Write a cosine function that has an amplitude of 2, a midline of 5 and a period of T.
Answers
phase shift is 0
General equation
y=AcosB(x-C)+Dc is phase shift
y=AcosBx+DMidline is D
y=AcosBx+5A is amplitude
y=2cosBx+5B is period
2π/TSo
Final equation
y=2cos(2πx/T)+5Not mandatory from now
For some special cases 2π/T=omega
So Equation yields
y=2cos([tex]\omega x[/tex])+5Answer:
[tex]f(x)=2 \cos (2x)+5[/tex]
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven:
Amplitude = 2 ⇒ A = 2[tex]\sf Period=\pi \implies \dfrac{2 \pi}{B}=\pi \implies B=2[/tex]mid-line = 5 ⇒ D = 5Inputting the given values into the standard form:
[tex]\implies f(x)=2 \cos (2x)+5[/tex]
Related Questions
I need to know this asap
Answers
Answer:
Output: 3
Step-by-step explanation:
(x, y)
(Input, Output)
(2, 3)
In the sequence $$1,2,2,4,8,32,256, each term (starting from the third term) is the product of the two terms before it. For example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). This sequence can be continued forever, though the numbers very quickly grow enormous! (For example, the $14 term is close to some estimates of the number of particles in the observable universe.) What is the last digit of the $35 term of the sequence
Answers
The sequence is recursively defined by
[tex]\begin{cases}a_1 = 1 \\ a_2 = 2 \\ a_n = a_{n-1} a_{n-2} & \text{for } n \ge 3\end{cases}[/tex]
By this definition,
[tex]a_{n-1} = a_{n-2} a_{n-3} \implies a_n = a_{n-2}^2 a_{n-3}[/tex]
[tex]a_{n-2} = a_{n-3} a_{n-4} \implies a_n = (a_{n-3} a_{n-4})^2 a_{n-3} = a_{n-3}^3 a_{n-4}^2[/tex]
[tex]a_{n-3} = a_{n-4} a_{n-5} \implies a_n = (a_{n-4} a_{n-5})^3 a_{n-4}^2 = a_{n-4}^5 a_{n-5}^3[/tex]
[tex]a_{n-4} = a_{n-5} a_{n-6} \implies a_n = (a_{n-5} a_{n-6})^5 a_{n-5}^3 = a_{n-5}^8 a_{n-6}^5[/tex]
and so on.
Recall the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, 21, …}, where the next term in the sequence is the sum of the previous two terms. If [tex]F_n[/tex] is the n-th Fibonacci number, then continuing the pattern above we would arrive at
[tex]a_n = {a_2}^{F_{n-1}} {a_1}^{F_{n-2}} = 2^{F_{n-1}}[/tex]
Notice that the sequence of positive powers of 2 leaves a periodic sequence of residues mod 10 :
[tex]2 \equiv 2 \pmod{10}[/tex]
[tex]2^2 \equiv 4 \equiv 4 \pmod{10}[/tex]
[tex]2^3 \equiv 8 \equiv 8 \pmod{10}[/tex]
[tex]2^4 \equiv 16 \equiv 6 \pmod{10}[/tex]
[tex]2^5 \equiv 2 \times 2^4 \equiv 2 \times 6 \equiv 2 \pmod{10}[/tex]
[tex]2^6 \equiv 2^2 \times 2^4 \equiv 4 \times 6 \equiv 4 \pmod{10}[/tex]
and so on; the period of this sequence of residues is 4.
The period of [tex]F_n[/tex] taken mod 4 is 6 :
[tex]\{1, 1, 2, 3, 5, 8, \ldots\} \equiv \{1, 1, 2, 3, 1, 0, \ldots\} \pmod 4[/tex]
(This follows from the "properties" section in the link in comment. In this case, π(4) = 3/2 × 4 = 6.)
It follows that
[tex]34 \equiv 4 \pmod 6 \implies F_{34} \equiv 3 \pmod 4 \implies 2^{F_{34}} \equiv 2^3 \equiv 8 \pmod{10}[/tex]
which means the last digit of [tex]a_{35}[/tex] is 8.
find an ordered pair for 4 solution for -5x+y=6
Answers
⇒ Choose three values for [tex]x[/tex] and substitute in to find the corresponding [tex]y[/tex] values.
[tex](0,6),(1,11),(2,16)[/tex]
Which equation is graphed here?
y−1=−13(x−1)
y−1=−13(x+1)
y+4=3(x−1)
y−4=−3(x+1)
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through (negative one, four) and (one, negative two).
Answers
Answer: Choice D
y-4 = -3(x+1)
========================================================
Explanation:
Let's first find the slope of the line through (-1,4) and (1,-2)
[tex](x_1,y_1) = (-1,4) \text{ and } (x_2,y_2) = (1,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 4}{1 - (-1)}\\\\m = \frac{-2 - 4}{1 + 1}\\\\m = \frac{-6}{2}\\\\m = -3\\\\[/tex]
The slope is -3, which tells us that the answer must be choice D.
Choices A,B, & C can be eliminated because choices A and B have a slope of -13, while choice C has a slope of 3.
Refer to the point-slope format [tex]y-y_1 = m(x - x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point the line goes through.
hhhhhhhhhhhhhhhhhhhhhhh
Answers
Answer:
i think its D.
Step-by-step explanation:
i just counted
What is the quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1)? 2 x superscript 4 baseline minus 3 x cubed minus eleven-halves 2x2 x – 3 – startfraction 6 over x squared minus 2 x 1 endfraction 2x2 – x 2x2 x – 3
Answers
The answer choice which represents the quotient of the polynomials given is; 2x² +x -3.
What is the quotient of the polynomial division?According to the task content, the quotient of the polynomial division; (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is required;
Hence, it follows from long division of polynomials that the required quotient is; 2x² +x -3.
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Answer:
D: 2x² +x -3
Step-by-step explanation:
I am a number I am not an odd number I am higher than 90 I am not higher than 100 If you subtract me from 100, you get nothing. what number am I?
(will mark brainliest)
Answers
Answer:
100
100 is not an odd number, its higher than 90 but not 100
and 100-100=0
Step-by-step explanation:
Hope it helps
Sin(15) × cos(15) × cos(30)
Answers
Answer:
0.2165 to the nearest ten thousandth.
Step-by-step explanation:
Sin(15) × cos(15) × cos(30)
= 0.258819 * 0.965926 * 0.866025
= 0.216506
NEED HELP PLEASE ANSWER ASAP!
Answers
Answer:
(2) Graph 2
Step-by-step explanation:
Question 40
| 2x + 3 | > 7It means the absolute value has to be greater than 7At x = -5 and x = 2, the absolute value is 7So, the numbers between them won't be includedThe points have an open dotx < -5 and x > 2(2) Graph 2A cylindrical can has a volume of, 1250 cubic centimetres. What is the height of the can if its radius is 8 centimetres? Round your answer to the nearest tenth.
Answers
A cylinder is a three-dimensional structure formed by two parallel circular bases connected. The height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.
Given the volume of the cylinder is 1250 cm³, and the radius of the cylinder is 8 cm. Therefore, the volume of the cylinder can be written as,
[tex]\text{Volume of the cylinder} = \pi r^2h[/tex]
[tex]1250 = \pi \times (8)^2 \times h\\\\h = 6.217\rm\ cm[/tex]
Hence, the height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.
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Using f(x) = 4x + 6 with a domain of {-1, 0, 2), find the range.
A. {10, 6, 15)
B. {2, 14)
C. {-4, 0, 8}
D. {2, 6, 14}
Answers
Answer:
D
Step-by-step explanation:
Start by plugging in all the domain values (domain means input) into the function.
f(-1) = 4(-1) + 6 =-4+6=2
f(0) = 4(0) +6=0+6= 6
f(2) = 4(2) +6 = 8+6=14
Josie is trying to select a green block out of a bucket that has 4 green blocks and 8 other colors. max is rolling a die and is trying to get a 1 or a 2. who has a better chance of getting their desired result?
Answers
Answer: Max. Max has a 49% chance of getting a 1 or 2 when Josie only has a 33% chance of getting a green block
............................................................................
The hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The measure of the other leg of the triangle is 5.1961 units.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Let the length of the other leg can be represented by x.
Given the hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Therefore, the measure of the other legs can be written as,
Hypotenuse² = 3² + x²
6² = 3² + x²
36 = 9 + x²
x² = 27
x = √27
x = 5.1961
Hence, the measure of the other leg of the triangle is 5.1961 units.
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PLEASE HELP ASAP!!!
(k12 students appreciated!!)
What are the zeros of the function?
ƒ(x)= x^3+x^2-6x
Answers
Answer: x = 0, x = -3, x = 2
Step-by-step explanation:
f(x) = x^3 + x^2 - 6x
f(x) = 0
x^3 + x^2 - 6x = 0
x(x^2 + x - 6) = 0
x = 0 or
x^2 + x - 6 = 0
D = b^2 - 4ac = 1 - 4*(-6) = 25
x = (-b - sqrt(D))/(2a) = (-1 - 5)/2 = -3 or
x = (-b + sqrt(D))/(2a) = (-1 + 5)/2 = 2
can someone help me with this thank you
10+5h = 25
thank you thank you thank you
Answers
Answer:
h=3
Step-by-step explanation:
Here's the explanation
Move 10 to the other side
5h=25-10
5h=15
h=15/5
h=3
10+5h=25
10+5h-10=25-10
5h=15
[tex]\frac{5h}{5}=\frac{15}{5}[/tex]
h=3
the answer is 3
whats the answer to this. In circle K with m \angle JKL= 144m∠JKL=144 and JK=6JK=6 units, find the length of arc JL. Round to the nearest hundredth.
Answers
The length of arc JL is 24.46 units see attachment for diagram.
What is an arc?An arc is a part of the circumference of a circle that meets two radii of a circle to form a sector.
Analysis:
From bigger triangle, if we bisect 144, the line meets JL at 90°.
To find AL,
sin 72 = AL/6
AL = 6 sin 72 = 5.71
To find the angle at O
∠O = 2∠K ( twice angle at circumference is equal to angle at center)
∠O = 2 (144) = 288°
For smaller right-angled triangle,
sin 144 = AL/OL
sin 144 = 5.71/OL
OL = radius of circle = 5.71/0.587 = 9.73 unit
length of arc JL = ∅/360 x 2πr
= 144/360 x 2 x 3.142 x 9.73 = 24.46 units
In conclusion, the length of arc JL is 24.46 units
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Mrs. thomas wants to put a table in the corner of a room. she considers the measurements of these tables. table 1 length: 1.5 feet width: 2.4 feet diagonal: 3.0 feet table 2 length: 3.2 feet width: 2.8 feet diagonal: 4.0 feet table 3 length: 2.4 feet width: 3.2 feet diagonal: 4.0 feet table 4 length: 2.6 feet width: 1.8 feet diagonal: 3.0 feet the walls forming the corner meet at a 90º angle. which table will fit snugly in the corner? table 1 table 2 table 3 table 4
Answers
Table 3 will fit snugly in the corner of the room.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
From the given data we will check the value of the diagonal by applying the Pythagorean theorem.
So by using the Pythagorean theorem:-
D ² = L² + W²
D² = ( 2.4 )² + ( 3.2 )²
D² = ( 5.76 + 10.24 ) = 16
D = √16 = 4 feet
Therefore table 3 will fit snugly in the corner of the room.
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Answer:
Table 3.
Step-by-step explanation:
Person above is correct, I'm takin the test!!
Find uv.
v
u
640
10
w
write your answer as an integer or as a decimal rounded to the nearest tenth.
uv =
Answers
The value of uv to the nearest tenth or as an integer is 3.1 units
How to find side of a right triangle?uv is the adjacent side of the right triangle.
uv can be found using trigonometric ratios as follows:
Therefore,
tan 63 = opposite / adjacent
Hence,
tan 63 = 6 / adjacent
cross multiply
uv tan 63 = 6
divide both sides by tan 63
uv = 6 / tan 63
uv = 6 / 1.96261050551
uv = 3.05716906145
uv = 3.1 units
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If cos is x=0.25, find sin x
A) sin x ≈ 0.97
B) sin x ≈ 0.75
C) sin x ≈ 0.0625
D) sin x ≈ 0.03
Answers
Answer:
In quadrant I, the answer is A. sin(x) ≈ 0.97
A number is given three successive discounts of 20%, 25% and 20%; Three successive increases of 20%, 25% and 20% are made to the resulting number, resulting in a number that differs from the original by 408 units. Calculate the original number.
Answers
Answer:
3000
Step-by-step explanation:
The multiplier associated with each percentage change (p) is (1 +p). We can use this fact to relate the original number to the modified number.
__
discounted numberLet x represent the original number. Then the discounted number is ...
x(1 -20%)(1 -25%)(1 -20%) = x(0.8)(0.75)(0.8) = 0.48x
increased numberAfter those discounts, the increased number is ...
(0.48x)(1 +20%)(1 +25%)(1 +20%) = (0.48x)(1.2)(1.25)(1.2) = 0.864x
differenceThe difference from the original is ...
x - 0.864x = 408
0.136x = 408 . . . . simplify
x = 3000 . . . . . . . divide by the coefficient of x
The original number was 3000.
Marcus states that the polynomial expression 3x3 – 4x2y y3 2 is in standard form. ariel states that it should be y3 – 4x2y 3x3 2. explain which student is correct and why.
Answers
The correct student is Marcus because the power of the polynomial decreases till 0
How to determine the correct student?The polynomial expressions are given as:
Marcus: 3x³ - 4x²y + y³ + 2
Ariel: y³ - 4x²y + 3x³ + 2
The standard form of a polynomial with the variable x is:
P(x) = ax³ + bx² + cx + d
This means that the power of the polynomial decreases till it gets to 0
Using the above form as a guide, the correct student is Marcus.
Marcus is correct because the power of the polynomial decreases till it gets to 0
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GIRL NO!!!! IM FAILING CAN SOMEONE HELP ME ASAP ON THIS SCREEN SHOT
Answers
Answer:
d = 306 m
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (10, 20) and (x₂, y₂ ) = (280, 164) ← house and beach coordinates
d = [tex]\sqrt{(280-10)^2+(164-20)^2}[/tex]
= [tex]\sqrt{270^2+144^2}[/tex]
= [tex]\sqrt{72900+20736}[/tex]
= [tex]\sqrt{93636}[/tex]
= 306 m
Answer:
The distance from Francesca's house to the beach is 306 meters.
Step-by-step explanation:
Use the Pythagorean Theorem to find the straight-line distance from Francesca's house to the beach.
Step 1 Find the length of the horizontal leg.
The length of the horizontal leg is the absolute value of the difference between the x- coordinates of the points (280,20) and (10,20).
|280 - 10| = 270
The length of the horizontal leg is 270 meters
Step 2 Find the length of the vertical leg.
The length of the vertical leg is the absolute value of the difference between the y- coordinates of the points (280,164) and (280,20)
|164 - 20| = 144
The length of the vertical leg is 144 meters.
Step 3 Let a = 270 and b = 144. Let c represent the length of the hypotenuse. Use the Pythagorean Theorem to find c.
a² + b² = c²
270² + 144² = c² Substitute into the formula.
72900 + 20736 = c² Simplify.
93636 = c² Add.
√93636 = c Take the square root of both sides.
306 = c Simplify.
The distance from Francesca's house to the beach is 306 meters.
The first number in a pattern is 208. The pattern follows the rule subtract 18. What are the next three numbers? (3 points)
a
195, 183, 172
b
190, 183, 176
c
190, 181, 172
d
190, 172, 154
Answers
Answer:
d) 190,172,154
Step-by-step explanation:
208-18=190
190-18=172
172-18=154
PLEASE HELP MI AMOR ILL LOVE YOU FORVER I SWEAR
Answers
Answer:
x = 8
z = 65
Step-by-step explanation:
Through various rules, we are able to assert: (6x + 67)° = 115°.
Now, we want to solve for x:
6x + 67 = 115
6x = 48
x = 8
We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.
What is the expansion of the series sum from n equals 1 to 4 of 2 to the n plus 1 power question mark
2 + 4 + 6 + 8
2 + 4 + 8 + 16
4 + 6 + 8 + 10
4 + 8 + 16 + 32
Answers
The expansion of the series is 2 + 6 + 8 + 10
How to determine the expansion?The summation expression is given as:
[tex]\sum\limits^4_{n=1} 2(n + 1)[/tex]
When n = 1, we have:
2(n + 1) = 2(1 + 1) = 4
When n = 2, we have:
2(n + 1) = 2(2 + 1) = 6
When n = 3, we have:
2(n + 1) = 2(3 + 1) = 8
When n = 4, we have:
2(n + 1) = 2(4 + 1) = 10
So, we have:
[tex]\sum\limits^4_{n=1} 2(n + 1) = 2 + 6 + 8 + 10[/tex]
Hence, the expansion of the series is 2 + 6 + 8 + 10
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Answer:
The correct option is actually d. 4 + 8 + 16 + 32
Step-by-step explanation:
Which expression can you use that is equivalent to 5x - 2 ( 15 - x )
Answers
Answer:
7x - 30
Step-by-step explanation:
5x -2(15-x)
Distribute -2 to the parenthesis
= 5x -30 +2x
Combine like terms
7x-30
Find the surface area of the square pyramid.
A) 35 ft^2
B) 30 ft^2
C) 45 ft^2
D) 20 ft^2
Answers
Area of base
side²5²25ft²Area of one triangle side
1/2(2)(5)=5ft²Area of 4 sides
5(4)=20ft²TSA
20+25=45ft²
Answer:
C) 45 ft²
Step-by-step explanation:
Formulae
Area of a square = x² (where x is the side length)
Area of a triangle = 1/2 × base × height
The surface area of a square pyramid comprises:
square base4 congruent triangles⇒ area of square base = 5² = 25 ft²
⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²
⇒ Total surface area = area of square base + 4 triangular areas
= 25 + 4(5)
= 25 + 20
= 45 ft²
Pls answer this asap
Answers
Answer:
9.5 feet
Step-by-step explanation:
Area of square garden = side length²
⇒ 90 = l²
⇒ l = √90
⇒ l = 3√10
⇒ l = 9.5 feet (nearest tenth)
The length of one side lies between the whole numbers 9 and 10.
Answer:
9 and 10
side length = 9.5 ft (nearest tenth)
Step-by-step explanation:
Area of a square = s² (where s is the side length)
Therefore, if the square garden measures 90 ft², the length of one side will be √90.
To find the two whole numbers that √90 lies between, find the perfect square either side of 90.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...
Therefore, 90 lies between 81 and 100:
⇒ 81 < 90 < 100
Square root the numbers:
⇒ √81 < √90 < √100
⇒ 9 < √90 < 10
Therefore, the length of one side of Grandma's garden is between 9 and 10.
To estimate √90 to the nearest tenth, find the difference between the three numbers:
[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]
As 90 is almost in the middle of 81 and 100,
⇒ √90 = 9.5 (nearest tenth)
According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.
Last question!!! please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answers
6.7 meters
[tex]\bold{SOLUTION:}[/tex]
======================================================
Explanation:
Draw out a right triangle as you see below.
Let's use the pythagorean theorem to find 'a'
[tex]a^2 + b^2 = c^2\\\\a = \sqrt{c^2 - b^2}\\\\a = \sqrt{(9.9)^2 - (7.3)^2}\\\\a = \sqrt{44.72}\\\\a \approx 6.6873\\\\a \approx 6.7\\\\[/tex]
Okay so, i need help with this. It’s really important and I need to finish this paper before school tomorrow. Please help i will mark brainliest!!!!!
Answers
Answer:
5x^2 - 4x - 3 = 0
Step-by-step explanation:
For the equation
ax^2 + bx + c = 0
the roots are [-b +/- √(b^2 - 4ac)] / 2a
So comparing the terms to the values in the question:
a = 5
b = -4
c = -3
