Explanation:
The general template of a sine function is
y = Asin(B(x-C))+D
The value of B is the only thing that determines the period T. We ignore every other term.
It turns out that T = 2pi/B which can be solved to B = 2pi/T
Plug in the given period of T = 8pi and compute to get
B = 2pi/T
B = (2pi)/(8pi)
B = 2/8
B = 1/4
This means that the term out front of the x is 1/4 and the equation must be [tex]y = \sin\left(\frac{1}{4}x\right)[/tex] which matches with answer choice B.
If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
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35 devide 28 with decimals pls help I need help
Answer:
1.25
Step-by-step explanation:
28 * 1 = 28. 35 - 28 = 7.
Add a decimal after the 1 in your answer and after the 35 in your problem. Add a zero to make your 7 into 70.
28 * 2 = 56. 70 - 56 = 14
Add a zero to make your 14 into 140.
28 * 5 = 140
Daisy had 2 3/4
bags of mulch to put in her yard. Each bag will cover 235.5 ft2
. How much square feet will she be able to cover is she uses all of the bags of mulch?
help me plsssssss
Answer:
mmmmmmm
Step-by-step explanation:
n
Daisy will cover a total area of 647.625 square feet, if she uses all of the bags of mulch.
The amount of mulch is given as:
[tex]Bag = 2\frac 34[/tex]
The area covered by each bag is given as:
[tex]Area = 235.5ft^2[/tex]
If she uses all bags, the total area covered by the bags is:
[tex]Total = Bag \times Area[/tex]
So, we have:
[tex]Total = 2\frac 34 \times 235.5ft^2[/tex]
Rewrite the fraction as an improper fraction
[tex]Total = \frac {11}4 \times 235.5ft^2[/tex]
This gives
[tex]Total = \frac {2590.5}4 ft^2[/tex]
[tex]Total = 647.625 ft^2[/tex]
Hence, she will be able to cover a total area of 647.625 square feet
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The sum of 7/8 of a number and 20 is 34 at minimum
Answer:
7/8x ≥ 14
Step-by-step explanation:
(sum means addition in case you forgot)
You would start by writing 7/8x + 20 ≥ 34
You would then subtract 20 from both sides to isolate the variable x.
You would then have 7/8x ≥ 14
Answer ?? It’s multiplicity
HELP ME PLEASEEEEEE I WILL GIVE BRAINLIEST
Answer:
DE, EW, WD
Step-by-step explanation:
From shortest line to longest line this would be the correct order.
Which is NOT true?
16 + 3 = 11 + 8
16 = 16
16 - 4 = 7 + 6
16 = 19 - 3
Answer:
16 - 4 = 7 + 6
Step-by-step explanation:
16 - 4 = 12
7 + 6 = 13
PLS ANSWER 30 POINTSSS
Answer:
letter B po
Step-by-step explanation:
basta letter B may ganyan din kame eh
The value of the digit 2 in 425.3 is *
Answer:
20 which is twenty
Step-by-step explanation:
searched it up on chrome
What location on the line would you find the constant of proportionality?
Answer:
2.4
Step-by-step explanation:
The constant of proportionality is y=kx which should 2.4
Determine the area of the yellow sector
Answer:
146 is the answer im positive
Can the sum of two palindromic numbers be another palindromic number?
Answer:
Every positive integer can be written as the sum of three palindromes, numbers that remain the same when their digits are reverse. For example, 389 = 11 + 55 + 323. This holds not just for base 10 but for any base b ≥ 5.
From 175 yards away, a marksman hit 14/50 of the targets last year.
Find the perimeter and area of this polygon.
Answer:
perimeter=114
AREA= 308
Step-by-step explanation:
A^2 + B^2=C^2
then A+B=+C= P for triangle
52= triangle perimeter
rectangle:
(l+w)*2=p for rectangle=62
then add 52+62= 114
AREA- Triangle
b*h/2
22*10=220
220/2
= 110
AREA- Rectangle
l*w=A
22*9=198
ADD BOTH AREAS
198+110=308
HOPE IT HELPS
A rectangular pool is 6 meters wide and 8 meters long. If you swim diagonally across the pool, how many meters would you be swimming?
If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.
Given the following data:
Width of rectangle = 6 metersLength of rectangle = 8 metersTo determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.
Note: The diagonal side of the rectangular pool represents the hypotenuse.
Mathematically, Pythagorean's theorem is given by the formula:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
Substituting the given parameters into the formula, we have;
[tex]Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}[/tex]
Hypotenuse = 10 meters.
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I have a Statistics question
Answer:
we're your question
Step-by-step explanation:
again please
Answer:
Yes
Step-by-step explanation:
what is it
Of 92 adults selected randomly from one town, 61 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Group of answer choices 0.582 < p < 0.744 0.548 < p < 0.778 0.536 < p < 0.790 0.566 < p < 0.760
A 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
The formula for calculating the confidence interval is expressed as;
[tex]CI=p \pm z \cdot\sqrt{\frac{P(1-p)}{n} }[/tex]
p is the proportion = 61/92 = 0.66n is the sample size = 92z is the z-score at 90% = 1.645Substitute the given parameters into the formula to have:
[tex]CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(1-0.66)}{92} }\\CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(0.34)}{92} }\\CI =0.66\pm 1.645(0.0495)\\CI=0.66 \pm 0.0814\\CI = (0.582, 0.744)[/tex]
Hence a 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
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Emma has nickels and five dollar bills in her pocket. The number of nickels is Five less than three times the number of five. Let f represent the number of dollar bills. Write an expression of the number of nickels.
Answer:
since the number of nickels is 10 so the expression is5+5
The number of nickels is 10 so the expression is n = 3f - 5
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that Emma has nickels and five dollar bills in her pocket. The number of nickels is Five less than three times the number of five.
Consider that f represent the number of dollar bills.
The expression "The number of nickels is" is equivalent to "n =";
Also, "three times the number of five dollar bills" is equivalent to "3*f"
"eight less than three times the number of five dollar bills" is equivalent to "3*f - 5"
Then the expression is n = 3f - 5
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If you live 1.5 miles from school and you walk at a rate of 3mph, when should you leave home in order to arrive at school by 9:00?
Work Shown:
time = distance/speed
time = (1.5 miles)/(3 mph)
time = (1.5/3) hours
time = 0.5 hours
time = 30 minutes
It takes 30 minutes to walk to school, so you should leave a half hour before 9:00. Subtracting 30 minutes from 9:00 gets you to 8:30. If anything, you should start a little bit before 8:30 just in case something might slow you down for one reason or another.
Solve the following inequality 17 less than or equal to negative 3X +2 less than or equal to 26.. what is the answer
Answer:
-5 less than or equal to x less than or equal to -8
Step-by-step explanation:
You have to isolate x.
Start with removing +2.
Take 2 away from both sides
15 less than or equal to -3x less than or equal to 24
Then, the only thing you have to isolate after that is -3, you have to remove it from x.
Since -3x is multiplying, you have to divide by -3 on the other sides.
15 divided by -3 is -5
24 divided by -3 is -8
Therefore,
The answer is...
-5 less than or equal to x less than or equal to -8
Which is the equivalent of 0.00000000989 in proper scientific notation?
Answer:
9.89×10^-9
Step-by-step explanation:
0.000 000 009 89 = 9.89×10^-9
__
We have introduced spaces in the number to make the digits easier to count. (Some technical publications will write the number with thin spaces for just that reason.) The most-significant digit is in the 9th place to the right of the decimal point, so has a place value of 10^-9.
13. This shows a part of a multiplication table. Find the missing numbers. Explain how you found the numbers.
35 40
42 ?
? ?
The missing numbers in the multiplication table are 49, 48 and 56 respectively
Given:
35
42
?
35 = 7 × 5
42 = 7 × 6
? = 7 × 7 = 49
40
?
?
40 = 8 × 5
? = 8 × 6 = 48
? = 8 × 7 = 56
Multiplication table is a mathematical table showing the products of each of integers such as 7 and 5, 1 and 10, 13 and 12 etcTherefore, the missing numbers in the multiplication table are 49, 48 and 56 respectively
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Cuál sería el interés producido durante tres años, por un capital de s/30 000, al 5%
Answer:
2%
Step-by-step explanation:
Answer: la respuesta a tu pregunta es 2%
que tengas un gran día / noche!
How do I figure this out
Answer:
D
Step-by-step explanation:
yeah-ya....................... right?
Answer:
D
Step-by-step explanation:
hope it help correct me if wrong
in Emma's supply box a pencil weighs 3ounces.her scissors weigh 3 ounces more than the pencil and a bottle of glue weigh three times as the scissors how much those the bottle of the glue weigh in pounds and ounces.
Answer:
18 Ounces which is equal to 1 pound and 2 ounces
Step-by-step explanation:
pencil weighs 3 ounces
scissors weighs =pencil+3 ounces =6 ounces
bottle of glue=3*scissors which is equal to 18 Ounces simple 16 ounces = 1 pound
Thanks
A line passes through the point (-2, -6) and has a slope of
2
No
Write an equation in slope-intercept form for this line.
In developing an interval estimate of the population mean, if the population standard deviation is unknown _____.
Answer:
the sample standard deviation and t distribution can be used
Step-by-step explanation:
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, 1) and point (4, 2) rounded to the nearest tenth?
Answer:
√(4 - ( - 3))^2 + (2 - 1)^2
√(4 + 3)^2 + (2 - 1)^2
√49 + 1
√50
7.07 = 7.1 units
PLEASE HELP IF YOU ANSWER BOTH I WILL GIVE
1. BRAINLIEST
2. 5 STARS
3. HEARTS
Answer:
both of your answers are b
Step-by-step explanation:
20. difference means subtract
21. assosiative property has to deal with three numbers while communitive is 2 numbers
graph { (2/3) (2,4) (-3/4)}
Answer 56
Step-by-step explanation:
