The equation of motion for a weight suspended from a particular spring is given by p(t)=2sint3+5cost3p(t)=2sint3+5cost3, where p(t)p(t) is the displacement from the equilibrium position in centimeters, and tt is the time elapsed in seconds. at what time does the weight first reach the equilibrium position?
Final answer:
To find the time at which the weight first reaches the equilibrium position, set the equation of motion equal to zero and solve for t.
Explanation:
The equation of motion for the weight suspended from the spring is given by p(t) = 2sin(t/3) + 5cos(t/3), where p(t) is the displacement from the equilibrium position in centimeters and t is the time elapsed in seconds. The weight first reaches the equilibrium position when the displacement p(t) equals zero. To find the time at which this occurs, we set the equation equal to zero and solve for t.
2sin(t/3) + 5cos(t/3) = 0
Using trigonometric identities, we can rewrite the equation as:
2sin(t/3) = -5cos(t/3)
Dividing both sides by cos(t/3), we get:
2tan(t/3) = -5
Therefore, to find the time at which the weight first reaches the equilibrium position, we need to solve the equation 2tan(t/3) = -5 for t.
what is 37% of 600? what are the steps.
If the following fraction is reduced, what will be the exponent on the p? -5p^5q^4/ 8p^2q^2
A. 5
B.4
C.3
D.2
Answer: D. 2
Step-by-step explanation:
How do you solve 18-n divded by 2 (which is underneath the 18-n) is less than or equal to 6?
The compound probability of two events, E and F 1/8 , is ; the probability of E is 1/2 and of F is 1/3 . In two or more complete sentences, explain why E and F are not independent.
Event E and event F are not independent because:
[tex]P(E\bigcap F)\neq P(E)\times P(F)[/tex]
Step-by-step explanation:We know that two event A and event B are said to be independent if:
P(A∩B)=P(A)×P(B)
Here we have two events as E and F such that:
[tex]P(E\bigcap F)=\dfrac{1}{8}[/tex]
[tex]P(E)=\dfrac{1}{2}[/tex]
and [tex]P(F)=\dfrac{1}{3}[/tex]
This means that:
[tex]P(E)\times P(F)=\dfrac{1}{2}\times \dfrac{1}{3}\\\\\\i.e.\\\\\\P(E)\times P(F)=\dfrac{1}{6}\neq P(E\bigcap F)[/tex]
Hence, the events E and F are not independent.
How much time does it take light to travel from the moon to the earth, a distance of 384,000km?
When would it be useful to sort data in descending order? why?
graph -3/4 passing through (1,4)
32% of 300 is what number? A.96 B.64 C.32 D.90
32% = 0.32
300 * 0.32 =96
Answer is A
You invest 5000 in an account at 5.5% per year simple intrest how much will you have in the account at the beginning of the 6th year
starting at home, luis traveled uphill to the hardware store for 30 minutes st just 8mph. he then traveled back home along the same path downhill at a speed of 24 mph. what is his average speed for the entire trip from home to the hardware store and back?
Melvin has game and education apps on his tablet. He noticed that he has 3 game apps for every 2 education apps. Which of the following is another way to write this ratio?
A pencil and a ruler cost 2.50 together. The ruler costs $1.00 more than the pencil. How much is the pencil
Help!
Write 0.78% as a decimal and as a fraction
A) 78; 39/500
B) 0.078; 39/50,000
C) 0.0078; 39/5,000
D) 0.78; 39/50
What is the future value of a $1,500 investment, earning 10 percent interest
per period, after two periods? (Round your answer to the nearest cent.)
convert to polar form y=3x^2
The polar form for the given expression is sin(θ)=3r−3rsin²(θ)
To convert the equation y = 3x² into polar form, we substitute[tex]\( x = r\cos(\theta) \) and \( y = r\sin(\theta) \)[/tex], where R is the radius and theta is the angle.
[tex]So, \( y = 3x^2 \) becomes:\[ r\sin(\theta) = 3(r\cos(\theta))^2 \][/tex]
Now, we can simplify this equation:
[tex]\[ r\sin(\theta) = 3r^2\cos^2(\theta) \]\[ r\sin(\theta) = 3r^2\cos^2(\theta) \]\[ \frac{r\sin(\theta)}{r^2} = 3\cos^2(\theta) \]\[ \frac{\sin(\theta)}{r} = 3\cos^2(\theta) \]\[ \frac{\sin(\theta)}{r} = 3(1 - \sin^2(\theta)) \]\[ \frac{\sin(\theta)}{r} = 3 - 3\sin^2(\theta) \]\[ \sin(\theta) = 3r - 3r\sin^2(\theta) \][/tex]
This equation describes the curve in polar coordinates.
Suppose you value a special watch at $100. you purchase it for $75. on your way home from class one day, you lose the watch. the store is still selling the same watch, but the price has risen to $85. assume that losing the watch has not altered how you value it. what should you do?
If f(x) = x - 5, then match each of the following.
1. f(-1) -3
2. f(0) -6
3. f(1) -5
4. f(2) 0
5. f(5) 3
6. f(8) -4
Math Mean Help Please!
Rounding to the nearest tenth, what is the mean of 100, 75, 40, 90, 80, 100, 92, 88, 80, 84, 100.
Pressure (in pounds per square foot) on a diver at a depth of "d" feet: "P" = 64d + 2112
Solve for "d"
Bethany wants to estimate the value of (4.296 x 10^11) x (1.8614 x 10^-14). Which statement about the estimate is true?
A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.
B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.
C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.
D. The number will be less than 1 because when adding the exponents,
11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.
A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?
Final answer:
There are 2600 different possible student IDs when a student ID consists of one letter followed by two digits that can repeat, calculated as 26 possible letters multiplied by 10 possible digits for each of the two digit positions.
Explanation:
The question asks how many different student IDs are possible if an ID consists of a letter followed by two digits, with the digits being allowed to repeat. To calculate the possible combinations, we multiply the number of options for each component of the ID. There are 26 letters in the alphabet and 10 possible digits (0-9) for each of the two positions that follow the letter, allowing for repetition.
The calculation is therefore 26 letters × 10 digits × 10 digits = 2600 possible combinations. Each component is independent of the others, so this follows the fundamental principle of counting in combinatorics.
what is the greatest whole number that rounds to 54,300
A list of elements from which the sample may be drawn is called a
Quadrilateral ABCD is similar to quadrilateral EFGH the length of the three longest side in quadrilateral ABCD are 24 feet 16 feet and 12 feet long if the two shortest sides of quadrilateral EFGH feet long and 18 feet long how long is the fourth side on quadrilateral ABCD ?
When all sides of a quadrilateral are transformed, the resulting quadrilateral will be similar to the transformed quadrilateral. The fourth side of ABCD is 6 feet
We have the lengths of ABCD in descending order to be:
[tex]Side\ 1 = 24[/tex]
[tex]Side\ 2 = 16[/tex]
[tex]Side\ 3 = 12[/tex]
We have the lengths of EFGH in ascending order to be:
[tex]Side\ 4 = 9[/tex]
[tex]Side\ 3 = 18[/tex]
The missing side of ABCD is the fourth side, and it can be solved using the following equivalent ratios:
Side 4 : Side 3 of ABCD = Side 4: Side 3 of EFGH
Substitute the values of the known sides
[tex]Side\ 4 : 12 = 9 : 18[/tex]
Express as fraction
[tex]\frac{Side\ 4 }{ 12} = \frac{9}{ 18}[/tex]
Multiply both sides by 12
[tex]Side\ 4 = \frac{9}{ 18} \times 12[/tex]
[tex]Side\ 4 = \frac{1}{2} \times 12[/tex]
[tex]Side\ 4 = 6[/tex]
Hence, the fourth side of ABCD is 6 feet
Read more about similar quadrilaterals at:
https://brainly.com/question/85384
a dime is flipped 3 times. What is the probability that TAILS occurred all 3 times?
The hypergeometric distribution is used when samples are taken from an infinite population with replacement.
The hypergeometric distribution describes the probability of a certain number of successes in samples taken without replacement from a finite population, not an infinite one as stated in the question.
The hypergeometric distribution is a statistical model used to calculate probabilities in experiments where samples are drawn without replacement from a finite population. Unlike the statement presented in the question, the hypergeometric distribution is not used for infinite populations nor for sampling with replacement; that would be the domain of the binomial distribution.
500 is 10 times as much as
what is the distance between (-5,5) and (2,6) rounding to the nearest hundred
at the beginning of the summer, Conan had $180 in the bank. Each week he deposits another $64 that he earns mowing lawns. Is his account balance proportional to the number of weeks since he started mowing lawns?
Answer:
no, because the initial 180 gets in the way
Step-by-step explanation: