3. Based on the graph of the trigonometric function,
what is the period?
4. Based on the graph of the trigonometric function,
what is the amplitude?
Answers
Answer:
4. ☐ A \(\displaystyle \frac{1}{3}\)
☐ B \(\displaystyle 2\)
☑ C \(\displaystyle 3\)
3. ☐ A \(\displaystyle \frac{\pi}{3}\)
☐ B \(\displaystyle \pi\)
☑ C \(\displaystyle 6\pi\)
Step-by-step explanation:
\(\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}) \\ y = -2cos\:\frac{1}{3}x\)
\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1\frac{1}{2}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{1}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2\)
OR
\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2\)
The above information can help you interpret the graph much better. First off, JUST IN CASE you needed to know the trigonometric equation(s) of this graph, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = -2sin\:\frac{1}{3}x,\) in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle 1\frac{1}{2}\pi\:unit\) to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK \(\displaystyle 1\frac{1}{2}\pi\:unit,\) which means the C-term will be negative, and perfourming your calculations, you will arrive at \(\displaystyle \boxed{-1\frac{1}{2}\pi} = \frac{-\frac{\pi}{2}}{\frac{1}{3}}.\) So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}).\) Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \(\displaystyle [0, -2],\) from there to \(\displaystyle [-6\pi, -2],\) they are obviously \(\displaystyle 6\pi\:units\) apart, telling you that the period of the graph is \(\displaystyle 6\pi.\) Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\) in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow. Now, in this case, you were probably wondering why the negative was inserted in front of the amplitude in the equation(s). Well, here is why:
\(\displaystyle y = sin\:x \\ y = cos\:x\)
Knowing your parent functions, sine commenses upright from the origin, while cosine commenses one unit above the origin \(\displaystyle [0, 1].\) This should tell you that inserting a negative in front of the amplitude will REFLECT each crest over the midline. Well, there you have it.
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Related Questions
please give the correct answer and no links!
Answers
Answer:
KL ≈ 16.6 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos25° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{MK}{KL}\) = \(\frac{15}{KL}\) ( multiply both sides by KL )
KL × cos25° = 15 ( divide both sides by cos25° )
KL = \(\frac{15}{cos25}\) ≈ 16.6 ft ( to the nearest tenth )
a round pizza was cut into 9 sectors whose central angles are in the ratio of 1:2:3:4:5:6:7:8:9. what is the central angle of the largest piece?
Answers
The sum of the central angles is 360 degrees. If the ratios are 1:2:3:4:5:6:7:8:9, the sum of the ratios is 45. The central angle of the largest piece is 360 degrees / 45 = 8 degrees.
A round pizza cut into 9 sectors has its central angles in the ratio of 1:2:3:4:5:6:7:8:9. This means that the central angle of each sector is proportional to the ratio assigned to it. The sum of the central angles of all the sectors is 360 degrees, which represents a complete circle. The sum of the ratios is 45, which indicates that the central angle of each sector can be calculated by dividing 360 by 45. The central angle of the largest sector, which has a ratio of 9, is 360 divided by 45, which equals 8 degrees. In conclusion, the central angle of the largest sector of the pizza is 8 degrees.
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answer this: 25/x = 7/3
Answers
The solution to the proportional equation in this problem is given as follows:
x = 75/7.
How to solve the proportional equation?The proportional equation in the context of this problem is defined as follows:
25/x = 7/3.
The equation is proportional, meaning that we can obtain the value of x applying cross multiplication as follows:
7x = 25 x 3
7x = 75
x = 75/7.
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Let Z be a standard normal variable. Find P(-3.29 < Z < 1.37).
a) 0.9147
b) 0.8936
c) 0.8811
d) 0.9142
e) 0.9035
f) None of the above.
Answers
The cumulative probability up to 1.37 is 0.9142. The correct answer is d) 0.9142
To find P(-3.29 < Z < 1.37), where Z is a standard normal variable, we need to calculate the cumulative probability up to 1.37 and subtract the cumulative probability up to -3.29.
