Answer:
-2gf
Step-by-step explanation:
What is the period of the function given?
pls
Answer:
2. ☑ A [tex]\displaystyle f(x) = tan\:\frac{1}{2}x[/tex]
☐ B [tex]\displaystyle f(x) = tan\:2x[/tex]
☐ C x = [tex]\displaystyle 2tan\:x[/tex]
1. ☐ A [tex]\displaystyle \frac{\pi}{2}[/tex]
☐ B [tex]\displaystyle \pi[/tex]
☑ C [tex]\displaystyle 2\pi[/tex]
Explanation:
[tex]\displaystyle \boxed{f(x) = -cot\:(\frac{1}{2}x - \frac{\pi}{2})} \\ \\ y = Acot(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A[/tex]
OR
[tex]\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A[/tex]
Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS the tangent graph, if you plan on writing your equation as a function of cotangent, 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 [tex]\displaystyle y = cot\:\frac{1}{2}x,[/tex] in which you need to replase "tangent" with "cotangent", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the tangent 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 cotangent graph [photograph on the right] is shifted [tex]\displaystyle \pi\:units[/tex] to the left, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \pi\:units,[/tex] which means the C-term will be positive, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pi} = \frac{\frac{\pi}{2}}{\frac{1}{2}},[/tex] but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is [tex]\displaystyle y = -cot\:(\frac{1}{2}x - \frac{\pi}{2}).[/tex] Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are [tex]\displaystyle -\pi = x\:and\:\pi = x.[/tex] From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{2\pi} = \pi + \pi.[/tex] So, the period of this function is [tex]\displaystyle 2\pi.[/tex] Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = 0.[/tex]
Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.
I am delighted to assist you at any time.
Lisa uses 2 pieces of copper wire, each 9 feet long, for
each robot she builds. If she started with a 500-yard roll
of copper wire, which of the following represents the
number of yards of wire left on the roll after Lisa built r
robots? (3 feet = 1 yard)
Answer:
500 - 6r = t
Step-by-step explanation:
500 represents the amount of copper wire Lisa started with.
-6r represents how much copper wire (in yards) is used on the robot (9*2 / 3 = 6).
t represents the total wire left after Lisa builds r robots.
Simplify: (4x2 - 9x + 11)(x - 6)
A. 4x3 - 33x2 + 65x + 66
B. 4x3 - 33x2 + 65x - 66
C. 4x3 + 15x2 - 43x + 66
D. 4x3 - 15x2 - 43x - 66
Answer:
It's option B. 4x^3 - 33x^2 + 65x - 66
See the attached image for my work:
The expression 2-3i/4+2i
is equivalent to
Answer:
[tex] \frac{2 - 3i}{4 + 2i} = \frac{1 - 8i}{10} [/tex]
Step-by-step explanation:
To simplify an expression like this, we multiply top and ottom of the fraction (denominator and numerator) by the complex conjugate of the bottom (numerator). For a complex expression (a+bi), the complex conjugate is (a−bi). When we do the calculation, it will become clear why this works so well.
Note that (a−bi)/(a−bi) is just the same as 1, so when we do this multiplication the result is the same number we started with.
[tex] \frac{2 - 3i}{4 + 2i} = \frac{2 - 3i}{4 + 2i} \times \frac{4 - 2i}{4 - 2i } \\ = \frac{8 - 12i - 4i + 6 {i}^{2} }{16 + 8i - 8i - 4 {i}^{2} } \\ = \frac{8 - 16i + 6 {i}^{2} }{16 - 4 {i}^{2} } [/tex]
But
[tex] i = \sqrt{ - 1} \: so \: {i}^{2} = - 1 [/tex]
Using this and collecting like terms, we have:
[tex]\frac{8 - 16i + (6 \times - 1) }{16 - 4 ( - 1) } = \frac{2 - 16i}{20} = \frac{1 - 8i}{10} [/tex]
what is the shaded region known as
The shaded region of a circle formed by one line as shown in the image is called a segment.
Answer: segment
simplify the expression
{x1/15}to the power of 5
simplify the expression below
(x 1/15) 5
Using the law of indices we multiply the power outside the parenthesis with the power inside the parenthesis.
Therefore,
1/15 x 5 = 5/15 = 1/3
After multiplying the power, we reduce the fraction to it lowest term. By doing so we get the fraction power of 1/3.
our final expression will be like
(xA 1/15) A 5 multiply the power
(xA 5/15) reduce the fraction power to it lowest term
(1/x3)
I neeed helppp please due today
Step-by-step explanation:
y=x+6.......(1)
y=-3X-6....(2)
from eq (1), we get,
x=y-6....(3)
sub eq (3) in eq (2), we get
y= -3(y-6)-6
y= -3y+18-6
y+3y-12=0
4y=12
y=3
sub value of y in eq (3)
x=3-6
x=-3
Answer: (3, 3)
Step-by-step explanation:
There are three general ways of solving a system of equations:
EliminationSubstitutionGraphingWhen solving systems of equations with graphing, look for points that overlap with each other or cross, and that will be the solution for the system. There might be one, two, or more than two solutions.
Please refer to the attachment below for the graph of the two equations.
Red line: y = x + 6Blue line: y = -3x - 6Hope this helps!! :)
Please let me know if you have any questions
What is the square root of 1 to the second power
Answer:
1
Step-by-step explanation:
The second power and square root cancel each other (second power means squared by the way)
Patrick has a bag of sugar that contains 5 kg. He uses 3 kg of sugar to make a cake. How 65
much sugar does Patrick have left?
Answer:
2 kg
Step-by-step explanation:
5 - 3 = 2
Hey there!
First, read the the problem again and look for any clues. "Have left" is a phrase that would be used for subtraction. So, 5 kg - 3kg = 2 kg.
Patrick has 2 kilograms of sugar left.
Hope this helps!
Have a great day!
Which of the following is an example of dramatic irony in this scene?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Bottom tries to take over the play, but can’t get his cue right as Pyramus.
(Choice B)
B
Puck plays a trick on Bottom but ends up scaring the other actors.
(Choice C)
C
The other actors think Bottom is smarter than he actually is.
(Choice D)
D
Bottom doesn’t realize that Puck has given him an as’s head.
How does this dramatic irony impact the reader?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
It helps increase the reader’s sympathy for the other actors.
(Choice B)
B
It shows that Puck is a fan of theatrical performances.
(Choice C)
C
It explains the moral of the story, which is that bragging is wrong.
(Choice D)
D
It adds humor to Bottom’s next lines, after the others run away.
Divide. Write your answer as a fraction in simplest form.
−10 2/7÷(−4 4/11)= HELP PLS
Answer:
[tex] = \frac{33}{14} [/tex]
Step-by-step explanation:
[tex] - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )[/tex]
➡️ [tex] - \frac{72}{7} \div - ( \frac{48}{11} )[/tex]
➡️ [tex] \frac{72}{7} \times \frac{11}{48} [/tex]
➡️ [tex] \frac{3}{7} \times \frac{11}{2} [/tex]
➡️ [tex] \frac{33}{14} [/tex] ✅
help asap please, forgot how to do math :)
Answer:
x = 8
Step-by-step explanation:
A common pythagorean triplet is 7, 8, 9
Answer:
11.4
Step-by-step explanation:
Pythagorean theorem
[tex]7^{2}[/tex] + [tex]9^{2}[/tex] = [tex]x^{2}[/tex]
49 + 81 = [tex]x^{2}[/tex]
130 = [tex]x^{2}[/tex]
11.4 = x
Is -1 1/6 rational? HURRY
Answer:
yes
Step-by-step explanation:
since it can be expressed as a fraction, it is rational
Write 8/11 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answer:
0.72 repeat
Step-by-step explanation:
__
8 ÷ 11 =0.72
What is the equation of the line graphed below?
5
(2, 1)
O A. y=-2x
B. y -
C. y = 2x
o D. y = 1/2 x
Answer:
C. Y=2x
Step-by-step explanation:
I hope this help you
8x-2y+5z=-5
5x+2y-3z=7
Answer:
167
812
Step-by-step explanation:
I think it's correct and helping you get a great day:)
Identify next three numbers in this sequence: 3, 12, 6, 24, 18, …
options :
27, 13.5, 22.5
72, 36, 144
72, 66, 264
27, 21, 30
The factorization of x² + x + xy + y + zx + z is
Answer:
[tex] {x}^{2} + x + xy + y + zx + z \\ = x(x + 1 + y + y + z) + z \\ = x(x + 2y + z + 1) + z[/tex]
Jack paid 13.75 euros to buy 3 slices of pizza and 4 hot dogs. Sarah paid 9.75 euros to buy 2 slices of pizza and 3 hot dogs. What was the price of a slice of pizza?
Step-by-step explanation:
steps are in the picture above.
Note:if you need to ask any question please let me know.
1. y is inversely proportional to x. Given that x = 5 when y = 3.
a) show y=15/x
b) find y when x=45.
Answer:
a)
Step-by-step explanation:
Y=k/x........(1)
Put y and x in (1) to get:
3=k/5
K=15
Now put k=15 in (1):
Y=15/x
b)
Y=k/x as x=45
Y=15/45
Y=1/3
Simplify this expression:
4(1 – 3x) + 7x – 8
Step-by-step explanation:
4(1-3x)+7x-8
4-12x+7x-8
-12x+7x+4-8
-5x-4
7. Which of the following statements is not
true?
a. The square root of 112 is between 10 & 11.
b. The square root of 180 is between 13 & 14.
The square root of 12 is between 4 & 5.
d. The square root of 5 is between 2 & 3.
Answer:
c
Step-by-step explanation:
it is because in (a) the square root of 112. is 10.58 which is in between 10 and 11
(B) the square root of 180 is 13.42 which is between 13&14
(c) the square root of 12 is 3.46 which is not between 4&5
Answer:
C the square root of 12 is between 4&5.
Step-by-step explanation:
Which data set does the line plot represent? *
(IMAGE BELOW)
A) 0, 2, 2, 3, 3, 4, 6, 9, 9, 9, 10, 10
B) 0, 2, 3, 3, 3, 3, 4, 9, 9, 10, 10 , 10
C) 0, 2, 3, 3, 3, 4, 6, 9, 9, 10, 10, 10
D) 0, 2, 3, 3, 4, 4, 5, 6, 9, 9, 10, 10
list the following integers in descending order: -14, 0, -8, 3, -5, -3, 7
How did you determine the greatest value; and, how did you determine the least value?
Answer:
7, 3, 0, -3, -5, -8, -14
Step-by-step explanation:
I know 7 is the greatest value you add the most because to get to 7 from 0.
I know -14 is the least value because I subtracted the most to get to -14 from 0.
Find the 14th term of the geometric sequence 2, 4, 8, ...2,4,8,...
Answer:
14th term is 16,384
Step-by-step explanation:
I. When [tex]a_{n} = a_{1}(r^{n-1} )[/tex]
If n = 14, a = 2 and r = 2
[tex]a_{14} = 2(2^{14-1} )[/tex]
= 2([tex]2^{13}[/tex])
[tex]a_{14}[/tex] = 16,384
help asap show work and no links pls
Answer:
f(1) = 2 f(3) = 8 f(t) = 2^t
Step-by-step explanation:
you just plug in the number in the parenthesis next to f to x in the equation 2^x
An unknown metal having a mass of 287.8 g was added to a graduated cylinder that contained
31.47 mL of water. After the addition of the metal, the water level rose to 58.85 mL. Determine
the volume of the metal. Calculate the density of the metal using dimensional analysis.
The metal displaced a volume of
58.85 mL - 31.47 mL = 27.38 mL = 27.38 cm³
of water, which is to say the metal has this volume.
If the metal has a mass of 287.8 g, then its density is its mass per unit volume,
(287.8 g)/(27.38 cm³) ≈ 10.51 g/cm³
How many million bacteria were in the dish at 9 a.mt
Answer:it depends what was on it but i would say about 500
Step-by-step explanation:
write the statement factor theorem
Answer:
According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0. ... Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This proves the converse of the theorem.
PLEASE HELP! find the inverse matrix
Answer:
see explanation
Step-by-step explanation:
The inverse of a matrix A = [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] is
[tex]A^{-1}[/tex] = [tex]\frac{1}{ad-bc}[/tex] [tex]\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]
If ad - bc = 0 then the matrix has no inverse
A = [tex]\left[\begin{array}{ccc}11&-5\\3&-1\\\end{array}\right][/tex]
ad - bc = (11 × - 1) - (- 5 × 3) = - 11 - (- 15) = - 11 + 15 = 4 , then
[tex]A^{-1}[/tex] = [tex]\frac{1}{4}[/tex] [tex]\left[\begin{array}{ccc}-1&3\\-5&11\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-0.25&0.75\\-1.25&2.75\\\end{array}\right][/tex]
Answer:
Step-by-step explanation:
[tex]A=\begin{bmatrix}11&-5\\3&-1\end{bmatrix}\\det(A)=11*(-1)-3*(-5)=-11+15=4\\minor=\begin{bmatrix}-1&3\\-5&11\end{bmatrix}\\cofactor=\begin{bmatrix}-1&-3\\5&11\end{bmatrix}\\Transposed\ cofactor=\begin{bmatrix}-1&5\\-3&11\end{bmatrix}\\A^{-1}=\dfrac{Transposed\ cofactorx}{det(A)} =\begin{bmatrix}\dfrac{-1}{4} &\dfrac{5}{4} \\\\ \dfrac{-3}{4} &\dfrac{11}{4}\end{bmatrix}\\[/tex]
[tex]Proof:\\A*A^{-1}=\begin{bmatrix}11&-5\\\\3&-1\end{bmatrix}*\begin{bmatrix}\dfrac{-1}{4} &\dfrac{5}{4}\\\\ \dfrac{-3}{4}&\dfrac{11}{4}\end{bmatrix}\\\\\\=\begin{bmatrix}\dfrac{-11+15}{4} &\dfrac{55-55}{4}\\\\ \dfrac{-3+3}{4}&\dfrac{15-11}{4}\end{bmatrix}\\\\\\=\begin{bmatrix}1&0\\\\ 0&1\end{bmatrix}\\[/tex]
Bonus: method of Gauss 's pivot jointed