Question 2(Multiple Choice Worth 2 points)
(06.06 MC)
At an amusement park, the pendulum ride's movement from its starting position in meters can be represented by the equation f of x is equal to negative 4 times the cosine of the quantity x over 8 end quantity plus 4 period If x represents time measured in seconds since the ride first began, at what times will the pendulum's movement be 8 meters from its starting position?
Answers
Solving the trigonometric equations, the times at which the pendulum's movement will be 8 meters from its starting position are of:
[tex]x = 8\pi + 16n\pi[/tex] seconds.
What is the equation for the pendulum's position?It is given by:
[tex]f(x) = -4\cos{\frac{x}{8}} + 4[/tex]
It is 8 meters from its starting position when f(x) = 8, hence:
[tex]f(x) = -4\cos{\frac{x}{8}} + 4[/tex]
[tex]8 = -4\cos{\frac{x}{8}} + 4[/tex]
[tex]4 = -4\cos{\frac{x}{8}}[/tex]
[tex]\cos{\frac{x}{8}} = -1[/tex]
We have that:
[tex]\cos{x} = -1 \rightarrow x = \pi + 2n\pi[/tex]
Hence:
[tex]\frac{x}{8} = \pi + 2n\pi[/tex]
[tex]x = 8\pi + 16n\pi[/tex] seconds.
More can be learned about trigonometric equations at https://brainly.com/question/24680641
Related Questions
PLEASE BE QUICK
Which point represents the fraction 3/6
A B C D
Answers
Answer:
C
Step-by-step explanation:
Answer: C
Out of 6 spaces on number line, C is the 3rd one
It takes 4 people 6 days to build a wall. How long would it take 6 people to build the same wall?
Answers
Answer:
1 day
Step-by-step explanation:
4=6
2=3
2*3=6
so 3/3=1
It would take 6 people to build the wall 1 day
It takes 4 days to build the same wall with 6 people based on the given ratio.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
It takes 4 people 6 days to build a wall.
The number of people days taken = 4 x 6 = 24 people takes
This means if one person wants to build them it takes 24 days.
For 6 people the time taken will be 24/6 = 4 days.
Hence "It takes 4 days to build the same wall with 6 people based on the given ratio".
For more information about ratios and proportions,
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NOPQ is a rhombus. Given ON=110 and OQ=176. find each measure
Answers
Answer:
I cannot see the attachment
Step-by-step explanation:
What quantity of parsley would you need to make a half recipe?
Answers
Answer:
7/16 of parsley
Step-by-step explanation:
Mr Wong spent $3750 on general expenses last month 20% of his general expenses
was electrioty charges. How much money did he pay for electricity charges laat
month?
Answers
Answer:
$750
Step-by-step explanation:
20% can also be written as 1/5 in fraction form (20/100)
3750 x 1/5 = 750
The distance around earth is 24,887 miles. How many kilometers is the distance around the earth.
Answers
Answer:
40051.744
Step-by-step explanation:
because im smart
[tex]1 \: mile = 1.60934 \: kilometers[/tex]
[tex]24887 \: miles = x \: kilometers[/tex]
[tex]x = 24887 \times 1.6934 [/tex]
[tex]x = 40 \: 051.65 \: kilometers[/tex]
Full question and options
Answers
Answer:
D
Step-by-step explanation:
A triangle is always determined by the names of its angles. If, for any reason, you wanted to label it by its side names(which I don't even think you can do but assuming you wanted to), you dont even have the names for all three sides here. So, it can only be d. A, X, and T are the three angle names for this triangle, so this is triangle ATX or AXT.
Answer:
ATX (option d)
Step-by-step explanation:
Sides of any polygon are called as vertices.
Vertices of the triangle or endpoints of the sides of the polygon are A, T and X.
Triangles can also be classified by their angles. In an acute triangle all three angles are acute.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS IF YOU DO THEN YOU GET REPORTED AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
BC=48
Step-by-step explanation:
BC=EF.
so x+37=4x+4
Move things over etc etc:
37=3x+4
33=3x
x=11
BC= x+37
If x=11 then BC= 11+37.
CAN SOMEBODY HELP ME
NO LINKS
Answers
Domain of this function is R or (-∞,∞)
Cuz this function of definable in each and every real number
Write down the corresponding side and angles from given congruent triangles.
Answers
Answer:
Hope the pictures will help you...........
10 brainlies!!!!! help with this question
Answers
Answer:
ok
Step-by-step explanation:
Write the following expression in terms of logs of x,y and z
Show steps
Answers
We can write the log expression in terms of the log of x, y, and z as expression 1/2(logx+2logy-8logz).
What is a logarithm?It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\\\log_ac = b[/tex]
We have an expression in logarithm:
[tex]=\rm log\sqrt{\frac{xy^2}{Z^8} }\\\\=log(\frac{xy^2}{Z^8})^{\frac{1}{2} }\\\\=\frac{1}{2}log(\frac{xy^2}{Z^8})[/tex] [tex](\rm loga^b = (b)log(a))[/tex]
[tex]\rm\frac{1}{2} (log(xy^2)-logz^8)[/tex] [tex](\rm log(\frac{a}{b} )= loga - logb)[/tex]
[tex]\rm\frac{1}{2} (log(x)+log(y^2)-logz^8)[/tex] [tex](\rm logab = loga+logb)[/tex]
[tex]\rm\frac{1}{2} (log(x)+2log(y)-8logz)[/tex]
Thus, we can write the log expression in terms of the log of x, y, and z as 1/2(logx+2logy-8logz).
Learn more about the Logarithm here:
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sorry for not putting the picture
Answers
Answer:
Answer bellow
Step-by-step explanation:
9cm⋅12cm=108cm²
17cm=108cm²
7cm=108cm²
9cm=108cm²
3cm=108cm²
Answer:
407
Step-by-step explanation:
9 x 17 = 153
9 x 16 = 135
(15 x 14) x 1/2 = 105
add em up...
153 + 135 + 105 = 407
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
I will mark brainlest
Answers
Answer:
option c
Step-by-step explanation:
-2,-1/4,1/4,0.5,4
I hope it helps you
What is the answer for -10+3--4+5?
Answers
Will give points please help
Answers
Answer:
Part A
Step-by-step explanation:
Did test for flvs, brainliest please ;)
The area of a rectangle is 27x2+27x-30 square feet. The length of the rectangle is 9x– 6 feet. What is the width of the rectangle?
Answers
Divide the polynomials to get the 3x + 5
Solve this for c: 2x + y = 10,
4x + 2y = c
Answers
4x + 2y = 20 so c = 20??
Dawn can paint of a wall in 1 hour. How
many walls can she paint in 2 hours?
Answers
Find the area of the highlighted cubes.
Answers
Answer:
15 cm
Step-by-step explanation:
area stands for amount of space in certain spot therefore the answer would be 15
BRAINLIST PLEASE!
In 2014, the average price of a new car was $37,600. For the period shown, new-car prices increased by approximately $1250 per year. If this trend continues, how many years after 2014 will the price of a new car average $46,350? In which year will this occur?
Answers
The year in which the average price of a new car would average $46,350 is 2021.
In which year would the price of a new car average $46,350?The price of a new car increases by $1250 per year. This is known as appreciation. The value of a new car can be represented with this equation:
Value of new car = value of the car now + (rate of increase x number of years)
Number of years = value of the new car - value of the car now) / rate of increase
(46350 - 37600) / 1250 = 7 years
7 + 2014 = 2021
To learn more about appreciation, please check: https://brainly.com/question/26847097
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Find the surface area of the cone in terms of π.
Answers
Answer:
161 × pi cm²
Step-by-step explanation:
we just had the question about the lateral surface area (which is the area of the "mantle" of the cone from the round bottom to the pointy top).
the whole surface area of a cone is then simply the lateral surface area plus the ground area, which is a circle.
so, we have
A = pi×r×sh + pi×r²
r = radius (remember, this is half of the diameter)
sh = slant height (the length of the "mantle" straight up from the ground to the top)
so, the surface area of our cone here is
A = pi×(14/2)×16 + pi×(14/2)² = pi×7×16 + pi×7² =
= 112×pi + 49×pi = 161 × pi cm²
The mean for the data in the dot plot is 5. What is the absolute deviation for the data point at 7?
Answers
Answer:
The answer is 2. Hope this helps!
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Find the surface area of the prism.
Answers
[tex]s \: a \: = (2 \times \frac{1}{2} \times 4 \times 6) + (3 \times 2 \times 5) \\ [/tex]
[tex]s \: a \: = 24 + 30[/tex]
[tex]s \: a \: = 54 \: \: {yd}^{2} [/tex]
is (x-4) a factor of f(x)=x^3-2x^2+5x+1 explain your reasoning
Answers
Answer:
No.
Step-by-step explanation:
It's simpler than you might expect.
If [tex](x - 4)[/tex] is a factor, then it means that it the function [tex]f(x) = x^3 - 2x^2 + 5x + 1[/tex] can have [tex](x - 4)[/tex] factorised out.
This means that we can say [tex](x - 4) = 0[/tex]
Therefore [tex]x = 4[/tex]
If we put [tex]x = 4[/tex] into the equation:
[tex]f(4) = (4)^3 - 2(4)^2 + 5(4) + 1\\= 64 - 32 + 20 + 1\\= 53[/tex]
We didn't get 0, therefore it isn't a factor!
which expression is equivalent to (x^9yz^4)^5
Answers
Applying the rule of exponent, the equivalent expression is: [tex]x^{45}y^{5}z^{20}[/tex]
What is the Rule of Exponents?One of the rules of exponents is given as, [tex](xy)^m=(x^m)(y^m)[/tex].
Therefore, given:
(x9yz4)5
To find the equivalent expression, apply the rule of exponents as shown below:
[tex](x^9yz^4)^5=(x^{9*5})(y^5)(z^{4*5})[/tex]
[tex](x^9yz^4)^5=x^{45}y^5z^{20}[/tex]
Therefore, applying the rule of exponent, the equivalent expression is:
[tex]x^{45}y^{5}z^{20}[/tex]
Learn more about the rule of exponents on:
https://brainly.com/question/847241
During a basketball game a player makes 12 of 18 free throws attempted. Write the ratio as a fraction reduced to lowest terms
Answers
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
12 out of 18 free throws is also equal to the fraction [tex]\frac{12}{18}[/tex]. To simplify this fraction, we have to find out the greatest common factor (GCF) of 12 and 18. It turns out that the GCF of 12 and 18 is 6. So, we have to divide the fraction by 6 to reduce it to its lowest terms.
[tex]\frac{12}{18} /\frac{6}{6} =\frac{2}{3}[/tex]
I hope this helps! Have a lovely day!! :)
The product of two rational numbers is 6.If one of them is 8,find the other number.
With steps also please.
Answers
Answer:
0.75
Step-by-step explanation:
The "product" is a result of multiplication, so we know we are multiplying eight with something to get six. 0.75 is a rational number, and when multiplied by eight, gives six.
So, 0.75 * 8 = 6
The other number is 0.75
{( - 1, 2), (0, 3), (1, 4)}
Which algebraic equation gives the correct rule for the table?
Answers
Answer:
The rule for the input-output table below is: add 1.5 to each input number to find its corresponding output number. Use this rule to find the corresponding output numbers. To find each output number, add 1.5 to each input number. Then, write that output number in the table.
Stacy performed an experiment in which she rolled a six-sided die multiple times. The results are shown below.
Based on the results above, predict the number of times a 3 would be rolled it Stacy performs the experiment a total of 480 times
A. 63
B. 102
C. 87
D 141
Answers
Answer:
5/9
Step-by-step explanation:
Let the probability of getting a multiple of 3 is "A"
Let the probability of getting an even number is "B"
Total number of outcomes=36
Total number of favourable outcomes of either a multiple of 3 or an even number are
(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)
That is we have 20 favourable outcomes
Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=
total number of outcomes
favourable outcomes
Therefore, after substituting the values we get
probability=\frac{20}{36}probability=
36
20
After simplification we will get
probability=\frac{5}{9}probability=
9
5
is answer letter D.141