Using a standard normal distribution table or a calculator, we can find:
P(Z < 1.37) ≈ 0.9147 (rounded to four decimal places)
P(Z < -3.29) ≈ 0.0006 (rounded to four decimal places)
To find the desired probability, we subtract the cumulative probability up to -3.29 from the cumulative probability up to 1.37:
P(-3.29 < Z < 1.37) ≈ P(Z < 1.37) - P(Z < -3.29)
≈ 0.9147 - 0.0006
≈ 0.9141
Therefore, the correct answer is d) 0.9142
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A blue sqaure is placed inside a large yellow square The centres of the squares are aligned one over the other one side of the square is (3x + 2)cm and the other side is (8 - x)cm the area of the blue square is 36% the area of the yellow square. Find the dstance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Answers
Answer:
the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
Step-by-step explanation:
From the information given;
A blue square is placed inside a large yellow square and the centres of the squares are aligned one over the other
So ; if one side of the square is (3x + 2)cm (i.e the blue side)
the other side is (8 - x)cm (i.e the yellow sides)
since the two shapes given are squares ; we can say that:
(3x+2)= (8 - x)
3x +x = 8 -2
4x = 6
x = 6/4
x = 1.5
Let replace x = 1.5 for the sides of the square and find the actual length of the square sides.
So, for the yellow side; we have:
= (8 - x)cm
= (8 - 1.5 ) cm
= 6.5 cm
We all know that the area of the square = l²
then the area of the yellow side = (6.5 cm )²
the area of the yellow side = 42.25 cm²
Let y be the distance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Since the blue region is inside the yellow region; to calculate for the side of the blue region ; we have:
(6.5y -y+y) cm
(6.5 - 2y )cm
The area of the blue side =( (6.5 - 2y )cm)²
The area of the blue side = (6.5 - 2y )² cm²
However; we are also given that :
the area of the blue square is 36% the area of the yellow square.
Thus;
(6.5 - 2y )² = 36/100 × 42.25
(6.5 - 2y )² = 0.36 × 42.25
(6.5 - 2y )² = 15.21
(6.5 - 2y ) = \(\sqrt{15.21}\)
(6.5 - 2y ) = 3.9
6.5 - 2y = 3.9
6.5 - 3.9 = 2y
2.6 = 2y
y = 2.6/2
y = 1.3 cm
Therefore , the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
where R is the region in the first quadrant bounded by the ellipse 4x2 +9y2 = 1.
Answers
The region R in the first quadrant bounded by the ellipse \(4x2 + 9y2 = 1\) is a special type of ellipse. \((x^2)/(a^2) + (y^2)/(b^2) = 1\), where a is the semi-major axis and b is the semi-minor axis. The region R in the first quadrant bounded by the ellipse\(4x2 + 9y2 = 1\) has an area of π/6.
In the given equation, the value of a is 1/2 and the value of b is 1/3. This ellipse is vertically aligned and centred at the origin. Since the region is confined to the first quadrant, it means that both x and y are greater than 0. Therefore, the limits of integration for x and y are 0 to a and 0 to b respectively.
The equation of the ellipse can be rewritten as \(y = ±(1/3)√[1 - 4x^2]\).
The top half of the ellipse is \(y = (1/3)√[1 - 4x^2]\) and
the bottom half is\(y = - (1/3)√[1 - 4x^2]\).
Thus, the integral is: \(∫∫ R 1 dA = ∫0^1 ∫0^(1/3) 1 dy dx,\) which is equal to the area of the ellipse. After integrating, we get the value as (1/2)π(a)(b),
which is equal to \((1/2)π(1/2)(1/3) = π/6.\)
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An education counselor records the number of high school graduates enrolled in community colleges, 4-year colleges, and universities. What scale of measurement is the type of college
Answers
The scale of measurement used for the type of college, i.e., community colleges, 4-year colleges, and universities, is a nominal scale.
A nominal scale is used for variables that can be classified into distinct categories, but there is no inherent order or numerical value associated with them. In this case, the three types of colleges are discrete categories, and there is no inherent order or numerical value assigned to them.
For instance, a student enrolled in a community college cannot be said to be superior or inferior to a student enrolled in a university; they are merely enrolled in different types of colleges. It is worth noting that a nominal scale is the weakest form of measurement because it does not provide any quantitative information about the variable being measured. Nonetheless, it is still useful in situations where the variable being measured is qualitative in nature and cannot be numerically quantified. In this case, the education counselor can use the nominal scale to analyze and compare the enrollment trends in different types of colleges among high school graduates.Thus, the scale of measurement used for the type of college, i.e., community colleges, 4-year colleges, and universities, is a nominal scale.Know more about the nominal scale.
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How do you find the inverse of f(x) = 3x -4? what is it?
Answers
Answer:
x= x/3 + 4/3
Step-by-step explanation:
A barn with the dimensions shown is to be painted. One gallon of paint covers 400 square feet. About how many gallons of paint are needed for one coat on the entire exterior of the barn, including the roof?
Answers
Approximately 4.5 gallons of paint would be needed for one coat on the entire exterior of the barn, including the roof.
To determine the number of gallons of paint needed for one coat on the entire exterior of the barn, including the roof, we need to calculate the total surface area that needs to be painted.
Let's consider the dimensions of the barn:
Length: 30 feet
Width: 20 feet
Height: 10 feet
First, let's calculate the surface area of the four walls. Since a rectangular barn has opposite walls with equal dimensions, we can calculate the area of one wall and multiply it by 4:
Wall area = Length * Height
= 30 feet * 10 feet
= 300 square feet
Now, multiply the wall area by 4 to account for all four walls:
Total wall area = Wall area * 4
= 300 square feet * 4
= 1200 square feet
Next, let's calculate the surface area of the roof, which is a rectangle:
Roof area = Length * Width
= 30 feet * 20 feet
= 600 square feet
Finally, we calculate the total surface area that needs to be painted by adding the wall area and the roof area:
Total surface area = Total wall area + Roof area
= 1200 square feet + 600 square feet
= 1800 square feet
Given that one gallon of paint covers 400 square feet, we can divide the total surface area by 400 to determine the approximate number of gallons needed for one coat:
Number of gallons = Total surface area / Coverage per gallon
= 1800 square feet / 400 square feet
= 4.5 gallons
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1 1/2 times 1 1/3 times 1 1/4 times 1 1/5
Answers
Answer: 3
Step-by-step explanation:
1 1/2 * 1 1/3 * 1 1/4 * 1 1/5
-> 3/2 * 4/3 * 5/4 * 6/5
-> 3
Answer:
3
Step-by-step explanation:
1 1/2*1 1/3*1 1/4*1 1/5
1 1/2=3/2
=3/2*1 1/3*1 1/4*1 1/5
1 1/3=4/3
=3/2*4/3*1 1/4*1 1/5
1 1/4=5/4
=3/2*4/3*5/4*1 1/5
1 1/5=6/5
=3/2*4/3*5/4*6/5
=4/2*5/4*6/5
=5/2*6/5
=6/2
6/2=3
Who can do this? Pls help
Answers
Answer:
15. 2
16. \(\frac{27}{16}\) or 1.6875
17. \(\frac{17}{30}\) or 0.5666666667
18. 5
19. \(\frac{35}{8}\) or 4.375
20. \(\frac{22}{5}\) or 4.4
Step-by-step explanation:
Find common denominators. Multiply then simplify (if possible).
PLEASE HELP ASAP
Apply the square root principle to solve (x-3)² + 9 = 0.
a. x=0,6
b. x=0,-6
c. x=-3+3i, -3 -3i
d. x=3+31,3-3i
Answers
The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
(x-3)² + 9 = 0
(x-3)²= -9
(x-3)=√-9
(x-3)=√9×√-1
(x-3)=±3i
x=3±3i
Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.
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Jylene and her brother had a total of $35.19 to buy school supplies. Jylene’s school supplies cost $12.78
Answers
Answer:
whats the question
Step-by-step explanation:
Answer:
What is the question???
Step-by-step explanation:
a retail store plans to build 4 new stores each year. they expect 1 store will go out of business every 3 1/2 years. how many years would it take to establish 30 stores core bites
Answers
It would take approximately 11.43 years to establish 30 stores.
Let's use x to represent the number of years it would take to establish 30 stores.
The store plans to build 4 new stores each year, so in x years, they will have built 4x stores.
That 1 store will go out of business every 3 1/2 years, which can be written as 7/2 years.
So in x years, 30/(4-1/2) = 40 stores will be in operation, and 40/x stores will go out of business.
So, we can write the equation:
40/x = 7/2
Solving for x, we get:
x = 80/7
Let's use x to indicate the period of time needed to open 30 shops.
The retailer intends to construct 4 additional stores year, totaling 4x stores after x years.
Every three and a half years—or seven and a half years—that one store will close its doors.
As a result, 40 stores will be open in x years and 40/x retailers will close their doors.
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the vertices of figure ABC are A(-4,1), B(5,3), and C(4,-2). If figure ABC is reflected over the line x=2, find the coordinates of vertex B'.
Answers
The coordinates of vertex B' are (-1,3)
What is reflection?Reflection is a mathematical transformation in which a image of an object is formed by flipping it over a reflection line a distance equal to the distance of the object from the reflection line.
Analysis:
When an object is reflected along the y-axis, only the the x-coordinate changes , if reflected along the x-axis, only the y-coordinate changes.
So vertex B' is a reflected vertex along the y- axis since it is at x=2
The distance of the x-coordinate of vertex B from the mirror line is 5-2 = 3
so the x-coordinate of vertex B' is going 3 units away from the mirror line which is at -1.
So the coordinates of vertex B' are (-1,3)
In conclusion, the coordinates of vertex B' reflected over the line X= 2 are (-1,3)
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Find the zeros and the vertical intercept of the function f(x) = -9x³+9x² - 2x. Give your answers as integers or reduced fractions. The zero(s) is/are ______
The horizontal intercept(s) is/are _____
Rhe vertical intercept is _____
Answers
The vertical intercept is (0, 0). Horizontal intercepts are the points where the graph of the function intersects the x-axis. At these points, the value of y is zero.
The function f(x) = -9x³+9x² - 2x can be factored as: -x(9x² - 9x + 2) .
The zeros can be obtained by setting the function equal to zero:-
x(9x² - 9x + 2) = 0
The zeros of the function are 0, 2/9, and 1.
To determine these solutions, we can use the Zero Product Property, which tells us that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. We can find the zeros of the function by setting each factor equal to zero and solving for x.
Thus, we have:Horizontal intercepts are the points where the graph of the function intersects the x-axis. At these points, the value of y is zero.
To find the horizontal intercepts, we set f(x) = 0 and solve for x.
Thus, we have:-9x³+9x² - 2x = 0x(-9x²+9x - 2) = 0
The horizontal intercepts of the function are -2/3, 0, and 2/3.
To determine these solutions, we can use the Zero Product Property, which tells us that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
We can find the horizontal intercepts of the function by setting each factor equal to zero and solving for x.The vertical intercept is the point where the graph of the function intersects the y-axis.
At this point, the value of x is zero. To find the vertical intercept, we set x = 0 and evaluate the function. Thus, we have:
f(0) = 0 - 0 + 0 = 0.
Therefore, the vertical intercept is (0, 0).
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ring-ring. *pick up phone* Hello, Einstein? I be needing some help.
Thank you.
Answers
Answer:
The one that you pick is correct
HELPPP
The letter ____ represents the location of –1.5 on the number line.
Answers
Anything to the left of zero is a negative number. Halfway between -1 and -2 is -1.5 (B)
T×Dot estimates that it takes 2.3 hours to paint a mile of center stripe on the highway. In addition, it takes about 45 minutes for the crew to get ready to paint.
Which equation best represents the total amount of tine it will take to paint the center stripe of a highway as a function of the number of miles to be painted?
Answers
The equation representing the total amount of time to paint the center stripe of a highway as a function of the number of miles to be painted is Total Time = 2.3m + 0.75
The total amount of time it will take to paint the center stripe of a highway can be represented by the equation:
Total Time = Time per Mile × Number of Miles + Setup Time
The time per mile is given as 2.3 hours, the number of miles to be painted is denoted as 'm', and the setup time is 45 minutes, which can be converted to hours by dividing by 60.
Therefore, the equation that best represents the total amount of time is:
Total Time = 2.3m + (45/60)
Total Time = 2.3m + 0.75
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find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 3y2, x = 3; about x = 3
Answers
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line is π/2 cubic units.
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line can be found using the formula for the volume of a solid of revolution.
In this case, the specified line is x = 3 and the given curves are x = 3y2.
The formula for the volume of a solid of revolution is V = ∫a b (πy2)dx.
To find the total volume of the solid, we need to integrate the volume of each cylindrical shell from y = -√(1/3) to y = √(1/3):
V = ∫-√(1/3)^√(1/3) 2π(3 - 3y^2)(2√(1/3)y)dy
Simplifying:
V = 4π√(1/3) ∫-√(1/3)^√(1/3) (3 - 3y^2)ydy
V = 4π√(1/3) (∫-√(1/3)^√(1/3) 3ydy - ∫-√(1/3)^√(1/3) 3y^3dy
V = 4π√(1/3) (3(0) - 3(1/4)(√(1/3))^4)
V = 4π√(1/3) (3/4)(1/3)
V = π/2
Therefore, the volume of the solid obtained by rotating the region bounded by the curves x = 3y^2 and x = 3 about the line x = 3 is π/2 cubic units.
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a gym membership is offered in January for $29.00 per month. If you pay upfront for the year you are given a 20% discount on the monthly cost. How much money do you save after a year by paying upfront rather than monthly?
Answers
Answer:
278.4 dollars
Step-by-step explanation:
So you know that each month is 29.00 dollars
You mutilpy that by 12 to find out the total cost for paying each month
That would be 348 dollars
So if you pay upfront that takes 20 percent off
So you take the 348 and take 20 percent off
That would be 69.6
So then to find the amount saved you subtract 69.6 from 348
Which would be 278.4 dollars
They saved 278.4 dollars
A concave shaving mirror has a radius of curvature of +31.5 cm. It is positioned so that the (upright) image of a man's face is 3.40 times the size of the face. How far is the mirror from the face? Number i Units
Answers
The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.
Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40
We know that the formula for magnification is given by:
m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :
f = r/2where,f = focal length of the mirror
Using the mirror formula:1/f = 1/v - 1/u
We know that a concave mirror has a positive focal length, so we can replace f with r/2.
We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u
Also, from the given data, we have :m = v/u
Substituting the value of v/u in terms of m, we get: u/v = 1/m
So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u
Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm
Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.
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1.To make paper mache, the art teacher mixes water and flour. For every 2
cups of water, she needs to mix in 3 cups of flour to make the paste. Which
of the following shows an equivalent ratio for the ratio of water to flour? I need an answer quick!!!!
Answers
Answer:
1:1.5 or 2:3 or 4:6 or 8:12, etc. is the ratio
Step-by-step explanation:
Merv bikes the same distance of 16 miles every day. The first day they take an hour to complete the 16 miles but each day they increase their speed which then decreases the amount of time they spend biking the same distance.
Speed in mph, x | 16 | 17 | 18 | 19 | 20 | 21 |
Time in hours, y | 1 | __ | __ | __ | __ | __ |
a.) What is the constant of variation for the equation?
b.) What is the rational equation that models this story and table?
c.) What is the excluded value for this equation?
d.) What is the time Merv spends biking 16 miles when he bikes at 21 mph?
Thank you :)
Answers
The answer of the questions are: a) constant of variation for the equation is k = y/x = 1/16 = 1/16. b) The rational equation that models the story and table is:y = kx Or, y = (1/16)x. c) the excluded value of this equation is zero. d) Merv spends (21/16) hours or 1.3125 hours or approximately 1 hour 19 minutes when he bikes 16 miles at 21 mph.
a) Constant of variation. The constant of variation in this equation is k. k is used to represent the ratio of the y-coordinate to the x-coordinate.The equation of variation in direct proportionality is y = kx. Here the x-coordinate is speed and the y-coordinate is time. Hence, k = y/x.The constant of variation for the equation is k = y/x = 1/16 = 1/16.
b) Rational equation that models the story and table. The rational equation that models the story and table is:y = kx Or, y = (1/16)x. Here y is the time taken to complete the 16 miles and x is the speed in mph.
c) Excluded value for this equation. The excluded value of this equation is zero because in the given equation we are dividing the y-coordinate by the x-coordinate. If the value of x is zero, then the division by zero is not possible and the value of y cannot be defined. Therefore, the value of x is always greater than zero.
d) Time taken to bike 16 miles when biking at 21 mph. Using the equation, y = (1/16)x, we can find the time Merv spends biking 16 miles when biking at 21 mph, which is:y = (1/16) × 21 = 21/16 hours. Therefore, Merv spends (21/16) hours or 1.3125 hours or approximately 1 hour 19 minutes when he bikes 16 miles at 21 mph.
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Identify the GCF, LCM, of 120 and 250.
Answers
Answer:
The GCF is 10
The LCM is 3,000
Work out x^2- 2x
when x =4
Answers
Answer:
8
Step-by-step explanation:
\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)
Question 1 3 pts Every Thursday of the semester you have been collecting times on the shuttle run for your 5th grade students. This data should be shown on a Line graph Bar chart Histogram Pie chart Question 2 3 pts Proportional data is best shown on a Pie chart Bar chart Histogram Line graph A
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Bar charts, histograms, and line graphs are the best representation for other types of data, like categorical data, frequency distribution, or time-series data, respectively.
Line graphs are one of the most commonly used charts in the educational field, especially for data collection. It is often used when dealing with continuous data, showing trends, and demonstrating changes over time. In this case, the collected data for the shuttle run of the 5th-grade students shows changes over time, which is why the line graph is the most appropriate way to represent it.
A Pie chart is the best representation for proportional data.Pie charts are a useful chart type when presenting proportional data. They show how much each slice of the pie represents as a percentage of the whole. Therefore, a pie chart is the best option when presenting proportional data to the viewers or readers.
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solve pls brainliest
Answers
Answer:
mixed no. 51/10
Improper fraction 5/1/10
Pls help A sector of a circle has a central angle measure of 120°, and an area of 15 square inches. What is the area of the entire circle? Area of the circle = square inches
Answers
The area of the entire circle is approximately 45.19 square inches.
To solve this problem, we can use the formula for the area of a sector of a circle:
Area of sector = (central angle / 360°) x π\(r^2\)
where r denotes the circle's radius.
We are given that the central angle measure of the sector is 120° and its area is 15 square inches. We can substitute these values into the formula:
15 = (120/360) x π\(r^2\)
Simplifying this equation, we get:
15 = (1/3)π\(r^2\)
Multiplying both sides by 3, we get:
45 = π\(r^2\)
Dividing both sides by π and taking the square root, we get:
r = √(45/π) ≈ 3.79 inches (rounded to two decimal places)
Now that we know the radius of the circle, we can use the formula for the area of a circle to find its area:
Area of circle = π\(r^2\)
Substituting r ≈ 3.79 inches into this formula, we get:
Area of circle ≈ π(3.79\()^2\) ≈ 45.19 square inches
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Blake has a total of 11,000 to invest in two accounts. one account earns 4% simple interest, and the other earns 5% simple interest. how much should be invested in each account to earn exactly $490 at the end of 1 year?
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Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.
Let's denote the amount of money Blake invests at 4% interest as "x" (in dollars) and the amount he invests at 5% interest as "11000 - x" (since the total investment is $11,000).
To earn interest, we can use the formula: Interest = Principal × Rate × Time
For the 4% interest account, the interest earned is:
0.04x × 1 (1 year) = 0.04x
For the 5% interest account, the interest earned is:
0.05(11000 - x) × 1 (1 year) = 550 - 0.05x
According to the problem, the total interest earned is $490. Therefore, we can set up the equation:
0.04x + (550 - 0.05x) = 490
Simplifying the equation:
0.04x + 550 - 0.05x = 490
-0.01x + 550 = 490
-0.01x = -60
x = 6000
Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.
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