The required standard equation is given as y(t) = 5.39 sin(4πt + 0.379π).
Given that,
To rewrite y(t)=2×sin 4pi t+5×cos 4pi t in the form y(t)=Asin (wt+Ф).
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here
We know that.
Asin(α + β) = Asinαcosβ + Acosαsinβ,
Comparing it with the given equation,
Asinα = 5
Acosα = 2
Taking the ratio of the equation,
sinα/cosα = 5/2
tanα = 5/2
α = 0.379π
Now,
Asin0.379π = 5
A = 5 / sin0.379
A = 5.39
Now,
The standard form equation is given as, y(t) = 5.39 sin(4πt + 0.379π) where ω = 4π.
Thus, the required equation is given as y(t) = 5.39 sin(4πt + 0.379π).
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A line segment has the endpoints F(2, -1) and G(-8, -1). Find the coordinates of its midpoint
M.
Write the coordinates as decimals or integers.
M=
Video
The coordinates of the midpoint of segment FG are (3,-1) which was found using midpoint formula.
How to find midpoints of a line segment?When it comes to practical application, the midpoint formula is rather straightforward.
Step 1: Determine the line segment or the two ends.
Step 2: Determine their coordinates.
Step 3: Add the x coordinates of both ends and divide by 2.
Step 4: Adding the y coordinates of both endpoints, divide by 2, and complete the step.
Step 5: As you specify the coordinates of any point, write the values that were acquired in Steps 3 and 4.
Given: Endpoints of a line segment are F(2, -1) and G(-8, -1).
We need to find the coordinates of its midpoint.
Using midpoint formula,
(a,b) = (x₁ + x₂)/2,(y₁ + y₂)/2
= (2-8)/2,(-1-1)/2
= 3,-1
So, coordinates are (3,-1)
Therefore, the coordinates of the midpoint of segment FG are (3,-1) which was found using midpoint formula.
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A graduated cylinder has 7mL (cm³) of water placed in it. An irregularly shaped rock is then dropped in the graduated cylinder and the volume
of the rock and water in the cylinder now reads 9mL (cm³). The mass of the rock dropped into the graduated cylinder is 24 grams
Find the volume of the rock dropped into the graduated cylinder.
V=
Hint: Do not forget your units!!!
Find the density of the rock dropped into the graduated cylinder.
D-
Hint Do not forget your units!!!
Blank 1:
Blank 2:
well, we had a cylinder with 7mL of water, in the rock goes and kaboom the volume for the cylinder and its contents is 9 mL, well, the displaced water from the rock is equivalent to its volume, as Archimedes would properly point out, so since it was 7mL and now is 9mL well, the extra 2mL is the volume of the rock :).
sidenote: Archimedes is Da Bomb!!!!
now, we know the rock weights 24 grams, and we also know its volume is 2mL, so its density is simply g/mL, or [tex]\cfrac{24g}{2mL}\implies 12~\frac{g}{mL}[/tex]
An element with a mass of 400 grams decays by 29.8% per minute. To the nearest
minute, how long will it be until there are 2 grams of the element remaining?
The time elapsed, to the nearest minute, until only 2 grams of the element remains is 15 minutes.
We have an element. The element has a mass of 400 grams. The element decays by 29.8% per minute. We need to find the time duration after which there will be only 2 grams of the element remaining. Let the initial mass of the element, the final mass of the element, the rate of decay, and the time elapsed be represented by the variables m, M, r, and t. We can write the equation as given below.
M = m(1 - r)^t
2 = 400(1 - 0.298)^t
0.005 = (0.702)^t
log(0.005) = t*log(0.702)
t = log(0.005)/log(0.702)
t = 14.97
The time taken, to the nearest minute, is 15 minutes.
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This graph appeared in a local newspaper after a recent election.
Roberts Wins by Wide Margin
Do you agree with the message in the graph title? Why or why not?
a.No, the three candidates were only separated by a margin of about 2%.
b.Yes, Roberts had twice as many votes as Johnson and four times as many as Gomez.
c.No, newspapers are always slanted towards the candidate they favor.
d.Yes, the bar for Roberts is a lot taller than the bars for Johnson and Gomez.
Please select the best answer from the choices provided
>>>>>THE ANSWER IS A<<<<<<
The correct statement regarding the message in the graph title is of:
a. No, the three candidates were only separated by a margin of about 2%.
What is shown on the bar graph?The bar graph shows the number of votes obtained by each candidate, which are listed as follows:
Candidate Johnson: 940 votes.Candidate Roberts: 980 votes.Candidate Gomez: 920 votes.These amounts of votes where quite close, however the bar graph has a bad scale, giving the idea that Roberts got about the double number of votes as Johnson and four times as Gomez.
This bad scale is also used to insert the word wide into the text of the article. However, due to the low absolute difference in the number of votes between these candidates, this work is not correct, and hence, option a is correct.
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a) Complete the table of values for y = 6 - 2x
Answer:
4x
Step-by-step explanation:
bcoz
y = 6 - 2x
6-2x = 4x
y=4x
L (-1,-2), M (3,6); ratio 5 to 3
I NEED HELP LIKE NOWW
The coordinates of the points dividing the line in 5:3 is (3/2, 3)
What is section formula?The section formula gives the coordinates of a point which divides the line joining two points in a ratio, internally or externally.
Given a line LM, passing through points (-1,-2) and (3,6) a point is dividing it in a ratio of 5:3
According to section formula,
(x, y) = (5*3 - 3*1)/8, (5*6 - 3*2)/8
(x, y) = (3/2, 3)
Hence, The coordinates of the points dividing the line in 5:3 is (3/2, 3)
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what fraction shows the number of hours saide's dog sleeps every 4 hours in a day? Complete the fraction.
The fraction that shows the number of hours Saide's dog sleeps every 4 hours in a day is 1/6.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
It should be noted that there are 24 hours in day. Since the dog sleeps for 4 hours in a day, the fraction will be:
= Number of hours slept / Total hours
= 4 / 24.
= 1/6
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BRAINLIST! WHEN ANSWERED!
What are two things to know about the OPPOSITE SIDES of a parallelogram?
1.
2.
Answer:
Opposite sides of a parallelogram are:
1. Congruent
2. Parallel
Step-by-step explanation:
Opposite parallel and congruent sides are the features of a parallelogram and are the criteria for a quadrilateral to be a parallelogram.
Which equation is the inverse of y = 16x² + 1?
Answer:f^-1(x)= square root x-1 over 4 and square root -square root over 4
Step-by-step explanation:
interchange the variables and solve for y
5)
4. Rectangle DEFG with vertices D(-4, 3), E(0, 2),
and G(-6, -5): (x,y) → (x + 4, y + 1)
F(-2,-6),
D'(__)
E' (_)
F'
G' (
The vertices of the transformed image D'E'F'G' is D'(0, 4) E' (4, 3) G'(-2, -4) F'(2, -5)
Rectangle DEFG with vertices D(-4, 3), E(0, 2),and G(-6, -5), F(-2,-6),
is transformed into an image as per (x,y) → (x + 4, y + 1 )
D(-4, 3)
x = -4, y = 3
The image D' will be (x + 4, y + 1) = (-4 + 4, 3 + 1 ) = (0, 4)
E(0, 2)
x = 0, y = 2
The image E' will be (x + 4, y + 1) = (0 + 4, 2 + 1 ) = (4, 3)
G(-6, -5)
x = -6, y = -5
The image G' will be (x + 4, y + 1) = (-6 + 4, -5 + 1 ) = (-2, -4)
F(-2, -6)
x = -2, y = -6
The image F' will be (x + 4, y + 1) = (-2 + 4, -6 + 1 ) = (2, -5)
Therefore, the vertices of the transformed image D'E'F'G' is D'(0, 4) E' (4, 3) G'(-2, -4) F'(2, -5)
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Which is bigger 5/8 or 3/5
Answer:
[tex] \frac{5}{8} and \: \frac{3}{5} \\ \\ \frac{5 \times 5}{8 \times 5} = \frac{25}{40} \\ \\ \frac{3 \times 8}{5 \times 8} = \frac{24}{40} \\ \\ \frac{25}{40} > \frac{24}{40} \\ \\ so \: \frac{5}{8} > \frac{3}{5} [/tex]can someone please help me it says to simplify it
Answer:
B
Step-by-step explanation:
[tex]\frac{1}{5}[/tex] b - 5( [tex]\frac{2}{5}[/tex] a - [tex]\frac{1}{10}[/tex] b ) + 4a ← distribute parenthesis by - 5
[tex]\frac{1}{5}[/tex] b - 2a + [tex]\frac{1}{2}[/tex] b + 4a ← collect like terms
= 2a + [tex]\frac{1}{5}[/tex] b + [tex]\frac{1}{2}[/tex] b ( express fractions with a common denominator of 10 )
= 2a + [tex]\frac{2}{10}[/tex] b + [tex]\frac{5}{10}[/tex] b
= 2a + [tex]\frac{7}{10}[/tex] b
show that the convergence of a series is not affected by changing a finite number of its terms. (of course, the value of the sum may be changed.)
Convergent Series:
A Convergent Series is a series whose partial sums tend to a specific member is called a limit.
∑ 1/2n = 1/2+ 1/4 + 1/8 + 1/16 +........
Given an infinite series ∑₁ ∞ an determine the series is convergence. Recall that we can actually do better with geometric series not only we can determine convergence but also divergence. We can also calculate geometric series.
Suppose we are given a series ∑ aₙ which is not quite a geometric series but becomes a geometric series for sufficiently large n. That is we can find an integer N such that aₙ = aₓⁿ for all n > N. we don't have a general formula for aₙ when n ≤ N. The values of aₙ for small n don't effect Sₙ is convergence or not.
As a moment of fact, we never used the fact that aₙ eventually become geometric. More general ∑aₙ is convergent series, we can add a finite number of terms to the be gaining of this series or remove a finite number of terms from the be gaining of the series without affecting the convergence of the series. For Example: if ∑aₙ convergence then so does
10 + 10¹⁰ + 10 ¹⁰⁰ + 10¹⁰⁰⁰ + ∑aₙ
Similarly, if ∑aₙ convergence then,
a₁₀₀₀ +a₁₀₀₁ +a₁₀₀₂ + ..... = ∑₁₀₀₀ ∞ aₙ
However, the fact that we are only adding finitely many terms to the series is essential. That is, when it comes to determining convergence of a series ∑aₙ , we can see that only the asymptotic behavior of ∑aₙ matter, that is, only the behavior of the sequence aₙ as n--- ∞ affects convergence.
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What is the correlation coefficient for the data (0, 3), (1, 2), (2,0)?
A0.54
B 0.93
-0.67
-0.98
Answer:
-0.98
Step-by-step explanation:
Answer:-0.98
Step-by-step explanation:
Pls help I forgot how to work out bearings
Note that because the graph is slightly deformed to the left, it is impossible to work out the exact bearing. Below, however, are steps on how to get the bearing of a map.
How do you work the bearings of a map?Calculate the angle clockwise from north to determine a bearing. Begin with the first site by drawing a vertical line symbolizing north. Draw a line from the starting point to the ending point. Calculate the clockwise angle formed by the north line and this line.
When measuring a bearing, three principles must be followed:
Always determine the angle counterclockwise.Always evaluate the angle from north to south.Always use a three-figure bearing (for example, 030° instead than 30°).Note that a bearing is an angle in degrees calculated clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.
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Find the greatest possible x-coordinate of point A such that for any point B on the y-axis between (-24) and 25, the segment AB has a common point with the line segment PQ, where P(5, -12), Q(5, 9).
Answer:
8.75
Step-by-step explanation:
You want the greatest possible x-coordinate of point A such that for any point B on the y-axis between (-24) and 25, the segment AB has a common point with the line segment PQ, where P(5, -12), Q(5, 9).
GeometryIf we designate the points on the y-axis as X(0, -24) and Y(0, 25), we find that point A must lie in the triangle bounded by lines XY, XP, and YQ. The x-coordinate of the point of intersection of lines XP and YQ will be the greatest x-coordinate that point A can have.
EquationsThe line through points (x1, y1) and (x2, y2) can be written as ...
(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
This equation is readily simplified to general form ax+by+c = 0.
Line XP
(-12-(-24))(x -0) -(5-0)(y -(-24)) = 0
12x -5y -120 = 0
Line YQ
(9 -25)(x -0) -(5 -0)(y -(25)) = 0
-16x -5y +125 = 0
We want the value of x that satisfies these equations. That can be found by subtracting the second equation from the first:
(12 -5y -120) -(-16x -5y +125) = (0) -(0)
28x -245 = 0
x = 245/28 = 8.75
The greatest x-coordinate is x = 8.75.
need the answer for b quickly. it's the thing you put at the start of a axis when there a unequal gap. looks like this(_/\/\/\_) I forgot the name for it
150 cm
look at the beginning of the axis. it goes 140 to 160. then 160 to 170. it isnt in order. the missing mumber is 150
Evaluate 5 (2)² – 6.
5(2)² - 6 =
use three unit multiplier to convert 314 inches to kilometers
Answer:
Step-by-step explanation:
314 inches * (1 foot / 12 inches) * ( 1 meter / 3.28084 foot) * ( 1 kilometer / 1000 meter)
0.0079755997 Km
Please I need help please
Answer:
Step-by-step explanation:
1=88
2=42
3=42+25+x=180
3=180-67
Which of the following is a multiple of 2 and 4?
The multiple of 2 and 4 is 48.
A number that is the result of a given number and another natural number is called a multiple of that number. To find the multiple of a number, multiply the number by any whole number.
The given options are A. 50, B. 58, C. 54, and D.48.
The multiples of 50 can be written as,
[tex]50=2\times5\times5[/tex]
The multiples of 58 can be written as,
[tex]58=2\times29[/tex]
The multiples of 54 can be written as,
[tex]54=2\times3\times3\times3[/tex]
Therefore, the first three options are not multiples of both 2 and 4.
The multiples of 48 can be written as,
[tex]\begin{aligned}48&=2\times2\times2\times2\times3\\&=4\times2\times2\times3\end{aligned}[/tex]
Therefore, 48 is a multiple of 2 and 4.
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The complete question is -
Which of the following is a multiple of 2 and 4?
A. 50 B. 58 C. 54 D.48
Dracula is broke. He had to borrow $5 from you. Now you are broke. You have to borrow $5 from your brother franjenstein. Now Frankenstein is broke. He has to borrow $2 from Dracula. How can everybody be paid back in just one payment i
Answer:
Have Dracula pay you $5
Step-by-step explanation:
This whole thing happened because Dracula was broke. If $5 is given to Dracula, he can give you back $5 so you can return 5$ to Frankenstein. Then Frankenstein can give $2 back to Dracula.
“Solve the following systems of equations using any method” ( elimination, substitution, graphing)
Answer:
(0, 3)===========================
Given systemy = 2x + 3y = - 3x + 3Solve by substitution/elimination2x + 3 = - 3x + 32x + 3x = 3 - 35x = 0x = 0y = 2*0 + 3y = 3Answer:
x = 0y = 3Step-by-step explanation:
Forming the equation,
→ 2x + 3 = -3x + 3
Now the value of x will be,
→ 2x + 3 = -3x + 3
→ 2x + 3x = 3 - 3
→ 5x = 0
→ x = 0/5
→ [ x = 0 ]
Then the value of y will be,
→ y = -3x + 3
→ y = -3(0) + 3
→ y = 0 + 3
→ [ y = 3 ]
Hence, the value of y is 3.
solve the inequality
8<3(y-2)
Answer:
y>14/3
Step-by-step explanation:
Let's solve your inequality step-by-step.
8<3(y−2)
Step 1: Simplify both sides of the inequality.
8<3y−6
Step 2: Flip the equation.
3y−6>8
Step 3: Add 6 to both sides.
3y−6+6>8+6
3y>14
Step 4: Divide both sides by 3.
3y/3 > 14/3
Answer: y>14/3
Hope it helps!
Which sequence of transformations would result in an image that is similar and non- congruent to the pre-image?
Answer:
answer -a dilation followed by a translation
-a dilation followed by a reflection
-a reflection followed by a dilation
-a rotation followed by a dilation
Thank you for helping
Applying the inscribed angle theorem, we have:
9. B. m∠ABC = 70°
10. F. m∠Z = 54°
11. According to the two-tangent theorem, x is: D. 8 m
What is the Inscribed Angle Theorem?An inscribed angle in a circle has a measure that is half of the measure of the intercepted arc, based on the inscribed angle theorem.
What is the Two-Tangent Theorem?The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, the two tangents are equal to each other.
9. Measure of arc AC = 360 - 120 - 100
Measure of arc AC = 140°
m∠ABC = 1/2(measure of arc AC) [inscribed angle theorem]
m∠ABC = 1/2(140)
m∠ABC = 70° [option B]
10. Arc XYZ = 2(m∠X) [inscribed angle theorem]
Arc XYZ = 2(126) = 252°
Arc WXY = 360 - arc XYZ
Arc WXY = 360 - 252
Arc WXY = 108°
m∠Z = 1/2(arc WXY) [inscribed angle theorem]
m∠Z = 1/2(108)
m∠Z = 54° [option F]
11. x = 10 - 2 [two-tangent theorem]
x = 8 m [option D]
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Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of gems. The table below shows the number of gems Lulu received from three different adventures and the number of chests she needed to hold the gems
An equation to describe the relationship between g, the number of gems, and c, the number of chests is; g = 300c
How to solve Linear Equation Word Problems?
In adventure A, when number of gems is 600, we see that number of chests is 2. Thus;
Rate of gems per chests = 600/2 = 300 g/c
In adventure B, when number of gems is 1500, we see that number of chests is 5. Thus;
Rate of gems per chests = 1500/5 = 300 g/c
In adventure C, when number of gems is 4800, we see that number of chests is 16. Thus;
Rate of gems per chests = 4800/16 = 300 g/c
Thus;
There is a constant rate and we can say that the equation that shows the relationship between the two variables is;
g = 300c
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Complete question is;
Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of gems. The table below shows the number of gems Lulu received from three different adventures and the number of chests she needed to hold the gems.
Number of gems(g) Number of chests(c)
Adventure A 600 2
Adventure B 1500 5
Adventure C 4800 16
Write an equation to describe the relationship between g, the number of gems, and c, the number of chests.
Divide -6 2/5 / -4 3/7
Answer: 224/155
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. Convert proper Fractions to improper fractions!
-6 2/5/ -4 3/7=
=-32/5/-31/7
2. Multiply by switching Denominator and Numerator of the Fraction!
-32/5/-31/7=
-32/5*-7/31=
224/155=
1 69/155
3. Answer:1 69/155
Two shops, Lidal and Oldi, sell the same brand of toilet rolls but with different package sizes.
Calculate the price per 72 rolls for each shop.
Write which shop is the best value for money in the comment box.
8 for 2.80
9 for 3.24
The price of 72 rolls of toilet rolls in each shop is:
Lidal - $25.20Oldi - $25.92The shop with the best value for money is Lidal.
How to find the price?Lidal sells 8 toilet rolls for $2.80 and so if it was to sell 72 rolls, it would sell at a price of:
= Price per 8 rolls x Number of rolls / Number of rolls in packages
= 2.80 x 72 / 8
= 2. 80 x 9
= $25.20
Oldi sells 9 toilet rolls for $3.24 so the cost of 72 rolls would be:
= 3. 24 x 72 / 9
= 3. 24 x 8
= $25. 92
The shop with the best value for money is the cheaper one which is Lidal.
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convert 10/6 to a mixed number and reduce the fraction
Answer:
1 2/3
Step-by-step explanation:
How much does 6 go into 10? Only 1 time so the whole number will be 1.
Next, subtract 6 from 10 and you get 4.
1 4/6 reduces to 1 2/3
Answer: 1 2/3 (pls give me brainiest not to be greedy but pls)
Step-by-step explanation: