Answers
Answer:
[tex]a=36\: \sf ms^{-2}[/tex]
Step-by-step explanation:
[tex]\textsf{Displacement}\:x=4t^3-27t+8[/tex]
[tex]\implies \textsf{Velocity}\:v=\dfrac{dx}{dt}=12t^2-27[/tex]
[tex]\implies \textsf{Acceleration}\:a=\dfrac{dv}{dt}=24t[/tex]
At the moment the direction of motion of P reverses, the velocity of P will be zero. Therefore, find the value of t when v = 0:
[tex]\implies v=0[/tex]
[tex]\implies 12t^2-27=0[/tex]
[tex]\implies t^2=\dfrac{27}{12}=\dfrac94[/tex]
[tex]\implies t=\pm\sqrt{\dfrac94}=\pm\dfrac32[/tex]
As time is positive, P reverses when t = 3/2 s
To find acceleration at this time, simply substitute the found value of t into the equation for acceleration:
[tex]\implies a=24(\frac32)[/tex]
[tex]\implies a=36\: \sf ms^{-2}[/tex]
Related Questions
A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = –2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, Alpha?
Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Fail to reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Fail to reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Answers
The answer is: Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Trina purchases 10 tickets from a charity raffle. Each ticket in the raffle has 6 different numbers between the numbers 1 and 20. If there is only one prize, what is the probability of Trina winning the prize? Express your solution as a fraction in reduced form.
Answers
The probability of winning when there is only one prize, is:
P = 1/2,790,720
How to find the probability?
Each ticket has 6 different numbers, in order, from 1 to 20.
The first number has 20 options.The second number has 19 options (because the numbers can't repeat).The third number has 18 options, and so on.The total number of possible combinations is given by the product between the numbers of options, so there are:
C = 20*19*18*17*16*15 = 27,907,200 possible tickets.
So, if Trina purchases 10 tickets, she has a probability of 10 out of 27,907,200 winning (when we assume that there is only one prize)
Then the probability is:
P = 10/27,907,200 = 1/2,790,720
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X + 4y = 7 4x - 3y = 9 equivalent equation and solution
Answers
Answer:
x = 3, y = 1
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}x+4y=7\\ 4x-3y=9\end{bmatrix}[/tex]
Solve:
[tex]\mathrm{Substitute\:}x=7-4y[/tex]
[tex]\begin{bmatrix}4\left(7-4y\right)-3y=9\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}28-19y=9\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x=7-4y[/tex]
[tex]\mathrm{Substitute\:}y=1[/tex]
[tex]x=7-4\cdot \:1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{The\:Answer\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=3,y=1[/tex]
Check Answer:
3 + 4(1)
7 (1) = 7
True
4(3) - 3(1)
12 - 3 = 9
True
Hence, x = 3 , y =1
~lenvy~
An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. What are the appropriate hypotheses?
H0: μ = 76.4 versus Ha: μ < 76.4, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ < 77.1, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ > 77.1, where μ = the true mean height of all trucks
Answers
The Hypotheses are; Null Hypothesis; H₀: μ = 76.4 and Alternative Hypothesis; Hₐ: μ > 76.4 where μ is the true mean height of all trucks.
How to Define Hypotheses?We are given;
Population Mean; μ = 76.4 inches
Sample Mean; x' = 77.1 inches
Sample standard deviation; s = 5.2 inches
Sample size; n = 100 trucks
Now we can thus define the hypotheses as;
Null Hypothesis; H₀: μ = 76.4
Alternative Hypothesis; Hₐ: μ > 76.4
where μ is the true mean height of all trucks
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|-9| + |12| = ?
Question options:
A -3
B 3
C -21
D 21
Answers
Answer:
21
Step-by-step explanation:
-9=9
9+12=21
3x+1=38 solve and check please
Answers
Hello!
The first step is to subtract 1 from both sides.
[tex]\bf{3x+1=38}[/tex]
[tex]\bf{3x=37}[/tex]
Now, divide both sides by 3:
[tex]\bf{\displaystyle\frac{37}{3} }[/tex]
Can this fraction be simplified? Nope.
Why? Because 37 and 3 do not have any common factors, except 1 (and what's the point of dividing by 1?)
