This is what the questions/answers say for #16-19 or last picture if you can't read it, please answer all questions
16. The number of hours of sunlight in a particular location S(t) can be modeled by the function S of t equals 12 plus 2 times the sine of the quantity 2 times pi over 365 times t end quantity comma where t is the number of days after January 1st. (That is, t = 0 means January 1st.) After how many days will there be 12 hours of sunlight for the first time during the year?
365 over 4 days
365 over 2 days
1095 over 4 days
1095 over 2 days
17. A student was asked to prove the trigonometric identity tangent of one half times x plus cotangent of one half times x equals 2 times cosecant x period Which of the following could be the first step in proving the identity?
the quantity 1 minus cosine x end quantity over sine x plus sin x over the quantity 1 minus cosine x end quantity equals 2 times cosecant x
sine x over the quantity 1 plus cosine x end quantity plus the quantity 1 plus cosine x end quantity over sine x equals 2 times cosecant x
the quantity 1 minus cosine x end quantity over sine x plus the quantity 1 minus cosine x end quantity over sine x equals 2 times cosecant x
I only
II only
I and II only
I, II, and III
18. Based on the graph of the trigonometric functions f (θ) = 4sin θ + 1 and g (θ) = cos 2θ, at what value(s) on the interval [0, 2π) does f (θ) = g (θ)?
0, π
pi over 2 comma 5 times pi over 2
5 times pi over 4 comma 7 times pi over 4
pi over 4 comma 3 times pi over 4 comma 5 times pi over 4 comma 7 times pi over 4
19. Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b = 2?
Answers
Problem 9 (#16)
In order to figure out when the amount of sunlight becomes 12 hours for the first time, we need to have [tex]S(t)=12[/tex] and solve the function for [tex]t[/tex]:
[tex]\displaystyle S(t)=12+2\sin\biggr(\frac{2\pi}{365}t\biggr)\\\\12=12+2\sin\biggr(\frac{2\pi}{365}t\biggr)\\\\0=2\sin\biggr(\frac{2\pi}{365}t\biggr)\\ \\0=\sin\biggr(\frac{2\pi}{365}t\biggr)\\\\\pi=\frac{2\pi}{365}t\\\\365\pi=2\pi t\\\\\frac{365}{2}=t[/tex]
Thus, B is the correct answer
Problem 10 (#17)
Recall the half-angle identity [tex]\displaystyle \tan\frac{x}{2}=\frac{1-\cos x}{\sin x}=\frac{\sin x}{1+\cos x}[/tex]Hence, [tex]\displaystyle \cot\frac{1}{2}x=\frac{1}{\tan\frac{1}{2}x }=\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}[/tex]So, you could techincally say that the first two options work as each function has their respective identities true for each option.
Thus, I and II is the correct answer
Problem 11 (#18)
[tex]f(\theta)=g(\theta)\\\\4\sin\theta+1=\cos2\theta\\\\4\sin\theta+1=1-2\sin^2x\\\\2\sin^2\theta+4\sin\theta=0\\\\2\sin\theta\bigr(\sin\theta+2)=0[/tex]
[tex]\displaystyle 2\sin\theta=0\\\\\sin\theta=0\\\\\theta=\{0,\pi\}[/tex]
[tex]\sin\theta+2=0\\\\\sin\theta=-2[/tex]
The solution is indeterminate since -2 does not fall in the range of [tex][-1,1][/tex].
Thus, A is the correct answer
Problem 12 (#19)
Recall that the period of a tangent function [tex]y=a\tan(bx-c)+d[/tex] is [tex]\frac{\pi}{|b|}[/tex]. Hence, if [tex]b=2[/tex], then the period of the tangent function is [tex]\frac{\pi}{2}[/tex]. Since I can't see the graphs, you need to identify which graph has a period of [tex]\frac{\pi}{2}[/tex] (meaning the distance between two vertical asymptotes is pi/2), or post this problem again with the graphs.
Related Questions
F(x) = x+2-3 choose correct transformation
Answers
Hope this helps
ANSWER THE FOLLOWING:
Answers
Answer:
1. (a) 1/12
(b)35/36
(c) 31/36
2. Blue - 1/3
Red- 4/15
Find the (LCD) 5/6 and 11/8
Answers
Answer:
24
Step-by-step explanation:
First we write the first few multiples of 6 (the first denominator) :
6,12,18,24,30
Now we write the first few multiples of 8 (the second denominator) :
8,16,24,32,40
As we can see 24 is the lowest number that appears in both list.
Therefore it is the LCD of 5/6 and 11/8
Coach Morrison used the graph below to track the total miles the girl’s and boy’s track teams ran each day for a week.
Answers
If the area of the following parallelogram is 30 square centimeters, what is the length of the base?
25 cm
5 cm
6 cm
150 cm
Answers
Answer: 6 cm
Step-by-step explanation:
The formula for the area of a parallelogram is
hb=a
Where
b is the base
h is the height (5 for this)
and a is the area (30 for this)
Let's sub these values into our equation
[tex]5b=30[/tex]
Divide both sides by 5 to isolate b
[tex]5b=30\\\frac{5b}{5} =\frac{30}{5} \\b=6[/tex]
The base is 6cm long.
Answer:
Base = 6 cm
Step-by-step explanation:
Given:
[tex]\text{Area of parallelogram} \text{ = 30 cm}^{2}[/tex]
[tex]\text{Height of parallelogram = 5 cm}[/tex]
Formula:
[tex]\text{Area of parallelogram} = \text{Base} \times \text{Height}[/tex]
Substitute the height and the area of the parallelogram:
[tex]:\implies 30 \ \text{cm}^{2} = \text{Base} \times 5[/tex]
Divide both sides by 5:
[tex]:\implies \dfrac{30}{5} = \dfrac{\text{Base} \times 5}{5}[/tex]
Simplify both sides:
[tex]:\implies 6 \ \text{cm} = \text{Base}[/tex]
Help help help math math
Answers
Answer:
48
Step-by-step explanation:
just multiply 16 x 3 and you will your answer
Answer:
48 Oz.
please make this answer brainliest If I helped you!
Step-by-step explanation:
1lb = 16 Oz.
3lb = 48 Oz.
16x1=16
16×3=48
2/3 of the pizza was left over from last night. Then, Marcy ate another 2/9 of it. Which of the following statements is true?
A.Very little of the pizza is left.
B.About half of the pizza is left.
C.Most of the pizza is left.
Answers
Answer:
B.About half of the pizza is left.
Step-by-step explanation:
When we solve:
2/3 of the pizza was left over from last night. Then, Marcy ate another 2/9 of it.
We get 4/9.
The length of a rectangle is 3 feet longer than its width.
If the perimeter of the rectangle is 54 feet, find its length and width.
Answers
Answer:
Length = 15ft
Width = 12ft
Step-by-step explanation:
First, re-read the problem until you acknowledge it and can put it into your own words.
This is what I did:
Find the area of a rectangle by first finding the length and the width. Note that:
L = Length
W = Width
Find L and W
We will need formula:
P=2L+2W
A=LW
The length of a rectangle is 3 ft longer than its width :
L = 3 + W Equation [1]
"the perimeter of the rectangle is 30 ft" means
P = 54 Equation [2]
P = 54 = 2L + 2W
54 = 2(3+W) + 2W
54 = 6 + 2W + 2W
54 = 6 + 4W
48 + 4w
12 ft = w
L = 3 + W
L = 3 + 12
L = 15 ft
Area if needed
A = L*W
A = (12 ft)*(15 ft)
A = 180 sq ft
Kavinsky
5-6y^2=113 solve by square roots
Answers
Answer:
[tex]y=\frac{\sqrt{113}-5 }{-6}[/tex]
Step-by-step explanation:
[tex](5-6y)^2=113[/tex]
[tex]\sqrt{(5-6y)^2} =\sqrt{113}[/tex]
[tex]5-6y=\sqrt{113}[/tex]
[tex]-6y=\sqrt{113} -5[/tex]
[tex]y=\frac{\sqrt{113}-5 }{-6}[/tex]
I hope this helps!
