The function f(t) = 25 sin (pi over 2t) + 10 models the temperature of a periodic chemical reaction where t represents time in hours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take? (5 points)
A. Maximum: 25°; minimum: 10°; period: pi over 2 hours
B. Maximum: 35°; minimum: 35°; period: 8 hours
C. Maximum: 100°; minimum: −15°; period: pi over 2 hours
D. Maximum: 35°; minimum: −15°; period: 4 hours
Answers
By graphing the given function
The correct option is D
D. Maximum: 35°; minimum: −15°; period: 4 hours
Answer:
The correct answer is: Option: D
D. Maximum: 35° ; minimum: −15° ; Period: 4 hours
Step-by-step explanation:
We are given a function f(t) as:
[tex]f(t)=25\sin (\dfrac{\pi}{2}t)+10[/tex]
We know that the maximum value of the function is obtained when the sine function is maximum.
i.e. when sine takes the value=1
and the minimum value of the function is obtained when the sine function is minimum.
i.e. when sine takes the value= -1
Hence, the minimum value of the function is:
-25+10= -15
and the maximum value of the function is:
25+10=35
Also the period of the function of the type:
[tex]f(x)=a\sin(bx)+c[/tex]
is:
[tex]Period=\dfrac{2\pi}{b}[/tex]
Hence, here we have: b=π/2
Hence, period is:
[tex]Period=\dfrac{2\pi}{\dfrac{\pi}{2}}\\\\\\Period=4[/tex]
Hence, option: D is the correct answer.
Related Questions
hey can you please help me posted picture of question
Answers
y = f (x)
The domain of the function is:
values of x for which it is defined.
The range is:
values of and for which it is defined.
The inverse is:
x = f (y)
The domain of the function is:
values of and for which it is defined.
Answer:
TRUE
option A
Domain of the function is Range of its Inverse.
Range of the function is Domain of its Inverse.
This is because the function and its inverse are a reflection about the line x= y, as a result the x values get translated to y values.
7-x = -2 whats the awnser
Answers
9 = x
If you're wanting the value of x, the answer is ...
x = 9
_____
You can always solve an equation like this by subtracting one side, then dividing by the coefficient of x, then adding the opposite of the constant. If you choose to subtract the right side, these steps will give you ...
9 -x = 0 . . . . . . subtract -2 from both sides
-9 +x = 0 . . . . . divide by the coefficient of x, which was -1
x = 9 . . . . . . . . .add the opposite of the constant, so add 9
Whatever you do to one side of the equation, you must also do to the other side. When we say "subtract -2", we mean "subtract -2 from both sides of the equation."
What is the highest decimal number that can be represented by two binary digits?
Answers
___________________
The answer is 3.
Bonus: Here is a fun challenge, try to decipher what Im saying here. (Use an online binary website.)
01001001 01100110 00100000 01111001 01101111 01110101 00100000 01100110 01101001 01101110 01100100 00100000 01101111 01110101 01110100 00100000 01110111 01101000 01100001 01110100 00100000 01110100 01101000 01101001 01110011 00100000 01110011 01100001 01111001 01110011 00101100 00100000 01001001 00100000 01110111 01101001 01101100 01101100 00100000 01100110 01101111 01101100 01101100 01101111 01110111 00100000 01111001 01101111 01110101 01110010 00100000 01100010 01110010 01100001 01101001 01101110 01101100 01111001 00100000 01100001 01100011 01100011 01101111 01110101 01101110 01110100 00100000 00111010 00101001
Nikhil gets paid a 5 percent commission on every pair of shoes that he sells. He earned $1.00 on the last pair of shoes that he sold. The expression that can be used to represent x, the price of the shoes, is mc005-1.jpg What was the price of the shoes?
Answers
.05s=f(s)
.05s=1
s= $20
Answer:
$20.00 is the correct answer
Step-by-step explanation:
I promise this is correct
a gardener at Blair's Arboretum is making displays of roses with 192 red 120 yellow and 168 pink roses to choose from if she wants to use all of the flowers in the displays need to be identical what is the greatest number of displays she can create
Answers
f(x)=e^(x) where it is translated 1 unit right and 2 units down
Answers
1) It is tanslated 1 unit right:
g(x)=f(x-1)→g(x)=e^(x-1)
2) and 2 units down:
h(x)=g(x)-2→h(x)=e^(x-1)-2
Answer: e^(x-1)-2
A taxi driver estimates that his earnings are $240 on a fine day and $320 on a wet day. What are his expected earnings on a day with probability of rain of 0.45?
Answers
Probability of not raining=1-0.45=0.55
The expected earning will be given by:
E(x)=240(0.55)+320(0.45)
E(x)=132+144
E(x)=276
Answer: $276
Devonte used the change of base formula to approximate log 8 25. Which expression did Devonte use?
A.log 8/25 B.log8/log25 C.log 25/8 D.log25/log8
Answers
Answer:
D.
Step-by-step explanation:
Solve for r.
4r-9s=K
Answers
Final answer:
To solve for 'r' in the given equation, add 9s to both sides and then divide by 4, resulting in r = (9s + K) / 4.
Explanation:
To solve for r in the equation 4r - 9s = K, we need to isolate r on one side of the equation. Here's how we can do this:
Add 9s to both sides of the equation to get 4r = 9s + K.Divide both sides of the equation by 4 to solve for r, resulting in r = (9s + K) / 4.Now, we have r expressed in terms of s and K, which is the desired form.At the grocery store, an 8-inch cherry pie costs $4.39 and a similar 10-inch cherry pie cost $6.15. which is the better deal?
Answers
for the 10 inch pie you are paying about 61 cents per inch
so the 8 inch pie is a better deal
hope this helped
oh and to get those numbers divide 4.39 by 8 and 6.15 by 10
Find the value of x for which m//n
A.
10
B.
12
C.
40
D.
52.
Answers
(3x+12)°=48°
Solving for x:
3x+12=48
3x+12-12=48-12
3x=36
3x/3=36/3
x=12
Answer: Option B. 12
Answer:
The answer is D. 52
Step-by-step explanation:
edg 2020
Find the center, vertices, and foci of the ellipse with equationx^2/144+y^2/2525 = 1
Answers
The largest denominator is a^2 and the smallest denominator is b^2, then:
a^2=144→sqrt(a^2)=sqrt(144)→a=12
b^2=25→sqrt(b^2)=sqrt(25)→b=5
The equation is of the form:
x^2/a^2+y^2/b^2=1
This is an ellipse with center C=(h,k) at the Origin → C=(0,0) and major axis on the x-axis and minor axis on the y-axis.
The vertices have coordinates:
V'=(-a,0) and V=(a,0)
Replacing a=12
V'=(-12,0) and V=(12,0)
The foci have coordinates:
F'=(-c,0) and F=(c,0)
c^2=a^2-b^2
c^2=144-25
c^2=119
sqrt(c^2)=sqrt(119)
c=sqrt(119)
Then the coordinates of the foci are:
F'=(-sqrt(119),0) and F=(sqrt(119),0)
Answers:
Centrer: C=(0,0)
Vertices: V'=(-12,0) and V=(12,0)
Foci: F'=(-sqrt(119),0) and V=(sqrt(119),0)
Jewelry is commonly weight in carats.Five carats are equivalent to one gram.How many grams of gold are contained in 24-carat gold chain
Answers
What is the inverse function of f(x)=5x-3
Answers
The inverse function of f(x) = 5x - 3 is found by switching x and y to solve for x, resulting in the inverse function f⁻¹(x) = (x + 3) / 5. This process is part of understanding function transformations that change a function's graph.
Finding the Inverse Function
Find the inverse function of f(x) = 5x - 3. To find the inverse, we need to switch the roles of x and y. So we first write y = 5x - 3. We then solve this equation for x to get x as a function of y. Performing the steps:
Add 3 to both sides: y + 3 = 5x.
Divide both sides by 5: (y + 3) / 5 = x.
This new equation x = (y + 3) / 5 represents the inverse function. To use the proper notation, we replace y with f⁻¹(x) and x with y, giving us f⁻¹(x) = (x + 3) / 5.
Understanding Function Transformations
When considering transformations such as f(-x) or f(2x), these changes to the independent variable result in specific alterations to the graph of the function, such as reflections across the y-axis or horizontal shrinkage by half.
Which is the range for this set of data 38,17,55,40
Answers
Answer:
38
Step-by-step explanation:
Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2?
6 over 7 plus 2 equals 2 and 6 over 7
6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7
6 over 7 times 6 over 7 equals 36 over 49
6 over 7 divided by 2 equals 6 over 14
Answers
6 over 7 to the power of 2
(6/7) ^ 2
By power properties we can rewrite the expression as:
(6/7) * (6/7)
Calculating we have:
(6/7) * (6/7) = 36/49
Answer:
6 over 7 times 6 over 7 equals 36 over 49
A person in a balloon which is 2,000 feet above the airport finds that the angle of depression to a ship out at sea is 21°. Find the horizontal distance between the balloon and the ship.
Answers
The horizontal distance between the balloon and the ship can be calculated using the tangent function is 1639 feet.
To find the horizontal distance between the balloon and the ship, we can use the tangent function in trigonometry. Let's denote the horizontal distance as x, and the distance between the balloon and the ship along the ground as y.
We have the angle of depression (21°) and the altitude of the balloon (2,000 feet). We can set up the equation:
tan(21°) = y / (2,000 + y)
Now, we need to solve for y:
tan(21°) * (2,000 + y) = y
y * tan(21°) = 2,000 * tan(21°) - y * tan(21°)
y * (1 - tan(21°)) = 2,000 * tan(21°)
y = (2,000 * tan(21°)) / (1 - tan(21°))
Now, calculate the value:
y ≈ (2,000 * 0.364) / (1 - 0.364)
y ≈ 728 / 0.636
y ≈ 1,148.17
Now that we have the value of y, we can find the horizontal distance x using the Pythagorean theorem:
[tex]x^2 + y^2 = (2,000)^2\\x^2 + (1,148.17)^2 = 4,000,000\\x^2 = 4,000,000 - 1,319,441.98\\x^2 = 2,680,558.02\\x = 1,638.84 (rounded)[/tex]
The horizontal distance between the balloon and the ship is approximately 1,639 feet.
Horizontal distance = height of balloon / tangent(angle of depression) = 2000 / tan(21°) ≈ 5243.87 feet.
To find the horizontal distance between the balloon and the ship, we can use trigonometry, specifically the tangent function.
Let's denote:
- [tex]\( h \)[/tex] as the height of the balloon above the ground (2,000 feet in this case).
- [tex]\( \theta \)[/tex] as the angle of depression (the angle formed between the line of sight from the balloon to the ship and the horizontal ground).
Given that the angle of depression [tex]\( \theta \)[/tex] is 21°, we can use the tangent function:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
In this case, the opposite side is the height of the balloon above the ground (2,000 feet), and we want to find the adjacent side, which represents the horizontal distance between the balloon and the ship.
So, we have:
[tex]\[ \tan(21°) = \frac{2000}{\text{horizontal distance}} \][/tex]
To find the horizontal distance, we rearrange the equation:
[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \][/tex]
Now, we can calculate this:
[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \approx \frac{2000}{0.381} \approx 5243.87 \text{ feet} \][/tex]
So, the horizontal distance between the balloon and the ship is approximately 5243.87 feet.
hey can you please help me posted picture of question
Answers
The solution is shown below:
(8 - 3i)(6 + 5i)
= 8(6 +5i) - 3i(6 + 5i)
= 48 + 40i - 18i - 15i²
= 22i + 48 - 15(-1)
= 22i + 48 + 15
= 22i + 63
= 63 + 22i
The circle graph shows the different types of books that Yubo enjoys reading
Which two types of books does Yubo spend a total of of her time reading?
Choose exactly two answers that are correct.
A.
Fiction
B.
Mystery
C.
Poetry
D.
History
Answers
History=0.4~40%
Poetry=0.3~30%
hence we can conclude that the answer is:
C. Poetry
D. History
Answer:
its really History and Mystery hope i hlaaaaaaaaaaaaaaaaped
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6. The estimated value of is 3.14. The measure of the angle subtended by the arc is
Answers
The measure of the subtended angle by the arc is approximately 1.20 radians or 68.75 degrees. This is determined using the formula θ = s/r to find the subtended angle.
Explanation:To find the subtended angle, we need to use the formula θ = s/r, where s is the arc length and r is the circle's radius. The area of the circle with radius r, is πr², and given that it is 78.5 cm², we first need to find the radius. By solving the area equation, we get r = √(78.5/π), or approximately 5.00 cm. Using the radius in the angle formula (θ = 6/5.00), we get θ to be approximately 1.20 radians. However, if the question is asking for the result in degrees, we need to convert the result from radians to degrees by using the conversion factor 180/π. Thus, θ = 1.20 * (180/π) which gives approximately 68.75 degrees.
Learn more about Subtended Angle here:https://brainly.com/question/17158173
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Calculate the circle's radius first from the given area. Then, find the circumference of the circle and compare the arc length to the circumference to obtain the subtended angle. Therefore, the subtended angle is approximately 68.79 degrees.
Explanation:The subject of this question falls under the domain of geometry in Mathematics, where we identify the measure of angle subtended by a certain arc. In order to achieve this, we must understand that a complete circle with a 360-degree angle covers an arc length equivalent to its circumference. If we know the radius of the circle, calculated from the area, we can compare the known arc length to the circumference of the circle to find the angle subtended.
First, we find the radius using the given circle area using the formula [tex]A=\pi r^2[/tex], which gives r= √(A/π). So r= √(78.5 cm² / 3.14) =approx. 5cm. Now, the full circumference of a circle (C) is 2πr, which gives [tex]C = 2*3.14*5 cm = 31.4 cm.[/tex] The full angle covered by the circumference is 360 degrees. To find the angle subtended by an arc of length 6cm, we calculate as follows: (6 cm / 31.4 cm) * 360 degrees = approx. 68.79 degrees.
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hey can you please help me posted picture of question
Answers
(11 - 7i) - (16 - 11i)
= 11 - 7i - 16 + 11i
= -5 + 4i
So, the answer to this question is option B
1. You have the following expression:
(11-7i)-(16-11i)
2. If you want to substract both terms, you obtain:
11-7i-16+11i
(11-16)+(-7+11)
3. Then, you obtain the following result:
-5+4i
4. Therefore, as you can see, the correct answer is the second option (option B), which is:
B. -5+4i
-3x - 7 = -6x + 2 ......................
Answers
+7 +7
---------------------------------------------------------------------------------------------------------------------
-3x = -6x+9
+6x +6x
---------------------------------------------------------------------------------------------------------------------
3x = 9
x = 3
"7 less than a number t" written as an algebraic expression is:
Answers
Answer: The expression for the given statement is [tex]t-7[/tex]
Step-by-step explanation:
We are given a statement:
7 less than a number t
Let the number be considered as 't'
'Less' in the above statement means subtraction operation.
The numerical value written before the 'less' operation is written after in the expression.
Thus, the expression for the given statement is [tex]t-7[/tex]
The algebraic expression for '7 less than a number t' is t - 7. This represents taking the number t and subtracting 7 from it.
Explanation:The question requires an algebraic expression. '7 less than a number t' translates to t - 7 in algebraic terms. The phrase 'less than' is a clear indication to subtract in math context. So, take the number t and subtract 7 from it, hence, t - 7 is our answer. This is a common way to express relative quantities and operations in algebra.
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You have $25 in your bank account. You make $7 per hour babysitting. How many hours must you babysit to have a total of $165 in your account?
Answers
You start with 25 dollars, you make 7 an hour:
7x + 25
Set this to 165:
7x + 25 = 165
Now subtract 25 from both sides:
7x = 140
Divide both sides by 7:
x = 20
So, you must babysit 20 hours.
Hope this helps!
