Which cosine function has maximum of 2, a minimum of –2, and a period of 2pi/3 ?
Answers
Given:
maximum = 2, minimum = -2
period = 2π/3
Find: the cosine function having those attributes stated above
Solution:
Cosine equations follow the pattern below:
[tex]y=Acos(B(x-C))+D[/tex]where A = amplitude, B = 2π/period, C = horizontal shift, and D = vertical shift.
Since the only given information is the period, let's calculate for the value of B.
[tex]B=\frac{2\pi}{period}\Rightarrow B=\frac{2\pi}{\frac{2\pi}{3}}=3[/tex]Out of the choices, only y = 2cos 3θ has the value of B which is 3. Hence, y = 2cos 3θ is the cosine function that has a maximum of 2, a minimum of –2, and a period of 2pi/3. (Option 3)
Related Questions
How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
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Answer:
Step-by-step explanation:
64.528 is the decimal
Which of the following expressions is equivalent to 2-3?A -2-31B-23C231D- 2-3
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2 - 3
the correct answer is letter C
If we follow the rules of the exponents, the power is negative so we change the negative sign writing the numerator in the denominator,
Here is a right triangle with a missing side length what is the missing side length
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Right Triangles
A right triangle is recognized because it has an interior angle of 90°.
In right triangles, the Pythagora's Theorem is satisfied.
Being a and b the shorter sides (also called legs) of the triangle, and c the longer side (called hypotenuse), then:
[tex]c^2=a^2+b^2[/tex]The triangle shown in the image has the two legs of values a=15 and b=8. The hypotenuse is c=x, thus:
[tex]x^2=15^2+8^2[/tex]Operating:
[tex]x^2=225+64=289[/tex]Solving for x:
[tex]x=\sqrt[]{289}=17[/tex]x = 17
Write an explicit rule for the following arithmetic sequence: 28, 38, 48, 58,
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When you have an arithmetic sequence you can use the next general formula to get the explicit formula:
[tex]a(n)=a(1)+d(n-1)[/tex]Where a(1) is the first term in the sequence, d is the difference between each term in the sequence, and n is the nth term
You have the sequence: 28,38,48,58
The difference in this sequence is d=10
The first term is: a(1)=28
Then:
[tex]a(n)=28+10(n-1)[/tex][tex]a(n)=28+10n-10[/tex][tex]a(n)=18+10n[/tex]Then, the explicit rule for the given arithmetic sequence is: a(n)=18+10nWhere can I find L1 and L4 for a missing vertical angles?
Answers
The vertical angle theorem states that the opposite angles formed by two lines that intersect each other are always equal to each other.
Then, if we apply this to the figure shown we can say that by the vertical angle theorem
[tex]\begin{gathered} L1=L3 \\ L2=L4 \\ Meaning\colon \\ L1=45.5 \\ L4=134.5 \end{gathered}[/tex]Rapheal is traveling in a straight line at a constant speed from point A to point B. His distance from point B in miles is -20t + 45, where t is the number of hours he has been traveling. What is his speed in miles per hour?
Answers
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
A and B are the two points of a straight line.Distance between two points is given as :d₀ = -20t + 45 miles
t = the number of hours of travelling.The starting time = 0
i.e. the initial position = 0
Then
we put t=0
At t=0
d₀ = -20(0) + 45
= 0 + 45
= 45 miles
the distance travel after starting first hour is :
T= d₁ & d₀
than we put t = 1
At t = 1;
d₁ = -20(1) + 45
= -20 + 45
= 25 miles
now
Difference between d₁ & d₀ is
d = d₁ - d₀
45 - 25 = 20 miles
Total distance covered = 20 miles
To find the speed we use formula:
Speed = distance/time
Speed=20/1
Speed = 20 miles/hour
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
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i inserted a picture of the questions 19 and 20 that i need help with.