Hi can someone help me pls
Answers
Answer:
f(x) = 45x + 5
Step-by-step explanation:
The parking fee for a minibus at an event is $5 entering the parking lot. There is an extra charge of $45 per passenger.
The formula that simulates the parking fee for this sentence is
f(x) = 45x + 5
This is because 45x represents the charge per passenger and we are using addition because the $5 minibus parking fee; to enter the parking lot - increases the total cost of the parking fee.
Car A uses regular gasoline at $1.21 a gallon and gets 19 miles per gallon (mpg) in town. Assume that
you drive 100 miles a week, or 400 miles a month. What is your gas bill each month?
Answers
Answer:
Step-by-step explanation:
Remark
If you drive 400 miles a month, and you get 19 miles per gallon, then you will need
gallons = miles / miles per gallon
Givens
m = 400
mpg = 19
Cost per gallon = 1.21
Solution
gallons = 400 / 19 = 21.05
You need to buy 21.05 gallons
1 gallon costs 1.21
21.05 gallons cost x Cross multiply
x = 1.21 * 21.05
Answer: x = 25.47 Cost for 1 month's fuel.
Write an equation to represent the following statement. jjj divided by 999 is 555. Solve for jjj. j=j=j, equals
Answers
Answer:
j ÷ 9 = 5
Step-by-step explanation:
If the statement says, j divided by 9 is 5, it is obvious you are dividing in this situation.
So the equation is, j ÷ 9 = 5
The next part says solve for j.
This part is pretty easy; all you have to do is do the opposite operation and multiply 9 by 5.
So, j = 45
[tex] \tt(6x4−2x3 +7x2 −x) + ( 7x4+ 2x3−5x + 7)[/tex]
[tex] \\ [/tex]
With Solution!!
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:\tt(6x {}^{4} −2x {}^{3} +7x {}^{2} −x) + ( 7x {}^{4} + 2x {}^{3} −5x + 7)[/tex]
[tex]\qquad \tt \dashrightarrow \:\tt6x {}^{4} −2x {}^{3} +7x {}^{2} −x + 7x {}^{4} + 2x {}^{3} −5x + 7[/tex]
Now, move all like terms aside :
[tex]\qquad \tt \dashrightarrow \:6 {x}^{4} + 7 {}x^{4} - 2 {x}^{3} + 2 {x}^{3} + 7 {x}^{2} - x - 5x + 7[/tex]
Add the like terms ~
[tex]\qquad \tt \dashrightarrow \:13 {}x^{4} + 7 {x}^{2} + 6x + 7[/tex]
Answer:
13(x)⁴ + 7(x)²-6(x) + 7
Explanation:
[tex]\hookrightarrow \sf (6x^4 -2x^3+7x^2-x)+(7x^4+2x^3-5x+7)[/tex]
remove the parenthesis
[tex]\sf \hookrightarrow 6x^4-2x^3+7x^2-x+7x^4+2x^3-5x+7[/tex]
group the variables
[tex]\hookrightarrow \sf 6x^4+7x^4-2x^3+2x^3+7x^2-x-5x+7[/tex]
add similar terms
[tex]\sf \hookrightarrow 13x^4+7x^2-x-5x+7[/tex]
simplify
[tex]\hookrightarrow \sf 13x^4+7x^2-6x+7[/tex]
If 8 pounds of ground beef cost $10.32, how much would 12 pounds cost?
Answers
Answer:
$15.48 for 12 lbs
Step-by-step explanation:
Check photo for work
The 12 pounds of ground beef cost is $15.48.
What is unitary method ?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
According to the question
8 pounds of ground beef cost $10.32
i.e 8 pounds of ground beef = $10.32
1 pounds of ground beef = [tex]\frac{10.32}{8}[/tex]
1 pounds of ground beef = $1.29
Therefore,
12 pounds of ground beef = 1.29*12
12 pounds of ground beef = $15.48
Hence, 12 pounds of ground beef is of $15.48.
To know more about unitary method here :
https://brainly.com/question/24406804
# SPJ2
There is a bag containing 7 red marbles, 2 blue marbles, 8 green marble and 12 yellow marbles. Rodolfo Ronaldo will choose 3 marbles without replacement. How many possible outcomes does this experiment have?
Answers
Answer:
22707
Step-by-step explanation:
What is the slope of
the line?
Give your answer as
a fraction in simplest
form.
Answers
Answer:
3/4
Step-by-step explanation:
The answer is 3/4, because we rise 3 and run 4 the formula is always rise over run, and thats why its 3/4
Hoped this helped!!
-15 divided by -1 2/3
Answers
Answer:
9
Step-by-step explanation:
15 / 5/3 = 15 x 3/5=9
Because a negative numebr divided by a negative number is always positive.
Answer:
9
Step-by-step explanation:
What is the value of 5 in 50.14
Answers
Answer:
5 is in hundreds place, 0 is in the tens place, 1 is in the tenths place and 4 is in the hundreths place.
Step-by-step explanation:
which is more likely to have a mass close to 3 kilograms small feather a five year old cat or a grown elephant or a peach. dont delete this question dbs at brainly (dbs = drag on balls)
Answers
Answer:
5 year old cat
Step-by-step explanation:
because a kg is about a pineapple
Algebra Find the value of x.
Answers
Answer:
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.y-step explanation:
Which expression represents that an unknown number x is no less than 6?
x < 6
x > 6
x ≤ 6
x ≥ 6
Answers
Answer:
x≥ 6
Step-by-step explanation:
hope this helps loves x please make me brainlest
Answer: your answer would be D. x ≥ 6
x is greater or equal to 6
Step-by-step explanation:
. Write an expression equivalent to 3w - 3w + 3w with just one term. - What property or properties applies?
Answers
Answer:
w(3-3+3)
Step-by-step explanation:
distibutitve property
Find the indicated measures, given that EA is a diameter
a) mDEF =
b) mEFG =
c) mAC=
d) Explain how you found each angle measure below. Be sure to show all of your work.
Answers
Using the knowledge of the measure of a semicircle, the measures in the circle given are:
a. m(DEF) = 152°
b. m(EFG) = 70°
c. m(CA) = 28°
What is the Measure of a Semicircle?Half of a circle is a semicircle = 180°.
Given the following:
m(CDE) = 152°m(FG) = 31°m(AG) = 110°m(DC) = m(EF) = 180 - 110 - 31 = 39° (semicircle)a. m(DEF) = [m(CDE) - m(DC)] + [m(EF)]
m(DEF) = (152 - 39) + 39
m(DEF) = 152°
b. m(EFG) = m(EF) + m(FG)
m(EFG) = 39 + 31 = 70°
c. m(CA) = 180 - 152 (semicircle)
m(CA) = 28°
Learn more about the measure of a semicircle on:
https://brainly.com/question/11983357
5
The length of each small square is
½inch.
What is the area of the rectangle?
A.
5 square inch
64
B.
5
16
square inch
C.
oo square inches
D. 2, square inches
Answers
Answer:5/16 sq inch
Step-by-step explanation:
muliply heigh by width
4/8 times 5/8
Train A travels 100 miles in 4 hours, Train B travels 196 miles in 7 hours, and Train C travels 375 miles in 15 hours. Which two trains are traveling at the same rate?
Answers
Answer:
Trains 1 and 2 are going the same speed :)
Step-by-step explanation:
We need to divide to solve :)
Train 1:
100/4 = 25
Train 2:
196/7 = 28
Train 3:
375/25 = 25
Trains 1 and 2 are going the same speed :)
Have an amazing day!!
Please rate and mark brainliest!!
6 Jenny is y2 years old and her daughter Allyson is y years old, If Jenny lives to the age of 13y,
Allyson will be y years old. How old is Allyson now? (Note: the difference in ages must
remain constant.)
Answers
Answer:
Allison is 7 years now, Jenny is 49 yeas now. Check. 13y = 13*7 = 91 will happen in 91-49 = 42 years. Jenny will be 7 + 42 = 49 years old at that time.
Step-by-step explanation:
The chart above shows the results of survey taken by a movie theater the theater asked what genre the movie goers preferred to see if the theater owner asked 100 people how many people would prefer drama? Round to the nearest whole number show your work
Answers
Answer:
The Cost of operating the theater if there are 100 people at a show is 20,000Rs.
Step-by-step explanation:
Theater is a place where the movies are shown in big screens and Speakers are used for the clear audio of the movie.
In a theater there will be 3 to 4 shows for a movie or different movie.
Theater can consist of 250 - 300 seats and can cost up to 250rs for a seat.
Consider a ticket cost of 200rs. For 100 people in a show ,
Cost = 200 × 100
Cost = 20,000.
Hence the cost of operating theater if there are 100 people at a show is 20,000Rs.
The Cost of operating the theater if there are 100 people at a show is 20,000Rs.
The theater is a place where the movies are shown on big screens and Speakers are used for the clear audio of the movie.
In a theater, there will be 3 to 4 shows for a movie or a different movie.
Theater can consist of 250 - 300 seats and can cost up to 250rs for a seat.
What is the meaning of cost?
The average cost of a college education has gone up dramatically.
Consider a ticket cost of 200rs.
For 100 people in a show,
Cost = 200 × 100
Cost = 20,000.
Hence the cost of operating a theater if there are 100 people at a show is 20,000Rs.
To learn more about the cost visit:
https://brainly.com/question/1153322
382.85 rounded to three significant figures
Answers
Answer:
382.85
Sig Figs
5
382.85
Decimals
2
382.85
Scientific Notation
3.8285 × 10^2
E-Notation
3.8285e+2
Words
three hundred eighty-two point eight five
Step-by-step explanation:
find the area of a circle whose radius is 14cm
Answers
Answer:
Formula for area of circle;
A = π[tex]r^{2}[/tex]
Where 'π' represents pi(3.14 or 22/7), and 'r' stands for the radius which is being squared.
What we know:
Radius = 14cmPlug in what we know;
A = π[tex]r^{2}[/tex]
(For pi I'll be using 3.14 instead of 22/7)
A = 3.14(14^2) ← (The symbol ' ^ ' means to the power of.)
A = 3.14(196)
A = 615.44, 615.44 centimetres is the area of this circle.
Answer:
≈[tex]615.44cm^2[/tex]
Step-by-step explanation:
So the equation for area of circle.
[tex]\pi r^2\\\pi 14^2[/tex]
So 14^2, or 14 x 14 is 196.
Now you can either keep it in terms of pi, 196pi, or times it by pi.
[tex]196*pi\\196*3.14\\615.44[/tex]
So the answer would be around 615.44cm^2
simplify 8+6x6/11 +7×2.
Answers
Answer:
Step-by-step explanation:
Answer:
[tex]\frac{44}{25}[/tex]
Step-by-step explanation:
1) Simplify 6 × 6 to 36.
[tex]\frac{8+36}{11+7*2}[/tex]
2) Simplify 8 + 36 to 44.
[tex]\frac{44}{11+7*2}[/tex]
3) Simplify 7 × 2 to 14.
[tex]\frac{44}{11+14}[/tex]
4) Simplify 11 + 14 to 25.
[tex]\frac{44}{25}[/tex]