Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period.
This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w = \frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{3\pi/8}[/tex]
Rewrite as:
[tex]T = \frac{8*2\pi}{3\pi}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the maximum and the minimum of [tex]\sin(\frac{3\pi}{8})[/tex] are:
[tex]\sin(\frac{3\pi}{8}) = -1[/tex] --- minimum
[tex]\sin(\frac{3\pi}{8}) = 1[/tex] --- maximum
Given that:
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the minimum height is:
[tex]h_{min} = 12 * -1 + 42 = 30[/tex]
The maximum is:
[tex]h_{max} = 12 * 1 + 42 = 54[/tex]
A cardiologist is interested in the average recovery period for her patients who have had heart attacks. Match the vocabulary word with its corresponding example.
-
The average recovery time for all heart attack patients that the cardiologist has or will treat
-
All heart attack patients that the cardiologist has cared for or will care for in the future
-
The average recovery time for the 32 heart attack patients
-
The 32 heart attack patients who were observed by the cardiologist
-
The list of all 32 heart attack patients' recovery times
-
The recovery time for a heart attack patient
Answer: See explanation
Step-by-step explanation:
1. The average recovery time for all heart attack patients that the cardiologist has or will treat. = Parameter
2. All heart attack patients that the cardiologist has cared for or will care for in the future = Population.
3. The average recovery time for the 32 heart attack patients = Statistics
4. The 32 heart attack patients who were observed by the cardiologist = Sample
5. The list of all 32 heart attack patients' recovery times = Data
6. The recovery time for a heart attack patient. = Variable
Factor over the complex numbers, if possible: x² + 2xyi - y2
What is the answer?
9514 1404 393
Answer:
(x +yi)²
Step-by-step explanation:
Comparing the given expression to the square of a binomial, we can determine the given expression to be a square.
(a +b)² = a² +2ab +b²
Here, we have a=x and b=yi. Then the factorization is ...
x² +2xyi +(yi)² = (x +yi)²
how to set this up to solve
Answer:
use the arthmetic mean
Step-by-step explanation:
if (-1,4) and (3,-2) are end points of diameter of the circle, then the equation of the circle is
Answer:
If you've more doubts you can ask :)
Step-by-step explanation:
If the centre of a circle is (a, b) and radius r, then the equation of the circle is :
[tex](x - x)^2 + (y-b)^2 = r^2[/tex]
First we will find the centre, (a , b):
[tex]a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1[/tex]
Find radius:
[tex]Radius, r = \frac{Diameter}{2}[/tex]
Diameter is the distance between (-1, 4) and (3, -2)
[tex]diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\[/tex]
[tex]= \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13} \ units[/tex]
Therefore , [tex]r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13} \ units[/tex]
Equation of the circle is :
[tex](x - 1)^2 +(y-1)^2 = 13[/tex]
How do you find the square root of 11? I need to show work
Answer:3.31662479036.
Step-by-step explanation:To find the square root of 11, use the long division method to get the approximate value. Therefore, √11 = 3.31662479036. Register at BYJU'S to learn other interesting mathematical concepts.
I need help with this problem
Answer:
x = 9 , jk = 42 , kl= 78
Step-by-step explanation:
Explained in the paper.
Goodluck
Answer:
x = 9
Step-by-step explanation:
[tex](4x+6)+(7x+15)=120[/tex]
[tex](4(9)+6)+(7(9)+15)=120[/tex]
[tex](36+6) + (63+15)=120[/tex]
[tex](42)+(78)=120[/tex]
x = 9
JL = 42
KL = 78
Given: g(x) = x - 4 and h(x) = 2x - 8. What is g(h(1011?
Answer:
[tex]g(h(1011)) = 2010[/tex]
Step-by-step explanation:
Given
[tex]g(x) = x - 4[/tex]
[tex]h(x) =2x - 8[/tex]
Required
[tex]g(h(1011)[/tex]
First, we calculate [tex]g(h(x))[/tex]
[tex]g(x) = x - 4[/tex]
Substitute h(x) for x
[tex]g(h(x)) = h(x) -4[/tex]
Substitute [tex]h(x) =2x - 8[/tex]
[tex]g(h(x)) = 2x - 8 -4[/tex]
[tex]g(h(x)) = 2x -12[/tex]
Substitute 1011 for x
[tex]g(h(1011)) = 2*1011 -12[/tex]
[tex]g(h(1011)) = 2022 -12[/tex]
[tex]g(h(1011)) = 2010[/tex]
Answer:
6
Step-by-step explanation:
just did it on egde 2021
please help !!! urgent ☹️
Answer:
20/8
=2.5
14×2.5=35
[tex] \frac{20}{8} = \frac{x}{14} \\ x = \frac{20 \times 14}{8} \\ x = \frac{280}{8} \\ x = 35[/tex]
cos90degrees cos30 degrees + sec-squared45degrees sin30degrees - cos270degrees sin180degrees
Step-by-step explanation:
[tex]\cos 90 \cos 30 + \sec^2 45 \sin 30 - \cos 270 \sin 180[/tex]
But we know that
[tex]\cos 90 = \cos 270 = \sin 180 = 0[/tex]
and
[tex]\sin 30 = \dfrac{\sqrt{3}}{2} \:\:\text{and}\:\: \sec 45 = \sqrt{2}[/tex]
so this leaves us with just
[tex]\sec^2 45 \sin 30 = (\sqrt{2})^2 \left(\dfrac{\sqrt{3}}{2} \right)= \sqrt{3}[/tex]
The distance from Nairobi, Kenya to Pretoria, South Africa is 3,969 kilometers. The distance from Cairo, Egypt to Tunis, Tunisia is 2,811 kilometers. Estimate the difference between these two distances by first rounding to the nearest hundred. i need help pleasee
Answer:
Step-by-step explanation:
3,969 = 4,000 rounded to nearest hundred
2,811=3,000 rounded to nearest hundred
therefore... the difference is 4,000 - 3,000 = 1,000 kilometers
Answer:1,100
Step-by-step explanation:
rounding 3,969 to the nearest hundreds is 4,000 and rounding 2811 to the nearest hundred is 2900. Now you subtract 4000-2900 = 1100.
What is length of DF?
Answer:
DF = 11
Step-by-step explanation:
From the question given above, the following data were obtained:
EH = 8
HG = 3
EF = DG
DF =?
Since, EF = DG, it also means that EG = DF.
Next we shall determine EG. This can be obtained as follow:
EG = EH + HG
EH = 8
HG = 3
EG = 8 + 3
EG = 11
Finally, we shall determine EF. This is illustrated below:
EG = DF
EG = 11
DF =?
11 = DF
Therefore,
DF = 11
Let’s Say I Left The House At 11:32 And Then I Came Back At 1:42, How Many Hours Have I Been Gone.
Example: 1hours and 20min
Just an example not the answer ^
i think the correct answer is 2 hours and 10 mins
PLEASE HELP!!!! WHOEVER GETS IT RIGHT GETS BRAINLIEST !!!!
FIND THE VALUE OF X
Answer:16 degree is the answer.
Since r and m are parallel:
10x-3=7x+45
3x=48
x=16
Choose each number that shows 4% as an equivalent fraction, decimal, or percent. Select all that apply.
Answer:
1/4
Step-by-step explanation:
4 divide in half so should be 1/4
What’s the function of f(x)=-2/3x -7 ?
Answer:
F(x) = -1/3 x^2 - 7x + C
The two given figures are similar. Which statements must be true? Select all that apply.
Answer:
angle B=74°
Step-by-step explanation:
the shapes are similar
Select all the possible names for the following angle
Answer:
The answers are options d and e
it says 10^-4
please help give brainliest
Answer:
jane is correct
Step-by-step explanation:
10⁻⁴ can be written as [tex]\frac{1}{10000}[/tex] and as 0.0001
find the perfect square
-6x=3x^2+9
Answer:
[tex] - 6x = 3 {x}^{2} + 9 \\ 3 {x}^{2} + 6x + 9 = 0 \\ {x}^{2} + 2x + 3 = 0 \\ so \\ ether \: x = - 2 \\ or \: x = 1 [/tex]
please help this is due today! geometry
Find the distance between the points (4.3) and (0, 3).
simplify the expression
7y − (6)2y − 12
Answer:
-5y-12
Step-by-step explanation:
Multiply 6 into 2y
7y-12y-12
-5y-12
A store manager can spend at most $1,000 a day for operating costs and payroll. It costs $100 each day to operate the store and $30 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at MOST.
30x + 100 < 1000
A. X > 30
B. X > 33
C. X < 33
D. X < 30
Answer:
x < 30
Step-by-step explanation:
Given the inequality expression that denotes the statement as;
30x+100 < 1000
Subtract 100 from both sides
30x + 100 - 100 <1000 - 100
30x < 900
Divide both sides by 30
30x/30 < 900/30
x < 30
Hence the required solution is x < 30
The number of employee the manager can afford a day is x < 30.
The given parameters:
Amount spent a day for operating cost = $1,000The operating cost of the store, = $100 per dayAmount paid to the employee = $30 per dayThe inequality of the number of employee the manager can afford a day is calculated as follows;
30x + 100 < 1000
collect similar terms together;
30x < 1000 - 100
30x < 900
divide both sides of the equation by 30;
[tex]x <\frac{900}{30} \\\\x <30[/tex]
Thus, the number of employee the manager can afford a day is x < 30.
