Answer:
f(x) = 2*cos(4*x) + 4
Step-by-step explanation:
This is obviusly a sinusoidal function, which can be written as:
f(x) = A*cos( w*x ) + M
Where:
A = amplitude
w = angular frequency
M = midline.
Remember that the maximum of a cosine
cos(x) = 1, when x = (2*n)*pi (for any integer n)
And the minimum is at:
cos(x) = -1, when x = (2*m + 1)*pi (for any integer m)
Whit this in mind, we know that we have a maximum when:
x = pi
then we want:
w*pi = (2*n)*pi
and a minimum at:
x = -3*pi/4
Then we want
w*(-3*pi/4) = (2*m + 1)*pi
In the minimum case, we have a "4" in the denominator that is kinda unfortunate, so we woud want to take w = 4 in order to remove it, and this will work really well for wath we want, because:
w*pi = 4*pi = (2*2)*pi (here we have n = 2)
w*(-3*pi/4) = 4*(-3*pi/4) = -3*pi = (2*-2 + 1)*pi (here we have m = -2)
Then we can take w = 4.
So the function is something like:
f(x) = A*cos(4*x) + M
The amplitude is equal to half of the difference between the maximum and the minimum values of y.
The maximum is:
y = 6
the minimum is:
y = 2
Half of the difference is:
A = (6 - 2)/2 = 2
A = 2
Then our function is:
f(x) = 2*cos(4*x) + M
The value of the midline is equal to the maximum minus the value of the amplitude (or the minimum plus the value of the amplitude)
M = Maximum - A = 6 - 2 = 4
M = Minimum + A = 2 + 2 = 4
Then the function is:
f(x) = 2*cos(4*x) + 4
Answer:
2cos (4/7x - 4pi/7) + 4
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
mm
Answer:
1938
Step-by-step explanation:
round to nearest thousandth
0.227
Answer:
is there another number after the 7 if so if it is 5 or bigger it rounds up but 1-4 rounds down
Step-by-step explanation:
Answer:
0.23!! =D
hundredths (1/100)
What is the sum of 10.347+4.178=
Answer:
The answer is 14.525
Step-by-step explanation:
10. 347
+ 4. 178
_________
14 . 525
Thus, the answer is 14.525.
True or false? A correct answer is worth (2 pts). Explain how you know for the additional (2 pts). Using complete sentence for (1 pts)
(5,2) is a solution to the equation 2x + 3y = 10.
answer (in words)
FALSE. the coordinate pair (5, 2) is not a solution to the equation [tex]2x+3y=10[/tex]. in order to figure out whether or not the statement is true or false, plug the [tex]x[/tex] and [tex]y[/tex] values from the coordinate pair (5, 2) into the given equation, [tex]2x+3y=10[/tex]. if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.
(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)
answer (algebraic/steps for solving)
first, plug in 5 for [tex]x[/tex] in the equation [tex]2x+3y=10[/tex].
[tex]2x+3y=10[/tex] ⇒ [tex]2(5)+3y=10[/tex]then plug in 2 for [tex]y[/tex].
[tex]2(5)+3y=10[/tex] ⇒ [tex]2(5)+3(2)=10[/tex]now your equation is [tex]2(5)+3(2)=10[/tex]. all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.
[tex]2(5)+3(2)=10[/tex] ⇒ [tex]10 + 3(2) = 10[/tex]multiply 3 · 2.
[tex]10 + 3(2) = 10[/tex] ⇒ [tex]10 + 6 = 10[/tex]add 10 + 6.
[tex]10 + 6 = 10[/tex] ⇒ [tex]16=10[/tex]16 and 10 are not equal, therefore (5, 2) is not a solution to the equation [tex]2x+3y=10[/tex]. in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.
i hope this helps! have a great rest of your day <3
plzzzz help meee.......
Answer: [tex]-3\hat{i}-6\hat{j}+2\hat{k}[/tex]
Step-by-step explanation:
Given
[tex]\vec{a}=2\hat{i}+4\hat{j}-5\hat{k}\\\vec{b}=\hat{i}+\hat{j}+\hat{k}[/tex]
[tex]\vec{c}=\hat{j}+2\hat{k}[/tex]
The addition of the three is [tex]\vec{a}+\vec{b}+\vec{c}[/tex]
[tex]\vec{a}+\vec{b}+\vec{c}=(2\hat{i}+4\hat{j}-5\hat{k})+(\hat{i}+\hat{j}+\hat{k})+(\hat{j}+2\hat{k})[/tex]
[tex]\vec{a}+\vec{b}+\vec{c}=3\hat{i}+6\hat{j}-2\hat{k}[/tex]
vector opposite to the vector [tex]\vec{a}+\vec{b}+\vec{c}\ \ \text{is}\ -(\vec{a}+\vec{b}+\vec{c})[/tex]
[tex]\therefore -(\vec{a}+\vec{b}+\vec{c})=-3\hat{i}-6\hat{j}+2\hat{k}[/tex]
There are 3 fourths as many cows as pigs on an animal farm. If there are 35 pigs and cows on the farm, how many of them are pigs?
-4(v + 1) = 2(1 - 20) - 6
Answer:
v=10
Step-by-step explanation:
-4(v+1)=2(1-20)-6
step 1
distribute the -4 to v and 1 and distribute the 2 to 1 and --20
-4xv=-4v-4x1=-4 2x1=2 2x-20=-40
now we have -4v-4=2-40-6
step 2 combine like terms
the only like terms are -6 and -40 2
-6+-40+2=-44
now we have
-4v-4=-44
step 3 add 4 to each side
4+-44=-40
-4+4 cancels out
were left with
-4v=-40
the last step is to divide each side by -4
-4/-4 cancels out
-40/-4=10
in conclusions
v=10
have a great day :D
* This is the correct answer, I have taken the test and am posting the answers in hopes of helping other people :] *
Based on the diagram, what is tanA?
Enter your answer in the boxes.
tanA=
Aw that's really nice of you thanks
thank you <3 appreciate it loads
Talia bas 26 $1 coins, 20-cent coins, 50-cent coins. The number of $1 coins is 6 more than the number of 20-cent coins. The total value of the coins is $17.20. How many 50-cent coins are there?
Answer:
8 fifty cents coin.
Step-by-step explanation:
Let's assign variable for the unknown number of coins.
Let there are 'x' number of $1 coins
'y' number of 20 cent coins
'z' number of 50 cent coints.
Totally there are 26 coins.
So, x+y+z=26
Now, there are 6 more $1 coins than 20-cent coins.
We can set up equation for this as
x= y+6
Now, total value of these coins is $17.20
We can setup equation as
100 x+20 y+50 z=1720
Now, substitute x as y+6
100(y+6) +20 y+50 z =1720
Distribute the 100 to get rid ( )
100 y+600 +20 y+50 z=1720
Combine like terms
120 y+50 z= 1120
Keep this equation as it is.
Plug in x as y+6 into x+y+z=26
y+6+y+z=26
2y+z=20
Now, take the two equations
2y+z=20
120y+50z=1120
Multiply first equation by -60 to eliminate the y terms when we add them.
-120y-60z=-1200
120y+50z= 1120
-------------------------
-10z =-80
Divide both sides by -10
z=8
Now, plug in z as 8 into 2y+z=20
2y+8 =20
Subtract both sides 8
2y=12
Divide both sides by 2
y=6
Now, plug in y, z values into the first equation.
x+6+8=26
x+14=26
Subtract both sides 14
x=12
So, there are eight 50-cent coins.
Caffeine leave the body or continuous rate of 18% per hour of Alexa drinking energy drink that contains 110 mg of caffeine how much caffeine will be in your bloodstream after 12 hours
Answer:
10.168 mg
Step-by-step explanation:
Amount of caffeine in body = 110 mg
Decreases at the rate of rate of 18% per hour
how much caffeine will be in your bloodstream after 12 hours
After the first hour;
New amount = 110 - (0.18 * 110) = 90.2 mg
After the second hour;
New amount = 90.2 - (0.18 * 90.2) = 73.964 mg
After the third hour;
New amount = 73.964 - (0.18 * 73.964) = 60.65 mg
After the fourth hour;
New amount = 60.65 - (0.18 * 60.65) = 49.733 mg
After the fifth hour;
New amount = 49.733 - (0.18 * 49.733) = 40.78 mg
After the sixth hour;
New amount = 40.78 - (0.18 * 40.78) = 33.44 mg
After the seventh hour;
New amount = 33.44 - (0.18 * 33.44) = 27.4208 mg
After the eighth hour;
New amount = 27.4208 - (0.18 * 27.4208) = 22.485 mg
After the ninth hour;
New amount = 22.485 - (0.18 * 22.485) = 18.4377 mg
After the tenth hour;
New amount = 18.4377 - (0.18 * 18.4377) = 15.119 mg
After the eleventh hour;
New amount = 15.119 - (0.18 * 15.119) = 12.40 mg
After the twelfth hour;
New amount = 12.40 - (0.18 * 12.40) = 10.168 mg
Rebecca's window store made a mosaic for the community center. The mosaic had a 7 × 7 array of different color square tiles. If each tile is 3 1/2 ft long, what is the area of the whole mosaic?
Answer:
600 1/4 ft²
Step-by-step explanation:
Window is a 7 * 7 square array
Length per tile = 3 1/2 ft long
Dimension of entire array :
3 1/2 * 7 by 3 1/2 * 7
7/2 * 7 by 7/2 * 7
49/2 by 49/2
Recall : Area of a square = a² ; where a = side length
Area of entire array :
49/2 * 49/2 = 2401 / 4 = 600 1/4 ft²
In ΔPQR, the measure of ∠R=90°, PQ = 5.7 feet, and RP = 3.8 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answer:48.1897 = 48.2
Step-by-step explanation: cos P= 3.8/5.7
P= cos-1 (3.8/5.7)
P=48.1897 = 48.2
a glass top of an office table is in the form of rectangle. The diagonal of the table have length 5x-11 and 2x+25
1.what is the value of x?
2.what us the length of the diagonal?
Answer:
1) The value of [tex]x[/tex] is 12.
2) The length of the diagonal is 49.
Step-by-step explanation:
1) If the glass is a rectangle, then both diagonal must have the same length, that is, the following equation must be solved:
[tex]5\cdot x - 11 = 2\cdot x + 25[/tex] (1)
We need some algebraic handling to determine the value of [tex]x[/tex]:
[tex]5\cdot x - 11 = 2\cdot x + 25[/tex]
[tex]5\cdot x - 2\cdot x = 25 +11[/tex]
[tex][5+(-2)] \cdot x = 36[/tex]
[tex]3\cdot x = 36[/tex]
[tex]x = 12[/tex]
The value of [tex]x[/tex] is 12.
2) If we know that [tex]x = 12[/tex], then the length of the diagonal ([tex]d[/tex]) is:
[tex]d = 2\cdot x + 25[/tex]
[tex]d = 49[/tex]
The length of the diagonal is 49.
Which number line shows point M at 4/3?
Answer:
D
Step-by-step explanation:
going to the number "4" 3 dots down is 4,3
Find the value of x to the nearest degree.
Answer:
A. 66
Step-by-step explanation:
180 - 90 = 90
90 - 24 = 66
Answer will be 66
Hope this helps!
Can Someone help me out
Answer:
D 0.9988
Step-by-step explanation:
Kevin is making a picture frame. He has a piece of trim that is 3 feet long.
How many 14−inch-long pieces can Kevin cut from the trim?
How much of a foot will he have left over?
Kevin can cut______ 14−inch-long pieces with______ of a foot left over.
1
Select the correct answer.
What is the general form of the equation of a circle with center at (a, b) and radius of length m?
OA. x + y2 - 2ax – 2by + (a? + b2 - m?) = 0
OB.
x+y + 2ax + 2by+ (a1 + b2 - m?) = 0
O c.
x + y2 - 2ax - 2by + (a + b-m) = 0
OD. x + y2 + 2ax + 2by + 32 + b2 =-m?
Reset
Next
The general form of an equation of a circle with center at (a, b) and radius of length m is x² + y² - 2ax - 2by + (a² + b² - m²) = 0.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Here center is given as (a, b).
Radius is given as m.
Substituting,
(x - a)² + (y - b)² = m²
x² - 2ax + a² + y² - 2by + b² = m²
x² + y² - 2ax - 2by + (a² + b²) = m²
x² + y² - 2ax - 2by + (a² + b² - m²) = 0
Hence the required equation is, x² + y² - 2ax - 2by + (a² + b² - m²) = 0.
Learn more about General Form of Circle here :
https://brainly.com/question/10618691
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Las calificaciones obtenidas por un grupo de 49 alumnos en una prueba con las siguientes: 3.0; 5.5; 4.4; 6.0; 4.3; 7.2; 4.7; 6.5; 6.7; 4.0; 5.9; 5.8; 1.4; 3.2; 5.8; 4.6; 4.1; 3.5; 6.8; 5.0; 5.9; 2.1; 4.2; 4.5; 4.1; 4.8; 2.8; 4.7; 7.7; 6.0; 3.0; 5.7; 4.5; 4.9; 3.3; 4.8; 4.7; 7.7; 6.0; 3.0; 5.7; 4.5; 4.9; 3.3; 4.8; 4.7; 5.2; 3.8; 6.1. Agrupa en siete intervalos estos datos y construye la tabla de frecuencias correspondientes, hallando los valores de la media, la mediana y la moda de los mencionados datos
Answer:
nosejgivuguvug7gug7g7g
Step-by-step explanation:
pol
Marissa went on a trip and drove her car throughout the day. The graph below shows Marissa's distance from the starting point of her trip for different segments of time
What’s the answer to this please?
Which of these factored expressions are equivalent to 15x+45? Select all that apply
A-3(5x+15)
B-5(3x+9)
C-15(x+3)
D-15(x+45)
Answer:
A, B, C
Step-by-step explanation:
15x+45
3 (5x + 15)
5(3x +9)
15(x + 3)
Mrs. Doan spends $36 at a carnival. This is 75% of the money she brings to the carnival. How much money does Mrs. Doan bring to the carnival?
Answer:
$48
Step-by-step explanation:
Find the area of the isosceles triangle
Answer:
could you add the picture? then i will edit my answer to give you the actual answer
Step-by-step explanation:
Which graph depicts the path of a projectile?
Answer:
The second option.
Answer:
its B
Step-by-step explanation:
round nearest hundredth
Answer:.
Step-by-step explanation:nearest hundredth the answer for this question is joe mama
Twenty students out of 80 kids had pizza for lunch. What is the percentage of students that had pizza for lunch?
Please help!!!
Answer:
25%
Step-by-step explanation:
20/80 = 2/8 = 1/4
1/4 = 0.25
0.25 x 100 = 25
so 25%
Answer:
0.25
Step-by-step explanation:
Divide 20 by 80
1/3 x - 6 = 3 what is the answer for x
Answer:
x = 3
Step-by-step explanation:
Answer:
x=27
Step-by-step explanation:
3.
Write a function rule for the table.
A. p = 7.50h
B. p = h + 15
C. p = 15h
D. h = 7.50p
Answer:
p = 7.50h
I got this correct, the answer is A. p= 7.50h
Step-by-step explanation:
The answer would be d because every two hours someone works they get $15 and for the equation we must know how much they work for one hour so that it works with the equation (we'd have to simplify it down do how much paid up per hour). so half of 15 is 7.5 so the equation would be p=7.50h (standing for $7.50 per hour).
The correct answer is: [D]: " p = 7.50 h " .
________________________________________________
The pay, "p" , is a function of the hours worked.
When h = 2, (h = number of hours);
the pay, "p" , is equal to " 7.50 * 2 " = 15.00 dollars" ; as shown on table.
When h = 4 ; p = " 7.50 * 4 = 30.00 dollars" ; as shown on table .
When h = 6 ; p = " 7.50 * 6 = 45.00 dollars" ; as shown on table.
When h = 8 ; p = " 7.50 * 8 = 60.00 dollars" ; as shown on table.
_____________________________________________________
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the largest angle.
Cristian brought d starbursts to school and combined them with Angel's j starbursts. He then split them equally among 8 friends. Write an expression to represent the situation.
Answer:
(d+j) ÷8
Step-by-step explanation: