Answer:
4. ☐ A [tex]\displaystyle \frac{1}{3}[/tex]
☐ B [tex]\displaystyle 2[/tex]
☑ C [tex]\displaystyle 3[/tex]
3. ☐ A [tex]\displaystyle \frac{\pi}{3}[/tex]
☐ B [tex]\displaystyle \pi[/tex]
☑ C [tex]\displaystyle 6\pi[/tex]
Step-by-step explanation:
[tex]\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}) \\ y = -2cos\:\frac{1}{3}x[/tex]
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1\frac{1}{2}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{1}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
The above information can help you interpret the graph much better. First off, JUST IN CASE you needed to know the trigonometric equation(s) of this graph, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, 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 = -2sin\:\frac{1}{3}x,[/tex] in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine 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 sine graph [photograph on the right] is shifted [tex]\displaystyle 1\frac{1}{2}\pi\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle 1\frac{1}{2}\pi\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-1\frac{1}{2}\pi} = \frac{-\frac{\pi}{2}}{\frac{1}{3}}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}).[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -2],[/tex] from there to [tex]\displaystyle [-6\pi, -2],[/tex] they are obviously [tex]\displaystyle 6\pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 6\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow. Now, in this case, you were probably wondering why the negative was inserted in front of the amplitude in the equation(s). Well, here is why:
[tex]\displaystyle y = sin\:x \\ y = cos\:x[/tex]
Knowing your parent functions, sine commenses upright from the origin, while cosine commenses one unit above the origin [tex]\displaystyle [0, 1].[/tex] This should tell you that inserting a negative in front of the amplitude will REFLECT each crest over the midline. Well, there you have it.
I am delighted to assist you at any time.
what is 200 rounded to the nearest ten
Answer:
200.
Step-by-step explanation:
-------- 200 -------
Hope that helps.
Change the following fraction to a decimal. 8 4/5 = ?
Answer:
The answer is 8.8
Step-by-step explanation:
4/5 x 20/20 = 80/100
80/100 = .8
Step-by-step explanation:
[tex]8 + \frac{4}{5} = \frac{40 + 4}{5} \\ = \frac{44}{5} = 8.8 \\ thank \: you[/tex]
Please give answer to the problem.
Evaluate the Expression (y+2)2 when y = -4
Answer:
4
Step-by-step explanation:
(y+2)^2
Let y = -4
(-4+2)^2
Parentheses first
(-2)^2
Exponents
4
Answer:
-4
Step-by-step explanation:
y = -4
Substituting y in the equation,
(-4+2)2
(-2)2 [Negative x Positive = Negative]
=> -4
Kay's mother's age is six more years than twice Kay's age. The sum of their ages
is 81. Find both of their ages.
Answer:
6x81=2
Step-by-step explanation:
Consider the two grading schemes above, with a homework average of 81 a class participation average of 57 a test average of 93 and a final exam grade of 87. If you calculate your grade with both teachers, what would the higher of the two grades be?
Select all solutions to the equation (2. — 4)(x + 5) = 0.
x = -1/2
x = 1/2
x = -2
x = 2
x = -5
x = 5
Answer:
At, x=-5
Step-by-step explanation:
(2-4)(x+5)=-2×0
Prove this
1-tan^2x/1+tan^2x=cos^2x-sin^2x
Answer:
see explanation
Step-by-step explanation:
Using the identity
tan x = [tex]\frac{sinx}{cosx}[/tex]
Consider the left side
[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]
= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ( multiply numerator and denominator by cos²x to clear fractions
= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex] ← ( cos²x + sin²x = 1 ]
= cos²x - sin²x
= right side , thus proven
Find the probability of “landing” in the shaded region of the figures below. Round your answer to the nearest hundredth.
3. Square with side length 40 ft
Answer:
Area of the square:
A = a² = 40² = 1600 ft²Area of the circle:
A = πr² = 3.14*(40/2)² = 1256 ft²Probability of landing in the shaded region:
P = 1256/1600 = 0.785 or 78.5%Answer:
78.5%
Step-by-step explanation:
We can find the area of both shapes then divide to find the probability.
Square area:
40 * 40 = 1600ft²
Circle area with diameter [ 1/4πd² ]:
1/4π(40)²
1/4π(1600)
0.785(1600)
1,256
Now divide both areas to find the probability.
1256/1600 = 0.785
0.785 * 100% = 78.5%
Best of Luck!
please help me I am stuck on this question
Answer:
(a) $3.00
(b)(i) $33.00
(b)(ii) $322.50
Step-by-step explanation:
(a)
100% = $20.00
1% = 100%/100 = 20/100 = $0.20
15% = 1%×15 = 0.2×15 = $3.00
so, he actually has to pay $20 + $3 = $23 per toaster.
or shorter and direct, since we calculate the extra 15% based on the original 100%, we can say he has to pay 115% of the basic price.
115% = 0.2×115 or = 100%×1.15 = 20×1.15
0.2 × 115 = $23
20 × 1.15 = $23
so, you can see the several ways to get to the result.
in any case, the profit is $26-$23 = $3 per toaster.
(b)(i)
100% new price = 100% old price + 20% = 120% old price
or 100% old price × 1.2
100% new price per toaster = 20×1.2 = $24.00
the new tax is increased TO 25% (not by 25%) be careful to see that detail.
so, we need to add 25% of the new price.
125% new price = 24×1.25 = $30.00
so, in order to make again $3 profit, the customer has to pay now $30+$3 = $33.00
(b)(ii)
100% (b)(i) selling price = $33.00
30% more means 130% of that, or 1.3×100%
33×1.3 = $42.90
so, the profit per toaster is now 42.90 - 30 = $12.90
when selling 25 of these toasters the profit is then
25×12.90 = $322.50
100 POINTS PLEASE HELP!!!!
Answer:
a. F=1.8c + 32
b. 71.6 degrees Fahrenheit
c. c=(F-32)/1.8
d. 28.3 degrees Celcius
Step-by-step explanation:
a. Given the two data points we can create an equation in slope-intercept form.
The y-intercept is 32
Slope can be found by doing 212-32/100-0 = 180/100 = 1.8
F=1.8c + 32
b. We can use this formula to solve for Fahrenheit
F=1.8(22)+32
F=71.6 degrees
c. Isolate c
F-32=1.8c
(F-32)/1.8=c
d. We can use this formula to solve for Celcius
(83-32)/1.8=c
c= 28.3333333 degrees
We can round that to 28.3 degrees Celcius
Answer:
a)F =1.8C +32
b) f(22) = 68 F
c) C = 5/9F -17 7/9
d) 28.3
slope= 5/9
B= -17 7/9
Step-by-step explanation:
x1 y1 x2 y2
0 32 100 212
(Y2-Y1) (212)-(32)= 180 ΔY 180
(X2-X1) (100)-(0)= 100 ΔX 100
slope= 1 4/5
B= 32
Y =1.8X +32
55 points. Please help fast. Fastest one (must be correct too) will get brainliest.
Answer:
Uhh I think some information is missing I am not sure tho
did i do it correctly if i didnt can u please answer it correctly and tell me how u did it
Answer:
You have done it wrong.
Step-by-step explanation:
4 3/7 - 5/7 = 3 5/7
We can change the equation to a improper fraction first.
4 3/7 = 4*7+3 = 31/7
31-5 = 26
Therefore the answer is 26/7.
simplify
The answer is equal to 26/7, or 21/7 + 5/7
Which is 3 5/7
Sorry but you did it wrong...
First you gonna make 4[tex]\frac{3}{7}[/tex] become 3[tex]\frac{10}{7}[/tex] ( 4 -> 3 [tex]\frac{7}{7}[/tex] - *you need to make it become the same denominator)
Lets do it: 3[tex]\frac{10}{7}[/tex] - [tex]\frac{5}{7}[/tex] = ...
Because in [tex]\frac{5}{7}[/tex] doesn't have a whole number so you will still keep 3
3[tex]\frac{10}{7}[/tex] - [tex]\frac{5}{7}[/tex] = 3.....
Next, you gonna subtract [tex]\frac{10}{7}[/tex] - [tex]\frac{5}{7}[/tex] = [tex]\frac{10-5}{7}[/tex] = [tex]\frac{5}{7}[/tex]
3[tex]\frac{10}{7}[/tex] - [tex]\frac{5}{7}[/tex] = 3[tex]\frac{5}{7}[/tex]
SO the answer for 4[tex]\frac{3}{7}[/tex] - [tex]\frac{5}{7}[/tex] is 3[tex]\frac{5}{7}[/tex]
Hope it helps, Studywell!
Marketing company said 259 emails on Monday 431 emails on Tuesday and some emails on Wednesday if the company sent about like 1300 emails over three days about how many emails did the company send on Wednesday
Answer:
610
Step-by-step explanation:
Given:
259 emails on Monday431 emails on Tuesday? emails on WednesdayTotal emails = 1300Add:
259 + 431 = 690
Subtract:
1300 - 690 = 610
So, on Wednesday 610 emails were sent out.
Hope this helped.
10. You bought a two magazine for $5 and some notepads for $3 each. You spent a total of $37. How many notepads did you buy? WILL NEED WORK WILL GIVE BRAINLIEST
Answer:
You bought 9 notepads.
Step-by-step explanation:
Buying two $5 magazines will cost $10. That means there's still $27 left to spend on notepads. If one notepad costs $3, then 27 / 3 = 9.
Answer:
9
Step-by-step explanation:
5x2=10
10+3x=37
3x=37
x=9
btw = notepads ur welcome!
Find the equation of the circle
(x + 2)2 + (y + 5)2 = 4
tve
when it is reflected about y = 2x + 1.
Answer:
2x+4+2y+10=4
2x+2y=4-10-4
2(x+y)=-10
x+y=-10/2
x+y=-5
x+2x+1=-5
3x=-6
x=-6/3
x=-2
A rectangle has a width of 3 units. The rectangle's length is 5 times its width.
What is the area of the rectangle?
Answer:
Answer= 45 units
Step-by-step explanation:
lengths = 3 units
width = 3x5= 15 units
area= length times width= 3x15= 45 units!
Hope this helps :)
find the domain of f/g.
Answer:
Al real numbers except 4/3
1. Which of the following is an example of like
terms?
a. - 16 and - 16x
b. x and x2
C, 50y and y
d. 20a and 2
X. X. X =
Rewrite expression with one exponent.
Answer: x^3
Step-by-step explanation:
Can someone plz help me it’s my last question plz (question 2)
Answer:45 ish
Step-by-step explanation:
What is the value of x in the equation 0.7x – 1.4 = -3.5?
O -7
Ο Ο Ο Ο
3
7
Find the volume of this object.
Use 3 for 1.
V=7r2h
Volume of a Cylinder
4 ft.
12 ft
Answer:
504 ft^3
Step-by-step explanation:
Ok, so we have the equation for the cylinder as well as the rectangular prism. Basically we're just going to find the volume of each of them separately and then add them together.
Let's start with the cylinder:
V(cylinder) = pi*r^2*h
pi = 3
d = 4ft
r = d/2 = 4/2 = 2ft
h = 12ft
V(cylinder) = (3)*(2^2)*(12)
V(cylinder) = 3*4*12
V(cylinder) = 144 ft^3
Now the rectangular prism:
V(rectangular prism) = l*w*h
l = 10ft
w = 6ft
h = 6ft
V(rectangular prism) = 10*6*6
V(rectangular prism) = 360 ft^3
Now we can add them together:
V(total) = 360 + 144
V(total) = 504 ft^3
Solve. 4x + 3 = 47
A x= 11 B x=40 C x=44 D x=50
Answer:
x=11
Step-by-step explanation:
a = 5, b = 4, and c = 2. so 2a= what
Step-by-step explanation:
2a = 10 because a = 5 and 2a means 2 × a which is the same as 2 × 5 and this equals 10.
hope this helps
oh my god help plssss ima rage
Answer:
d
Step-by-step explanation:
Farmer Lee wants to plant tomatoes and cucumbers together in rows. He has 54 tomato plants and 48 cucumber plants, and he wants each row to be the same.
What’s A= a+b divided by 2
Step-by-step explanation:
A=a+b/2
2×A=a+b
2A=a+b
2a-a=b
a=b
hope it helps
Answer:
A=2
and B=2
Step-by-step explanation:
If you add two plus two you get four, and divided by two you get 2.
URGENT ! HELP ME I WILL MARK BRAINLIEST !!
please faster !!!!
Step-by-step explanation:
230m...................
Answer: so the answer would actually b
Step-by-step explanation:
please please help me it's for my homework
Answer:
6/25
Step-by-step explanation:
.24 = 24/100 = 6/25
Answer:
6/25
Step-by-step explanation:
step 1 The decimal number = 0.24
step 2 Write it as a fraction
0.24/1
step 3 Multiply 100 to both numerator & denominator
(0.24 x 100)/(1 x 100) = 24/100
It can be written as 24% = 24/100 or 24/100
step 4 To simplify 24/100 to its lowest terms, find LCM (Least Common Multiple) for 24 & 100.
4 is the LCM for 24 & 100
step 5 divide numerator & denominator by 4
24/100 = (24 / 4) / (100 / 4)
= 6/25
6/25 is a simplest fraction for the decimal point number 0.24