Learn more about solution to inequality here: https://brainly.com/question/24372553
Deshaun has scored 86, 83, 93, and 79 on her previous four tests. What score does he need on his next test so that his average (mean) is 86?
Answer:
89
Step-by-step explanation:
341 ( total of previous 4 tests) + 89= 430
Divide 430 by 5 ( number of tests)
See the image for question :)
Answer:
it is simple just compare the ratios simple as that
but I will need to know all the formula s
The model below represents the sum of two mixed numbers.
Write an equation that shows the sum represented by the model.
Show your work.
Answer:
hey I am not sure about the answer but I guess this is the right answer:
(x+3)+x
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 10% in 10 years. What will be the population in 20 years? (Round your answer to the nearest person.)
510
Incorrect: Your answer is incorrect.
persons
How fast (in persons/yr) is the population growing at
t = 20?
(Round your answer to two decimal places.)
persons/yr
Answer:
The right answer is "605 persons".
Step-by-step explanation:
Given that,
⇒ [tex]\frac{dP}{dt} \alpha P[/tex]
or,
⇒ [tex]\frac{dP}{dt} =RP[/tex]
⇒ [tex]\frac{1}{R} \int\limits^{PT}_{500} {\frac{dP}{P} } = \int\limits^{t}_{0} dt[/tex]
⇒ [tex]\frac{1}{R} [log PT-log500]=t[/tex]
⇒ [tex]log[\frac{PT}{500} ]=Rt[/tex]
At t = 10 years,
⇒ [tex]PT=\frac{110}{100}\times 500[/tex]
[tex]=550[/tex]
∴ [tex]log[\frac{550}{500} ]=R\times 10[/tex]
[tex]R=\frac{log(1.1)}{10}[/tex]
At t = 20,
⇒ [tex]log{\frac{PT}{500} }=\frac{log \ 1.1}{10}\times 20[/tex]
[tex]PT=500\times (1.1)^2[/tex]
[tex]=605 \ persons[/tex]
3. It refers to the number of values an interval may contain
a. class interval
c. frequency
b. class width
d. range
Answer:
An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).
Step-by-step explanation:
thank me later
Only answer if you're very good at Math.
Given f (x) = x + 1 and g(x) = x^2, what is
( g o f) (x)?
A: ( g o f) (x) = x^2 + 1
B: ( g o f) (x) = (x + 1)^2
C: ( g o f) (x) = x ^ 2 + x + 1
D: ( g o f) (x) = x^2 (x + 1)
Answer:
Solution given:
f(x) = x +1 and g(x) = x²,
now
(gºf)(x) =g(fx)=g(x+1)=(x+1)²
B) (gºf)(x) = (x + 1)^2
what is 3/5 minus 5/11
Answer:
0.14545454545 Maybe
Step-by-step explanation:
Answer:
8/55
Step-by-step explanation:
The first thing you need to do is find a common denomintor.
The first denominator is 5, the other is 11.
If you multiply these together, you will get 55. This can not be reduced and still be divisable by 5 and 11, so this is your new denominator.
So for the 3/5 multiply both top and bottom by 11, since thats how many times bigger the denominatir needs to be:
3*11/5*11= 33/55
Then for 5/11 multiply both top and bottom by 5, since thats how many times bigger the denomator is to make 55:
5*5/11*5=25/55
Now we have:
33/55-25/55
When subtracting fractions, you are only subtracting the two numerators, and the denominators are unaffected:
33-25/55=8/55
So 8/55 is your answer.
Hope this helps!
Here are Barry Bonds's home-run totals, mostly for the San Francisco Giants,
during the years 1991 - 2005:
25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5
There are two outliers at opposite ends of this distribution: his 5 home runs in
2005 and his 73 home runs in 2001. Which of the following is a modified box
plot for this distribution?
A.
B.
C..
E.
The modified boxplot created for the distribution is boxplot E
Given the values :
25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5
The outliers in the values are : 5 and 73
Hence, the modified values are :
25, 34, 46, 37, 33, 42, 40, 37, 34, 49 , 46, 45, 45
Using a boxplot maker or excel, we could use the modified data to create a boxplot with the following properties as obtained from the boxplot shown below :
Median value = 40
Minimum = 25
Maximum = 49
First quartile = 34
Third quartile = 45.5
The modified boxplot has no outlier and it corresponds with the boxplot in option E
Learn more : https://brainly.com/question/1523909
Answer:
graph C
Step-by-step explanation: