0)=cos^2(0)=1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.
c) To sketch the graph of f^2+g^2, we need to add the squared y-values of f(x) and g(x) at each angle. For example, f^2+g^2(0)=sin^2(0)+cos^2(0)=0^2+1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.
25. Which is an example of an operation?
A) 12
B) 6ab
C) +
D) y
You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
(I know it's 119.954 years, but I have no idea how to get that)
Answer:
It take 119.954 years to earn $ 3000 without depositing any additional funds.
Step-by-step explanation:
Given:
Principal Amount, P = $ 150
Amount, A = $ 3000
Rate of interest, R = 2.5% compounded monthly.
To find: Time, T
We use formula of Compound interest formula,
[tex]A=P(1+\frac{R}{100})^n[/tex]
Where, n is no time interest applied.
Since, It is compounded monthly.
R = 2.5/12 %
n = 12T
[tex]3000=150(1+\frac{\frac{2.5}{12}}{100})^{12T}[/tex]
[tex]\frac{3000}{150}=(1+\frac{2.5}{1200})^{12T}[/tex]
[tex]20=(1+\frac{2.5}{1200})^{12T}[/tex]
Taking log on both sides, we get
[tex]log\,20=log\,(1+\frac{2.5}{1200})^{12T}[/tex]
[tex]1.30103=12T\times\,log\,(1.002083)[/tex]
[tex]T=\frac{1.30103}{12\times\,log\,(1.002083)}[/tex]
[tex]T=119.954[/tex]
Therefore, It take 119.954 years to earn $ 3000 without depositing any additional funds
in a boutique the ratio of pink flowers to blue flowers is 3 to 6 if there are 72 pink flowers how many flowers are there in the bouquet all together?
Is it possible for a segment to have more than one bisector? Explain your reasoning.
Final answer:
Yes, a segment can have more than one bisector. A bisector divides a segment into two equal parts.
Explanation:
Yes, a segment can have more than one bisector. A bisector of a segment is a line, segment, ray, or plane that divides the segment into two equal parts. Each bisector intersects the segment at its midpoint. Since the definition of a bisector doesn't specify uniqueness, there can be infinitely many bisectors of a given segment, especially in a two-dimensional plane.
For example, if you have a horizontal line segment, you could have one vertical bisector that divides it in the middle, but you could also have an infinite number of bisectors at various angles that also pass through the midpoint. Thus, there are multiple bisectors for any given line segment. Thus, consider two points A and B on a straight line segment AB. According to geometric principles, you can draw a perpendicular bisector that would be unique in the sense that it's the only line that both bisects AB and is perpendicular to it
Amersham station is the highest station in the London Tube at 147 meter above sea level. Waterloo station is the lowest station at 21 meters below sea level. What is the height difference?
Final answer:
The height difference between Amersham station (147 meters above sea level) and Waterloo station (21 meters below sea level) is 168 meters.
Explanation:
To find the height difference between Amersham station, which is the highest station in the London Tube at 147 meters above sea level, and Waterloo station, the lowest at 21 meters below sea level, we simply add the two values together, treating the below sea level as a negative altitude.
147 meters (Amersham altitude above sea level) + (-21 meters) (Waterloo altitude below sea level) = 168 meters.
Therefore, the height difference between Amersham and Waterloo stations is 168 meters.
Which of the following functions illustrates a change in amplitude?
A. y = 3cos4x
B. y = 1+sinx
C. y = -2-cos(x - pi)
D. y = tan2x
Answer:
Correct option is A.
Step-by-step explanation:
Given the following functions we have to choose the option which illustrates a change in amplitude.
Multiplying a sine or cosine function by a constant changes the graph of the parent function i.e results in change in the amplitude of function. Amplitude is the measure of distance from the sinusoidal axis to the maximum or the minimum.
Option A: y = 3cos4x
The parent function is f(x) = cos x.
The amplitude of function changes from 1 to 3.
Option B: y = 1+sinx
The parent function is f(x) = sin x
The amplitude remains same i.e 1
Option C: y = -2-cos(x - pi)
Here also remains same.
Option D: y = tan 2x
The tangent function does not have an amplitude because it has no maximum or minimum value.
Hence, correct option is A.
Answer:
y= 3cos4x
Step-by-step explanation:
what does x equal 3.2x = 64
divide 64 by 3.2 to get x
64/3.2 = 20
x = 20
Two women start at the same point. they walk in opposite directions for 3 meters, then turn right and walk another 4 meters. how far apart are they?
The total distance between the two women would simply be the sum of the hypotenuse formed by the triangular path they created.
For each women:
c^2 = a^2 + b^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
c = 5 m
Therefore the distance between the two is:
distance between the two women = 2 * c
distance between the two women = 10 m
Two thirds of a number reduced by 11 is equal to 4 more than the number. find the number. 2
use any method to solve the equation. If necessary, round to the nearest hundredth. 9x^2=17
The solution of the given quadratic equation is x = 1.37, - 1.37.
What is a quadratic equation?"A quadratic equation is an algebraic equation of the second degree in any variable."
Given quadratic equation:
9x² = 17
⇒ x² = (17 / 9)
⇒ x = ± √(17 / 9)
⇒ x = ± (√17) / 3
⇒ x = 1.37, - 1.37
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Find the greatest perfect square that is factor of the number. 650
The greatest perfect square that is a factor of 650 is 25
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves,
What is Prime Factorization?Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.
Given the number is 650
To determine the greatest perfect square that is a factor of the number 650.
We need to write 650 as the product of its prime factors, which is 650.
⇒ 650 = 2×5×5×13
So the pair is 5×5 which is 5² or 25
Hence, the greatest perfect square that is a factor of 650 is 25
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The following table shows the number of hours some students in two universities spend reading each week: School A 7 2 3 10 17 14 10 22 2 School B 9 10 16 18 20 15 17 18 14 Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points) Part B: Are the box plots symmetric? Justify your answer. (4 points)
Answer:
that persons work is correct im pretty sure
Step-by-step explanation:
Help plz fast with this question
90-7 =83 degrees
height = 3 miles
divide 3 by the cos of 83 degrees
3/cos(83) = 24.6165
rounded to nearest mile = 25 miles
The range of a relation is
A: the output (y) values of a relation
B: the input (x) values of the relation
C: a set of points that pair input values with output values
D: x and y values written in the form (x,y)
What is the area of triangle FGH? Round your answer to the nearest tenth of a square centimeter.
Answer: [tex]\text{Area}=9.8\ \text{square centimeter}[/tex]
Step-by-step explanation:
Given: The height of the triangle h= 3.0 cm
The base corresponding to the given height b= 6.5 cm
We know that the area of a triangle is given by :-
[tex]\text{Area}=\frac{1}{2}bh\\\\\Rightarrow\text{Area}=\frac{1}{2}(3)(6.5)\\\\\Rightarrow\text{Area}=\frac{19.5}{2}\\\\\Rightarrow\text{Area}=9.75\approx9.8\ \text{square centimeter}[/tex]
The integral represents the volume of a solid. describe the solid. π π 0 sin(x) dx
Factor 16x 2 + 16x + 4 completely.
a.(16x + 4)(x + 1)
b.(4x + 2)(4x - 2)
c.4(2x + 1)2
Helen uses 3/4 cup of oil and 1/3 cup of vinegar to make salad dressing. Which is closest to how many times 3/4 is as great as 1/3?
3
2
3/2
1/2
PLEASE ONLY ANSWER IF YOU KNOW FOR SURE!! :)
To prove that all circles are similar, you would use similarity blank?
Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.
Answer:
We are given,
The transformed function is [tex]f(x)=\sqrt{x+1}-5[/tex].
So, we can see that,
The parent function is [tex]f(x)=\sqrt{x}[/tex].
Then, we have,
The parent function is translated 1 units to the left to give [tex]\sqrt{x+1}[/tex].
Then, it is translated 5 units downwards to give the function [tex]\sqrt{x+1}-5[/tex].
Hence, we have,
The parent function [tex]f(x)=\sqrt{x}[/tex] is translated 1 unit to the left and 5 units down.The parent function f(x) = √x has been shifted 1 unit left and 5 units down
The parent function of a square root function is represented as:
[tex]f(x) = \sqrt x[/tex]
When the function is shifted 1 unit left, we have the following equation
[tex]f(x) = \sqrt {x + 1}[/tex]
When the function is shifted 5 units down, we have the following equation
[tex]f(x) = \sqrt {x + 1} - 5[/tex]
Hence, the parent function f(x) = √x has been shifted 1 unit left and 5 units down
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HELP PLEASE!!!!!
Kajan repeatedly rolled a die and he was getting frustrated that he could not roll his favourite number, which is three. What is the probability that the first three occurred on the tenth roll?
0.0323 0.0269 0.323 mc009-1.jpg
What is the solution to 7(a-1)=7
a scalene triangle has symmetry with respect to a line containing a median of the triangle . true or false
Answer:
False it never will
Step-by-step explanation:
Got it right on my test.
OQ is a diagonal of quadrilateral NOPQ. If NO=PQ, NQO=7y-37, and POQ=2y+93, find POQ such that NOPQ is a parallelogram. A.26° B.63° C.97° D.145°
Compare the functions shown below: f(x) = 4 sin (2x − π) − 1 g(x) is points and those points are (−1, 6) (0, 1) (1, −2) (2,−3) (3, −2) (4, 1) (5, 6) h(x) = (x − 2)2 + 4 Which function has the smallest minimum y-value?
Write the standard form of the line that contains a y-intercept of -3 and passes through the point (3, 0). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
The equation of the line in standard form that has a y-intercept of -3 and passes through the point (3, 0) is y = x - 3.
Explanation:The standard form of a line can be found using the formula y = mx +b, where 'm' is the slope and 'b' is the y-intercept. The y-intercept in this problem is -3, but we need to find the slope to complete the standard form of the line. Since our line passes through the point (3,0) and (0,-3), the slope, m, can be found by using the formula (y2-y1)/(x2-x1), which gives us a slope of 1. So the equation of our line in standard form is y = x - 3.
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A ladder is leaning against a wall. The top of the ladder is 9 feet above the ground. If the bottom of the ladder is moved 3 feet farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?
The number of ways to listen to 4 different cds from selection of 15 cds
Answer:
32,760 is the correct answer, the first person is wrong! Took the test and this is it!
Step-by-step explanation:
What is the simplified form of the following expression? 5√8-√18-2√2
A. 2√2
B. 5√2
C. 9√2
D. 15√2
Answer:
Option (B) is correct.
To prove
As given the epression in the question is given by
[tex]= 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex]
Now simplify the above
Terms are written as
[tex]\sqrt{8} = \sqrt{2\times 2\times 2} = 2 \sqrt{2}[/tex]
[tex]\sqrt{18} = \sqrt{3\times 3\times 2} = 3 \sqrt{2}[/tex]
Put in the above expression.
[tex]= 5\times 2 \sqrt{2} -3 \sqrt{2} - 2 \sqrt{2}[/tex]
[tex]= 10 \sqrt{2} -5 \sqrt{2}[/tex]
[tex]=5 \sqrt{2}[/tex]
[tex]Therefore\ the\ expression\ 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\ is\ equivalent\ to\ 5 \sqrt{2} .[/tex]
The statement “Angles that measure more than 90 degrees are obtuse angles” has a counterexample