Hence, the answer is
[tex]\huge\boxed{\text{Answer:{\boxed{\circ\star{\frac{37}{3} }}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepOnLearning
[tex]\boxed{An~Emotional~Helper!}[/tex]
6. Didi took out a loan of S12,600 to buy a car. After one month, an interest fee of 0.5% on this
loan is added to what she owes. After the fee is added, she then makes a payment of $200 to
start paying off her loan.
Given that the interest fee will increase what she owes while the payment will decrease what
she owes, how much money does Didi owe after one month
Answers
Answer:
$12,463
Step-by-step explanation:
The amount owed after one month is the sum of the original amount and the interest fee, less the amount paid.
__
The interest fee is 0.5% of $12,600, so is ...
0.005 × $12,600 = $63
After her $200 payment, the amount Didi owes is ...
$12,600 +63 -200 = $12,463 . . . owed after 1 month
What are the solution(s) for the quadratic equation?
f(x)=x^2+12x+36
Please show work!
Answers
Let's see
[tex]\\ \rm\rightarrowtail x^2+12x+36=0[/tex]
[tex]\\ \rm\rightarrowtail x^2+6x+6x+36=0[/tex]
[tex]\\ \rm\rightarrowtail x(x+6)+6(x+6)=0[/tex]
[tex]\\ \rm\rightarrowtail (x+6)(x+6)=0[/tex]
[tex]\\ \rm\rightarrowtail x=-6[/tex]
Please help thank you
Answers
Answer:
Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.
Step-by-step explanation:
So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:
m = 28.8 g
When Donetle stands at point R, he is 1000 feet from point S at the base of a cliff.
When he looks up at an angle of 20 degrees, he sees a friend at the top of the mountain cliff at point T. Which measurement is the closest to the height of the mountain cliff in feet?
342
364
940
2747
Answers
Answer:
Step-by-step explanation:
The value of measurement of the closest to the height of the mountain cliff in feet is,
⇒ Mountain Height = 360 feet
Given that;
When Donetle stands at point R, he is 1000 feet from point S at the base of a cliff.
And, When he looks up at an angle of 20 degrees, he sees a friend at the top of the mountain cliff at point T
Hence, By graph we get;
⇒ tan 20° = Mountain Height / 1000
⇒ 0.36 = Mountain Height / 1000
⇒ 0.36 × 1000 = Mountain Height
⇒ Mountain Height = 360 feet
Thus, The value of measurement of the closest to the height of the mountain cliff in feet is,
⇒ Mountain Height = 360 feet
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Which of the following shows the true solution to the logarithmic equation solved below? log Subscript 2 Baseline (x) = log Subscript 2 Baseline (x 7) = 3. Log Subscript 2 Baseline left-bracket x (x 7) right-bracket = 3. X (x 7) = 2 cubed. X squared 7 x minus 8 = 0. (x 8) (x 1) = 0. X = negative 8, 1 x = negative 8 x = 1 x = 1 and x = negative 8 x = 1 and x = 8.
Answers
The value which shows the true solution to the given logarithmic equation is 1.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The given logarithmic equation is,
[tex]\rm log_{2} (x) + log_{2} (x +7) = 3.[/tex]
Use the addition property of log in the above expression.
[tex]\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0[/tex]
Solve the quadratic equation we get,
[tex](x+8)(x-1)=0[/tex]
x = -8, 1
Here, the logarithmic function is defined only for positive real numbers as its input.
Thus, the value which shows the true solution to the logarithmic equation solved above is 1.
Learn more about the domain and range of the function:
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Answer:X=1
Step-by-step explanation:b on edge
The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
A. 14 sec
B. 15 sec
C. 16 sec
D. 17 sec
Answers
Solving the system of equations, it is found that a viable time that the trains are side by side is given by:
B. 15 sec
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y = 14t^2[/tex]
[tex]y = 130t + 1200[/tex]
They will be side by side when:
[tex]14t^2 = 130t + 1200[/tex]
[tex]14t^2 - 130t - 1200 = 0[/tex]
It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:
[tex]\Delta = (-130)^2 - 4(14)(-1200) = 84100[/tex]
[tex]x_1 = \frac{130 + \sqrt{84100}}{28} = 15[/tex]
[tex]x_2 = \frac{130 - \sqrt{84100}}{28} = -5.71[/tex]
Time is a non-negative measure, hence option B is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
Answer:
B: 15 sec
Step-by-step explanation:
I took the algebra exam
Can someone please please tell me what the general form for (x-6)^2+(y-3)^2=16 is. I would really appreciate the help!
Answers
Answer:
x² + y² - 12x - 6y + 29 = 0
Step-by-step explanation:
Simplifying the equation using (a + b)² = a² + 2ab + b²:
(x - 6)² + (y - 3)² = 16
⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16
⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16
⇒ x² - 12x + 36 + y² - 6y + 9 = 16
General form of a circle = x² + y² + Cx + Dy + E = 0
Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.
Subtract 16 both sides:
⇒ x² - 12x + 36 + y² - 6y + 9 = 16
⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16
⇒ x² - 12x + 20 + y² - 6y + 9 = 0
Reorganizing the equation in general form:
x² - 12x + 20 + y² - 6y + 9 = 0
⇒ x² - 12x + 20 + y² - 6y + 9 = 0
⇒ x² + y² - 12x + 20 - 6y + 9 = 0
⇒ x² + y² - 12x + 20 - 6y + 9 = 0
⇒ x² + y² - 12x - 6y + 20 + 9 = 0
⇒ x² + y² - 12x - 6y + 29 = 0
Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.
Which number is written in scientific notation? 4. 5 times 10 Superscript negative 3 14. 5 times 10 Superscript 2 0. 78 times 10 Superscript negative 6 5. 7 times 4 Superscript 8.
Answers
The number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.
Given numbers are:
1)[tex]4.5*10^{-3}[/tex]
2)[tex]14.5*10^{2}[/tex]
3)[tex]0.78*10^{-6}[/tex]
4)[tex]5.7*4^8[/tex]
What is the scientific notation of numbers?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
In the first number [tex]1 < 4.5 < 10[/tex] multiplied by [tex]10^{-3}[/tex]
As per the definition [tex]4.5*10^{-3}[/tex] is written in scientific notation.
The Rest of the numbers do not follow the definition of scientific notation so they are not in scientific notation.
Hence, the number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.
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what number does 5a+ab represent when a =10 and b=-1
Answers
Answer:
5a + ab = 40
Step-by-step explanation:
Sub in 10 for a, making the equation 5 x 10 + 10 x b
Then sub in - 1 for b making it 5 x 10 + 10 x - 1
Then multiply making it 50 + - 10
Then subtract since adding negative is actually subtracting and you get 40
Hey there!
In order to evaluate this expression, all we should do is plug in the values of the variables and simplify.
We are given that
a=10
b=-1
Plug in the values:
5(10)+(10)(-1)
multiply 5 times 10 and 10 times (-1) and add the products:
50+(-10)
or... actually subtract.
50-10
40
Hence, the answer is
[tex]\boxed{\boxed{\bold{40}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
HURRY NEED THIS ASAP. A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company’s previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company’s production line on a specific day. A golf pro then randomly selects a ball, not knowing the type of ball, and hits it. The distance the ball travels is then measured. He continues this procedure until all 80 of the golf balls are hit. At the end of the session, the mean distance traveled for the new type of golf ball was found to the significantly greater than the mean distance for the original-style golf ball.
Which of the following is a valid conclusion?
Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
Inferences can be made about all the golf balls produced on that day; however, a conclusion cannot be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
Inferences cannot be made about all the golf balls produced on that day; and a conclusion cannot be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
Inferences cannot be made about all the golf balls produced on that day; however, the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
Answers
The conclusion based on the mean of the ball and the distance traveled is D. Inferences cannot be made about all the golf balls produced on that day.
How to deduce the inference?From the information given, a golf pro randomly selects a ball, not knowing the type of ball, hits it and end of the session, the mean distance traveled for the new type of golf ball was found to be greater than the mean distance for the original-style golf ball.
In this case, inferences cannot be made about all the golf balls produced on that day; however, the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
Learn more about mean on:
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Answer:
should be A. Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
Step-by-step explanation:
correct for edge, nov. 2022
Tina buys 5 pounds of potatoes for $4. 35 and 3 pounds of carrots for $3. 57 how much does 1 pound of potatoes cost
Answers
Answer:
1 pound of potatoes costs $0.87
Hi can u please help me with this and also an explanation thank u
Answers
Question 1: Area of the base
The base is a triangle⇒ Area of a Triangle --> [tex]\frac{1}{2}*(base)*(height)[/tex]
⇒ Area = [tex]\frac{1}{2} * 6 * 8 = 3 * 8 =[/tex] 24 square kilometers
Question 2: Height of Pyramid
Height of pyramid ⇒ distance from the tip of the figure to its base⇒ Height = 12 km
Question 3: Volume of a pyramidFormula for Volume of a pyramid ⇒ 1/3 * (base area) * (height)
⇒ [tex]\frac{1}{3} *24 * 12 = 8 * 12[/tex] = 96 cubic kilometers
Hope that helps!
if i was asked to think of a number and multiply it by 2, I could write this algebraically as 2x Write the following using x as your unknown. "I think of a number, take away 1 and multiply the result by 3.
Answers
Step-by-step explanation:
(x - 1)×3
a random number minus 1, and the result is multiplied by 3.
bingo !
Answer:
3(x - 1).
Step-by-step explanation:
Taken away 1 is x - 1
Multiply this by 3 is 3(x - 1).
A bakery made 100 donuts. In the display case, 40/100 were chocolate,
3/10 were glazed, and the rest were cinnamon. Which fraction of the donuts were cinnamon?
A.30/100
B.43/100
C.57/100
D.70/100
Answers
Answer:
Step-by-step explanation:
57 of them were cinnamon.
Explanation:
100-40 = 60 and 3 of those were glazed so that leaves us with 57
The sum of three consecutive, positive, even integers is 18
more than twice the smallest. The integers are_____.
Answers
Answer:
5, 6, 7
Step-by-step explanation:
5 + 6 + 7 = 18
Answer:
15,16,17
Step-by-step explanation:
The question states, The sum of three consecutive, positive, even integers is 18 more than twice the smallest.
Let a,b,c be positive integers
Let a be the smallest integer.
Because the answer says the sum of the integers has to be 18 more than 2 x the smallest integer. It means the situation can be represented as:
a + b + c = 2a + 18
Because these numbers are consecutive, meaning they are right besides each other. Every variable can be written in terms of a.
a = a
b = a + 1
c = a + 2
Now we can solve for a:
a + (a+1) + (a+2) = 2a + 18
a + a + 1 + a + 2 = 2a + 18
3a + 3 = 2a + 18
a + 3 = 18
a = 15
then we can fill in the rest.
b = (15) + 1 = 16
c = (15) + 2 = 17
Now we verify.
15 + 16 + 17 = 2(15) + 18 ?
15 + 16 + 17 = 48
2(15) + 18 = 48
We now have the solution. The consecutive numbers, are, and can only be
15,16,17
A pet store has 5 tanks of fish. Each tank has 30 fish. How many fish does the store have?
Answers
Answer:
30 fish
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
5 tanks with 30 fish each so 5x30
5x30=150
Nathan was asked to determine the quotient of 10 and 1/7. He claims that the quotient is 70. Which expression below could Nathan simplify to explain how he know his answer is right
A) 70 +1/7
B)10 +70
C)10 x 1/7
D) 70 x 1/7
Answers
Answer:
D
Step-by-step explanation:
The quotient is the result of dividing one number by another.
[tex]\frac{10}{\frac{1}{7} } = ?[/tex]
is how you would represent the quotient of 10 and 1/7.
The opposite of division is multiplication, and those we can rearrange that and get:
[tex]? * \frac{1}{7} = 10, or, ?/7 = 10[/tex]
or in other words, "what number divided by 7 is 10"
The answer becomes clearer, 70 is that number.
D represents this idea.
A system of equations is shown
Y=2x-5
Y=4x + 3
What is the solution to the system of equations?
A (-4,-13)
B(-4,3)
C (4,-13)
D (4,3)
Answers
Answer:
A. (-4,-13)
Step-by-step explanation:
y = 2x - 5
y = 4x + 3
-2(y = 2x - 5) ==> -2y = -4x + 10
y = 4x + 3 ==> y = 4x + 3
-2y = -4x + 10
y = 4x + 3
___________
-y = 13
/-1 /-1
y = -13
Now we find x, by substituting -13 for y
y = 2x - 5
-13 = 2x - 5
+ 5 +5
-8 = 2x
/2 /2
-4 = x
(x, y) ==> (-4, -13)
Check your answer:
y = 2x - 5
-13 = 2(-4) - 5
-13 = -8 -5
-13 = -13
This statement is correct
Hope this helps!
Line of best fit has a y intercept of 6 and goes through the point(4,22) what is the slope of the line
Answers
Answer:
0.7
Step-by-step explanation:
you have a slope of 6 and it goes through 4,22 so slope = rise over run so you would divide them
Shawn is typing a paper for class. He can type 1 5/14 pages in 1/3 of an hour. How many pages can shawn type in one hour?
Answers
Answer:
4 1/14
Step-by-step explanation:
1 5/14 x 3 = 4 1/14
Answer:
4 1/14 pages
Step-by-step explanation:
multiply 1 5/14 by 3
start by multiplying 1 by 3 which is 3
then multiply 5/14 by 3, you just have to multiply the 5 and you get 15/14 which is 1 1/14
add 3 and 1 1/14 and you get 4 1/14
Patrick is a comdeion who makes $120 for short performance and $260 for long performance. how much will he earn if he completes 11 short and 12 long performences?
Answers
Answer:
$4440 for all performances
Step-by-step explanation:
11 × ¢120 for short performances
12 × $260 for long performances
$1320 for short performances
$3120 for long performances
To get the totel you add them up
( $1320 + $3120)
The total is $4440
is x – 4 a factor of P(x) = x^4 - 4x^2 – 4x + 8 ? Explain.
Answers
Answer:
(x3 - 2x2 - 4) • (x + 2)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(((x4) - 22x2) - 4x) - 8
STEP
2
:
Checking for a perfect cube
2.1 x4-4x2-4x-8 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x4-4x2-4x-8
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x4-8
Group 2: -4x2-4x
Pull out from each group separately :
Group 1: (x4-8) • (1)
Group 2: (x+1) • (-4x)
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = x4-4x2-4x-8
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -8.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8
Find the value of c that makes the trinomial a perfect square. .
x² – 24x7c
Answers
Answer:
144
Step-by-step explanation:
The equation to find c is:
[tex](\frac{b}{2} )^{2}[/tex]
So put -24 into b:
[tex](\frac{-24}{2} )^{2}[/tex]
Which simplifies to:
144
So if you want to test this:
x^2 - 24x + 144
is
(x-12)^2
An object is attached by a string to the end of a spring. Fang throws the object upwards and starts a stopwatch at t=0t=0t, equals, 0 seconds. The object starts oscillating vertically in a periodic way that can be modeled by a trigonometric function.
The object's average height is -20\text{ cm}−20 cmminus, 20, start text, space, c, m, end text (measured from the top of the spring). It first achieves that average height on the way up at t=0.2t=0.2t, equals, 0, point, 2 seconds, and then again every 222 seconds. The object's maximum and minimum heights are each 5\text{ cm}5 cm5, start text, space, c, m, end text from its average height.
Find the formula of the trigonometric function that models the height HHH of the weight ttt seconds after Fang started the stopwatch. Define the function using radians.
\qquad H(t) =H(t)=H, left parenthesis, t, right parenthesis, equals
What is the height of the object after 0.60.60, point, 6 seconds? Round your answer, if necessary, to two decimal places.
Answers
The object attached to a string illustrates a sinusoidal trigonometric function
The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is -17.06 cm
How to determine the trigonometry function model?The trigonometry model of the object is a sine function represented by:
H(t) = Asin(B(t - c)) + D
The maximum height is 5 cm.
So, we have:
Amplitude, A = 5
The average height is - 20 cm.
So, we have
Vertical shift, D = -20
Its first average height is at t = 0.2.
So, we have:
Horizontal shift, C = 0.2
The period B is then calculated as:
B = π/t
The object reaches the maximum height every 2 seconds.
So, we have:
B = π/2
Substitute these values in H(t) = Asin(B(t - c)) + D
H(t) = 5sin(π/2(t-0.2))-20
Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20
The height of the object after 0.6 secondsSubstitute 0.6 for t in H(t)
H(0.6) = 5sin(π/2(0.6-0.2))-20
Evaluate
H(0.6) = -17.06
Hence, the object's height after 0.6 seconds is -17.06 cm
Read more about trigonometric functions at:
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