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WE are given that 9 tickets have a total cost of $94.50. To determine the price for each ticket we must find the quotient between the total amount spent and the number of tickets, like this:
[tex]\frac{94.50}{9}[/tex]Solving the operations we get:
[tex]\frac{94.50}{9}=10.5[/tex]Therefore, each ticket has a price of $10.50
Make the following conversions.5 pounds 16 ounces toa. Ounces:? ozb. Pounds: ? lbNote : I have attempted 80 ounces in 1 pound as the answers and it is incorrect
Answers
In order to calculate these conversions, we need to know the following conversion rate:
1 pound is equal to 16 ounces.
Knowing that, let's convert:
a. to ounces:
[tex]5\text{ pounds 16 ounces }=5\cdot16\text{ ounces + 16 ounces}=80\text{ + 16 ounces }=96\text{ ounces}[/tex]b. to pounds:
[tex]5\text{ pounds 16 ounces }=5\text{ pounds + 1 pound }=6\text{ pounds}[/tex]Which tree is growing faster?Tree 2*Tree 1 is growing1.5 inches everyweek.weeks 1|2|3|4|5inches 45678tallTree ?Tree 1
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the growing rate of the first tree
Tree 1 is growing 1.5 inches every week
STEP 2: Calculate the growing rate of the second tree
This implies the slope and is calculated using the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]By substitution,
[tex]m=\frac{5-4}{2-1}=\frac{1}{1}=1[/tex]The slope of 1 means that Tree 2 is growing at a rate of 1 inch per week
Hence, the tree that is growing faster is Tree 1 with a rate of 1.5 inches per week
ANSWER:
Tree 1
How many tiles of 8 cm² is needed to cover a floor of dimension 6 cm by 24 cm? A. 6 B. 12 C. 18 D. 24
Answers
Answer:
18 tiles.
Step-by-step explanation:
24x6= 144
144/8= 18
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Find the following. complete parts a-h. a. The first seven terms of the Fibonacci-like sequence with the seeds 0,3. *(parts b-h will appear as we answer this previous parts.) 7 parts in total for the question*
Answers
Recall that in a Fibonacci-like sequence, the sum of two consecutive terms yields the third term.
Mathematically,
[tex]t_n=t_{n-2}+t_{n-1}[/tex]Since we are given the first two terms, we can find the third term and so on...
F₁ = 0
F₂ = 3
[tex]\begin{gathered} F_3=F_2+F_1=3+0=3 \\ F_4=F_3+F_2=3+3=6 \\ F_5=F_4+F_3=6+3=9 \\ F_6=F_5+F_4=9+6=15 \\ F_7=F_6+F_5=15+9=24 \end{gathered}[/tex]Multiply -5 1/2 × 7 5/6 =
Answers
You have to multiply:
[tex]-5\frac{1}{2}\cdot7\frac{5}{6}[/tex]First write the compound fractions as impropper fractions.
To do so, divide the whole number by one to express it as a fraction and add both fractions:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}\to\text{ common denominator 2} \\ \\ \frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} 7\frac{5}{6}=\frac{7}{1}+\frac{5}{6}\to\text{ common denominator 6} \\ \frac{7\cdot6}{1\cdot6}+\frac{5}{6}=\frac{42}{6}+\frac{5}{6}=\frac{47}{6} \end{gathered}[/tex]Rewrite the multiplication using the corresponding impropper fractions:
[tex]-\frac{11}{2}\cdot\frac{47}{6}[/tex]And solve the multiplication, numerator * numerator and denominator*denominator:
[tex]-\frac{11}{2}\cdot\frac{47}{6}=-(\frac{11\cdot47}{2\cdot6})=-\frac{517}{12}[/tex]Order the lengths from least to greatest 19in 1yd 2ft 32in
Answers
19 in
1 yd
2ft
32 in
First, we have to convert all the length into a unique unit:
For example, inches:
Since
1 ft = 12 inches
2 ft = 2 x12 = 22 inches
1yd = 36 inches
Now, we have to order from least to greatest:
19 in-22in -32in-36in
In the original units:
19 in , 2ft, 32in ,1yd
explain why there are two zeros in the product of 5 x 40
Answers
EXPLANATION
There are two zeros in the product of 5x40 because multiplying the number 40 5 times give us the number 200 wich is a hundred type number.
Use disks and washers to find the volume of the solid the results when the area of the region y=x^3 y = 0, and x = 2 is revolved about the line x= 2
Answers
Solution
The functions that define the region in consideration are given below:
[tex]\begin{gathered} y=x^3 \\ y=0 \\ x=2 \end{gathered}[/tex]The Washer Method:
- Plotting these functions would help us visualize the question better. This is done below:
- The question would like us to revolve around the region about line x = 2. The region is bounded by the Blue, Red, and Green line. This requires that we use the formula given below:
[tex]\begin{gathered} V=\int ^b_a{f(y)\mathrm{dy}} \\ \text{where,} \\ a\text{ and }b\text{ are the bounds of the integration along the y-axis} \end{gathered}[/tex]-
We can represent the region bounded by the function by rearranging the functions as follows:
[tex]undefined[/tex]draw and label: ray LM
Answers
To draw a Ray; Draw a line with an arrowhead at one end of the line segmen:
Ray LM:
Please help with #4. The directions are with the pic below.
Answers
sphere: 12 pounds
cylinder: 108 pounds
Explanation:
Data:
. From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
. From balance B:
3 cubes = 5 spheres
Since 1 cube = 20 pounds
=> From balance B:
3 cubes * 20 pounds = 5 spheres
60 pounds = 5 sphere
60 / 5 = 5 / 5
12 pounds = 1 sphere
=> From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
3 spheres * 20 pounds + 1 sphere * 12 pounds = 1 cylinder + 2 spheres * 12 pounds
120 pounds + 12 pounds = 1 cylinder + 24 pounds
132 pounds = 1 cylinder + 24 pounds
132 pounds - 24 pounds = 1 cylinder + 24 pounds - 24 pounds
108 pounds = 1 cylinder
Find the value of z such that 0.04 of the area lies to the right of z. Round your answer toTwo decimal places.
Answers
The total area under the normal distribution curve is 1. z-scores are indicated in the horizontal axis below this curve. This means that the sum of areas under the curve at the left and at the right of a certain z-score must be equal to 1.
Then if the area at the right of the z-score that we are looking for is 0.04 the area at its left must be equal to 1-0.04=0.96. The area at the left of z is important because z-score tables usually show the areas at the left of several z-scores. Then the only thing that we have to do is look for the z-score associated with 0.96 in one of these tables. In your case the table that you should use is the one named "Normal Table -∞ to z". That table should look like this one:
As you can see the value 0.96 is associated with the row 1.7 and the column .05 which means that the z-score that meets that the area under the curve at its right is 0.04 is z=1.7+0.05=1.75.
AnswerThen the answer is 1.75
Facot the expression 81x^2-25 ?
Answers
Apply difference of two square
[tex]x^2-y^2\text{ = (x - y)(x + y)}[/tex][tex]\begin{gathered} 81x^2\text{ - 25} \\ =(9x)^2-5^2 \\ \text{Apply difference of two square} \\ =\text{ (9x - 5)(9x + 5)} \end{gathered}[/tex]Grandma’s Guide to Cooking MeasurementsDried Seasonings 1 pinch = 2 smidgens1 dash = 2 pinches1 sprinkle = 3 pinches1 teaspoon = 8 dashesBased on Grandma's guide to cooking, how many smidgens are in one teaspoon?Do not include units with your answer.
Answers
32
Explanation:1 pinch = 2 smidgens
1 dash = 2 pinches
Therefore, 1 dash = 2 x 2 smidgens
1 dash = 4 smidgens
1 teaspoon = 8 dashes
1 teaspoon = 8 x 4 smidgens
1 teaspoon = 32 smidgens
There are 32 smidgens in 1 teaspoon
Wayne is hanging a string of lights 89 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is 5 feet longer than twice its width. Find the length and width of the patio.
Answers
SOLUTION:
Case: Rectangles
Method:
The sum is:
w + w + 2w + 5 = 89
4w + 5 = 89
4w = 89 - 5
4w = 84
w = 84/ 4
w= 21 feet
The length, l
l = 2w + 5
l = 2( 21) + 5
l = 42 + 5
l = 47 feet
Final answer:
length of the patio, l = 47 feet
width of the patio, w= 21 feet
Find the value or measure. assume all lines that appear to be tangent are tangent.JK=
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In this problem we have that
mso
the formula to calculate the interior angle is equal to
msubstitute the given values
m
therefore
the answer is mplease help 50 points!
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Measure of angle 2 is 86 degrees
Measure of angle 3 is 94 degrees
Find the equation for the horizontal line passing through the point (-6,-6).
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SOLUTION
We are trying to get the equation for the horizontal line passing through the point (-6,-6).
( x1 , y 1 ) = ( 0, 0 )
( x2 , y2 ) = ( -6 , -6 )
Gradient, m = ( y2 - y1 ) / ( x2 - x1 )
m = ( -6 -0 ) / ( -6 - 0 )
m = -6 / - 6
m = 1
Then, using the equation of a line;
y - y 1 = m ( x - x 1 )
y - 0 = 1 ( x - 0 )
y = x
Solve them all pleaseeeeee
Answers
The solution to the inequalities will be,
( 5 ) y ≥ 2
( 6 ) x < 3
( 7 ) No solution.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
The given inequalities will be calculated as:-
-4 ≤ 4( 6y - 12 ) - 2y
-4 ≤ 24y - 48 - 2y
-4 ≤ 22 y - 48
22y ≥ 44
y ≥ 2
4x + 3 < 3x + 6
4x - 3x < 6 - 3
x < 3
-5r + 6 ≤ -5( r + 2 )
-5r + 6 ≤ -5r - 10
No solution
Therefore, the inequalities are solved above.
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In a newspaper, it was reported that the number of yearly robberies in Springfield in 2013 was 180, and then went down by 40% in 2014. How many robberies were there in Springfield in 2014?
Answers
As given that the number of yearly robberies in Springfield in 2013 was 180
And then went down by 40% in 2014.
So robberies were there in Springfield in 2014:
[tex]\begin{gathered} N=180-180\times\frac{40}{100} \\ N=180-72 \\ N=108 \end{gathered}[/tex]So robberies were there in Springfield in 2014 are 72
Plot the ordered pair (-4,-1) state which quadrant or on which axis the point lies
Answers
Answer:
Th
Explanation:
Given the ordered pair (-4, -1), we have that x = -4 and y = -1. Plotting this point, we'll have;
Quadrants are labeled in an anti-clockwise direction with the top right portion of the graph being the 1st quadrant. Looking at the plotted point, we can see that the point is in the 3rd quadrant.
HELP ME OUT PLEASE!!!!!!
Answers
Answer:
The First one (1.7,3.1)
Step-by-step explanation:
3x-2=-0.5x+4
3.5x=6
x=12/7
x≈1.7
sub x back into to find y
y≈3.1
What is the measure of a?
Answers
Answer:
Explanation:
Answer:
<A=32°
Explanation:
<BEC = 90° because it has the red half square and we know that <DCE = 42°. <ACB= 2x because <ACD and <DCB both =x. The equation we would set up is
90+(42+x) +2x=180
We get x=16.
Since <ACB = 2x we multiple 16 by 2
16*2=32
So <ACB =32°
Solve the equation 10x+14= - 2x+38 explaining all the steps of your solution as in the examples in this section.
Answers
To solve the given equation:
1. Add 2x in both sides of the equation:
[tex]\begin{gathered} 10x+2x+14=-2x+2x+38 \\ \\ \text{Combine like terms:} \\ 12x+14=38 \end{gathered}[/tex]2. Subtract 14 in both sides of the equation:
[tex]\begin{gathered} 12x+14-14=38-14 \\ \\ 12x=24 \end{gathered}[/tex]3. Divide both sides of the equation into 12:
[tex]\begin{gathered} \frac{12}{12}x=\frac{24}{12} \\ \\ x=2 \end{gathered}[/tex]Then, the solution for the given equation is x=2