25 + 7h = 165
h is the total number of hours you spend babysitting.
Solve for h to find how many hours you need to babysit to have a total of $165 in your bank account.
25 + 7h = 165
Subtract 25 from both sides.
7h = 140
Divide both sides by 7.
h = 20
You must spend 20 hours babysitting to have $165 in your bank account.
A pizza that was ordered for a party was already cut into 6 slices. If each serving of pizza was 1 3 of a slice, how many servings of pizza were available? A) 18 Eliminate B) 2 C) 1 18 D) 1 2
Answers
I serving size was 1/3 of a slice
1/3 * 3 = 1
3 serving sizes made one slice
Multiply this by the amount of slices
3 * 6 = 18
There are 18 serving sizes
The answer is 18
Hope this helps!
Suppose we calculate a 95% confidence interval for the population mean to be (6.93, 11.45). how do we interpret this?
Answers
The [tex]95\%[/tex] confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.
Further Explanation:
Explanation:
The formula for confidence interval can be expressed as follows,
[tex]\boxed{{\text{Confidence interval}}=\left( {\overline X \pm ME} \right)}[/tex]
ME represents the Margin of Error.
The confidence interval has two limits.
(1). Upper Limit
(2). Lower Limit
The upper limit can be calculated as follows,
[tex]{\text{Upper limit}}=\left( {X + ME}\right)[/tex]
The lower limit can be calculated as follows,
[tex]{\text{Lower limit}} = \left( {X - ME}\right)[/tex]
The given confidence interval is [tex]\left( {6.93,11.45}\right).[/tex]
The upper limit of the confidence interval is 11.45.
The lower limit of the confidence interval is 6.93.
The 95\% confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589
Answer details:
Grade: College
Subject: Statistics
Chapter: Confidence Interval
Keywords: Z-score, Z-value, confidence interval, confidence limit, 95 percent, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.
The four vertices of a rectangle drawn on a complex plane are defined by 1 + 4i, -2 + 4i, -2 – 3i, and 1 – 3i. The area of the rectangle is square units.
Answers
Answer:
The area of rectangle =21 sq units .
Step-by-step explanation:
Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.
Consider ABCD is a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.
First we find sides of rectangle
AB=vertices of B- vertices of A
AB= -2+4i-(1+4i)=-3
If complex number=a+biThen modulus=[tex]\sqrt{a^2+b^2}[/tex]Length of AB= [tex]\sqrt{(-3)^2}[/tex]=3 ( Because magnitude = length always positive )BC= Vertices of C - vertices of B
BC=-2-3i-(-2+4i)=-7i
Length of BC=[tex]\sqrt{(-7)^2}[/tex]=7 ( Magnitude always positive)
CD= vertices of D- vertices of C
CD= 1-3i-(-2-3i)=3
Length of CD= [tex]\sqrt{3^2}[/tex]=3 ( Magnitude always positive)
DA= vertices of A - vertices of D
DA= 1+4i-(1-3i) =7i
Length of DA= [tex]\sqrt{7^2}[/tex]=7 ( Magnitude always positive)
AB=CD and DA= BC
Length BC=7 units
Breadth AB=3 units
Area of the rectangle = [tex]length\times breadth[/tex]
Area of rectangle =[tex]AB\times BC[/tex]
Area of rectangle= [tex]3\times 7[/tex]=21 sq units .Q9 Q11.) Complete the first and second equations of the system of equations.
Answers
See picture below for the answer. Let me know if you have questions about the answer.
Pasha bought 3 pounds of onions for $2.67. which ratio is proportional to 3 pounds at $2.67?
Answers
Hope it helps
The average score on a standardized test is 750 points with a standard deviation of 50 points. What is the probability that a student scored more than 850 on the standardized test ?
Answers
z=(x-μ)/σ
where:
x=850
μ=750
σ=50
thus
z=(850-750)/50
z=2
thus
P(x>850)=1-P(x<850)=1-P(z<2)=1-0.9772=0.0228
Answer: P(x>850)=0.0228
Answer:
2%
Step-by-step explanation: