To find the absolute maximum and minimum values of a function, we find the critical points and endpoints. Evaluating the function at these points gives the maximum and minimum values.
Explanation:To find the absolute maximum and absolute minimum values of a function on a given interval, we need to find the critical points and endpoints of the interval.
To find the critical points of f, we need to find where the derivative of f is equal to zero or undefined. The derivative of f(t) = 9t + 9cot(t/2) is f'(t) = 9 - 9csc^2(t/2).
Setting f'(t) = 0, we have 9 - 9csc^2(t/2) = 0. Solving this equation, we get csc^2(t/2) = 1, which means sin^2(t/2) = 1. This gives us sin(t/2) = ±1. The critical points occur when t/2 = π/2 or t/2 = 3π/2. Solving for t, we get t = π or t = 3π as the critical points.
The endpoints of the interval are π/4 and 7π/4.
Now we evaluate the function f at the critical points and endpoints:
f(π/4) = 9(π/4) + 9cot(π/8) ≈ 6.566f(π) = 9π + 9cot(π/2) = 9πf(3π) = 9(3π) + 9cot(3π/2) = 27πf(7π/4) = 9(7π/4) + 9cot(7π/8) ≈ 46.607From these evaluations, we can see that the absolute maximum value occurs at t = 7π/4 and is approximately 46.607, while the absolute minimum value occurs at t = π/4 and is approximately 6.566.
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Nicole shines a light from a window of a lighthouse on a cliff 250 feet above the water level. Nick 10 feet above the water level in a ship off shore, finds that the angle of elevation of the light is 3°. Find the length of the line of sight (light beam) from the ship to Nicole.
We want to find the length of the light beam from the ship to Nicole.
We will see that the solution is 4,585.76 ft.
We can think of this situation as in a right triangle. The adjacent cathetus is the distance between the lighthouse and the ship. The opposite cathetus is the difference in height between Nicole's position and Nick´s position, it is equal to:
250ft - 10ft = 240ft
And the elevation angle is equal to 3°. So we know the angle and the opposite cathetus to this angle, and we want to find the hypotenuse, which is the length of the light beam.
Then we can use the relation:
Sin(θ) = (opposite cathetus)/(hypotenuse)
Solving it for the hypotenuse we get:
hypotenuse = (opposite cathetus)/sin(θ)
Replacing by the values that we know, we get:
hypotenuse = 240ft/sin(3°) = 4,585.76 ft
The length of the line of sight is 4,585.76 ft
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To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We are given the angle of elevation of the light, the height of the cliff, and need to calculate the length of the line of sight.
Explanation:To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We have a right triangle formed by the line of sight, the height of the cliff, and the distance from the ship to Nicole. We are given the angle of elevation of the light as 3° and the height of the cliff as 250 feet. Let's denote the length of the line of sight as x and the distance from the ship to Nicole as d. Using the tangent function, we can write:
tan(3°) = 250 / d
Simplifying this equation, we have:
d = 250 / tan(3°)
Now we can substitute the value of tangent of 3° and solve for d. Using a calculator, we find that:
d ~ 8424.78 feet
So, the length of the line of sight from the ship to Nicole is approximately 8424.78 feet.
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Which are ways to decompose the composite figure into simpler shapes that you have area formulas for? Check all that apply
Answer:
A,B and C
Step-by-step explanation:
Answer
a,b,c are the correct answer
Step-by-step explanation:
hope it helps you my luvs
The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample exceeds 104
Answer:
[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]
And we can use the complement rule and the normal standard distribution or excel and we got:
[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
We select a sample of n = 50 and we want to find the probability that:
[tex]P(\bar X >104)[/tex]
Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}} [/tex]
And using this formula we got:
[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]
And we can use the complement rule and the normal standard distribution or excel and we got:
[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]
F (x) = 5x-10 determine x when f (x) = 15
Answer: 5=x
Step-by-step explanation:
Ok, so if F(x)=15, then the equation would look like this: [tex]15=5x-10[/tex]
The next step would be to add the 10 over from the right to the left side to get [tex]25=5x[/tex]
Now divide both sides by 5 to get the answer.
can you solve this equation?
Answer:
x=31
Step-by-step explanation:
(x-31)/4=0
multiply each side by 4 so that you have x-31=0.
x-31=0
add 31 to each side.
x=31
Answer:
No, unless you set it equal to zero.
Step-by-step explanation:
(x-31)/4=0
((x-31)/4) times 4 = 0 times 4
x-31=0
x-31 +31 =0 + 31
x=31
"A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 90 miles. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train."
The rate of the passenger train is 100 miles per hour.
Given:
1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.
2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.
We can set up equations based on the distances traveled and the rates:
1. For the passenger train:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]
Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]
So, the rate of the passenger train is 100 miles per hour.
Round to 2 SF
646.42
plz
Answer:
650
Step-by-step explanation:
2sf= the first two figures
so you count to the first two sf numbers so in this case
it would be 64 then you look at the next one. But if it is 4 or below you round or if it is 5 and above you rounded up
in this case the third digit is a 6 so you would round up to 5
answer =650
The number 646.42 can be rounded to two significant figures by increasing the second significant figure up by one because the third figure is 6 which is greater than 5. Therefore, 646.42 becomes 650.
Explanation:You are requesting to round the number 646.42 to two significant figures (SF). Significant figures are the meaningful digits in a number. For example, in 646.42, there are five significant figures: 6, 4, 6, 4, 2.
To round to two significant figures, we look at the number in the third position, which is another 6. If this number is 5 or greater, we round the second significant figure up. If it is less than 5, we keep the second figure the same. Here, the next number after the two significant figure (6 and 4) is 6, which is more than 5, so you will round 4 up to 5.
Thus, rounded to two significant figures, 646.42 becomes 650.
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f(4)= ______
-11
-2
1
30
if g(x) = 2, x = _______
0
2
5
30
Answer:
f(4) = -11
If g(x) = 2 then x = 0
Step-by-step explanation:
here it asks to determine graphically, so we need to use the provided graph:
f(4) = -11 ( just notice the y-coordinate of the point of x-coordination 4)
If g(x) = 2 then x = 0 (just notice the x-coordinate of the point of y-coordination 2)
if 3n is an odd number, which of the following is an even number?
(a) 3n-1
(b) 3n+2
(c) 3n-2
(d) 3n +2n
Answer:
Option (a).
Step-by-step explanation:
It is given that 3n is an odd number.
We need to find an even number from the given options.
Even numbers: Which are divisible by 2.
Odd numbers: Which are not divisible by 2.
We need know that the numbers are alternatively even and odd.
If we add or subtract 1 from an odd number, we always get an even number.
If we add or subtract 2 from an odd number, we always get an odd number.
3n is an odd number. So,
3n-1 is an odd number.
3n+2 is an even number.
3n+2 is an even number.
3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.
Therefore, the correct option is (a).
what is 3y takeaway y
Answer:
y = 1/3
Step-by-step explanation:
PLEASE hurry !!!!!! y = 24x^2-14x+5
Answer:
(0.3,3)
Step-by-step explanation:
That is the vertex.
From an upstairs window, I can see my neighbor’s fence. The angle of depression is 7 degrees. If my window is 15 ft off the ground, how far is my neighbor’s fence from my house?
Answer:
1.84ft
Step-by-step explanation:
From the figure attached,
AB = Height of the window = 15ft
Let the distance between the base of the housr and the fence 'C' = xft
If the angle of depression = 7°
Then angle of elevation of the top of the fence from the house = 7°
Now from right triangle ABC,
tan7° = x/15
x = tan7°×15
x = 0.1227×15
x = 1.84ft
Therefore, distance of the house from the fence is 1.84ft
Witch expression has a product of 32.76?
Answer:
20.00+12.76 would give you that sum
Step-by-step explanation:
Answer:
0.00+12.76 would give you that sum
Step-by-step explanation:
Pls BRAINLIEST
You measure 50 textbooks' weights, and find they have a mean weight of 52 ounces. Assume the population standard deviation is 14.6 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
The 90% confidence interval = 48.603 < μ < 55.397
Explanation:
Given:
Mean = 52
Standard deviation = 14.6
Sample size, n = 50
Confidence Interval, c = 90%
c = 0.9
Significance level, α = 1 - c
= 1 - 0.9
= 0.1
Critical value, z(α/2) = z(0.05) = 1.645
Critical value = ± 1.645
Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]
[tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]
Limits of 90% confidence interval are given by:
Lower limit = μ - E
= 52 - 3.397
= 48.603
Upper limit = μ + E
= 52 + 3.397
= 55.397
Thus, 90% confidence interval = 48.603 < μ < 55.397
Mrs. Benton selects one student's work to display on a bulletin board each week. Each student's name is placed in a bag from which Mrs. Benton draws a name. What is the probability that an eighth grade student will NOT be selected? A) 3 /10 B) 2/ 5 C) 1 /2 D) 2/ 3
Answer:
1/2
Step-by-step explanation:
Which statements are true? Check all that apply.
The radius of the cone is 9 units.
The height of the cone is 15 units.
The height of the cone is 12 units.
The volume of the cone is represented by the
expression 17(15)?(9).
The volume of the cone is represented by the
expression 1.9(9)2(12)
Answer: ACE
The radius of the cone is 9 units
The height of the cone is 12 units
The volume of the cone is represented by the expression 1/3 pie (9)2(12)
Step-by-step explanation:
Which correctly uses bar notation to represent the repeating decimal for StartFraction 6 Over 11 EndFraction 0.5ModifyingAbove 4 with bar 0.54ModifyingAbove 54 with bar 0.ModifyingAbove 54 with bar 0.ModifyingAbove 545 with bar
Answer:
Option C is your Correct AnswerStep-by-step explanation:
Answer:
c .54 w/ bar
Step-by-step explanation:
6g=48 g=? Please hell
Answer:
g = 8
Step-by-step explanation:
We're going to isolate g to find out what it equals, so we have to divide both sides by 6.
6g=48
__ __
6 6
g = 8
The solution to the equation 6g = 48 is g = 8.
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
6g = 48
By dividing both sides of the equation by 6, we have:
g = 48/6
g = 8
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The volume of a gas "V" varies inversely with the pressure "P" put on it. If the volume is 360cm³ under a pressure of 20 kgcm2, then what pressure is needed for it to have a volume of 480cm³?
Answer:
[tex]15\,\,kg/cm^2[/tex]
Step-by-step explanation:
Given:
The volume of a gas "V" varies inversely with the pressure "P" put on it.
Volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex]
To find:
pressure when volume is 480 [tex]cm^3[/tex]
Solution:
As of a gas "V" varies inversely with the pressure "P" put on it,
[tex]V=\frac{k}{P}[/tex]
Here, k is a constant
As volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex], put [tex]V=360\,,\,P=20[/tex]
[tex]360=\frac{k}{20}\\k=360\times 20\\=7200[/tex]
So,
[tex]V=\frac{7200}{P}[/tex]
Put [tex]V=480[/tex]
[tex]480=\frac{7200}{P}\\P=\frac{7200}{480}\\=15\,\,kg/cm^2[/tex]
round to the nears ten 9.42?
Answer:
9
Step-by-step explanation:
In order to round to the nearest ten you must think: what is the nearest multiple of 10. For example, to round 68 to the nearest 10, the nearest whole number is 70, so the answer would be 70. However if you were to round 63 to the nearest 10, to would be 50 since that is the nearest multiple of 10
Answer:9
Step-by-step explanation:
Since the next number is below five you don’t round up it just stays the same
Circle A and circle B are similar. A. What is the similarity ratio of circle A to circle B? B. What is the circumference of each circle? Leave answers in terms of . C. What is the ratio of the Circumference of circle B to the Circumference of circle A? Simplify your ratio.
Answer: A) 5/2
B) 10pi for A and 4pi for B
C) 5/2
Step-by-step explanation:
Please find the attached file for the solution
determine if the listed line is tangent to the circle
Answer:
SEG KL is not a tangent coz Pythagoras theorem doesn't apply hereSEG GH is not a tangent coz Pythagoras theorem doesn't apply hereSEG GF is not a tangent coz Pythagoras theorem doesn't apply hereSEG FG is not a tangent coz Pythagoras theorem doesn't apply hereSEG XY is a tangent Pythagoras theorem apply here 24²+7²=25²SEG XY is not a tangent coz Pythagoras theorem doesn't apply herePLEASEEEEEW ANSWERRRRRRRRR QUICKKKKKMM
Answer:
multiply all the numbers
Step-by-step explanation:
Element X decays radioactively with a half life of 11 minutes. If there are 870 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 154 grams?
Answer:
It would take 27.5 minutes the element to decay to 154 grams.
Step-by-step explanation:
The decay equation:
[tex]\frac {dN}{dt}\propto -N[/tex]
[tex]\Rightarrow \R\frac {dN}{dt}=-\lambda N[/tex]
[tex]\Rightarrow \frac {dN}N=-\lambda dt[/tex]
Integrating both sides
[tex]\Rightarrow \int \frac {dN}N=\int-\lambda dt[/tex]
[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]
When t=0, N=[tex]N_0[/tex] = initial amount
[tex]ln|N_0|=-\lambda .0+c[/tex]
[tex]\Rightarrow c=ln|N_0|[/tex]
[tex]ln|N|=-\lambda t+ln|N_0|[/tex]
[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex]
Decay equation:
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
Given that, the half life of of element X is 11 minutes.
For half life, [tex]N=\frac12 N_0[/tex], t= 11 min.
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11[/tex]
[tex]\Rightarrow ln|\frac12}|=-\lambda . 11[/tex]
[tex]\Rightarrow -\lambda . 11=ln|\frac12}|[/tex]
[tex]\Rightarrow \lambda =\frac{ln|\frac12|}{-11}[/tex]
[tex]\Rightarrow \lambda =\frac{ln|2|}{11}[/tex] [ [tex]ln|\frac12|=ln|1|-ln|2|=-ln|2|[/tex] , since ln|1|=0]
N=154 grams, [tex]N_0[/tex] = 870 grams, t=?
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}[/tex]
=27.5 minutes
It would take 27.5 minutes the element to decay to 154 grams.
Answer:
60.6 minutes
Step-by-step explanation:
--------------------------------
What is the coefficient of x in the following expression?
1 - 10x + 4y
Evaluate the following expression for x = 15.
LaTeX: \frac{1}{5}1 5x - 12
Answer:
(1) The coefficient of x in this expression is -10.
(2) The value of the expression for x = 15 is -9.
Step-by-step explanation:
(1)
A coefficient is a numerical value that is placed before a variable or is multiplied by the variable in an algebraic equation.
For example, in the algebraic equation 4x² + 5y the coefficient of variable y is 5.
The expression given is:
1 - 10 x + 4 y
The coefficient of x in this expression is -10.
(2)
The expression provided is:
[tex]f(x)=\frac{1}{5}x - 12[/tex]
Compute the value of the expression for x = 15 as follows:
[tex]f(x)=\frac{1}{5}x - 12\\=(\frac{1}{5}\times 15) - 12\\=3-12\\=-9[/tex]
Thus, the value of the expression for x = 15 is -9.
What is the value of f(12)-f(8) when f(x)=3x+9
Answer:
12
Step-by-step explanation:
f(x)=3x+9
f(12) = 3*12 +9
36+9
45
f(8) = 3*8+9
=24+9
= 33
f(12) - f(8) = 45-33
12
An open-top box is to be made from a 70-centimeter by 96-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume? Enter the area of the square and do not include any units in your answer. Enter an improper fraction if necessary.
Answer:
[tex]177 \frac{7}{9} cm^2[/tex]
Step-by-step explanation:
Length of the Plastic Sheet= 96cm
Width of the plastic Sheet =70cm
If a square of side x is cut from each corner of the plastic sheet to form the box.
Length of the box=96-2x
Width of the box=70-2x
Height of the box =x
Volume of the box = LWH
Volume=(96-2x)(70-2x)x
The maximum volume of the box is obtained at the point where the derivative is zero.
[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]
Setting the derivative to 0.
[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]
Since we are looking for the minimum value of x,
[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]
18
Which transformation shows a reflection of ADEF?
Answer: B
Step-by-step explanation:
The reflection transformation in the second figure shows the correct reflection.
What are the types of translations?There are three types of translations -
reflectionrotationdilationGiven is a triangle ΔDEF.
It is asked to find the possible reflection of the triangle ΔDEF. After the reflection, the lines D'E' will be parallel and will be in the same orientation. So, we can see that the correct orientation is maintained only in the second transformation. So, the reflection transformation in the second figure shows the correct reflection.Therefore, the reflection transformation in the second figure shows the correct reflection.
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PLEASE HURRY I'M TAKING A TEST 20 PTS
Simplify the expression (in the picture)
Answer:
D
Step-by-step explanation:
2 ( x − 3 )
x ( x + 1 )
Answer:
ANSWER IS D
Step-by-step explanation:
Tickets to the school play cost $4.00 for adults and $2.00 for students. If 85 people attend the show, and the receipts totaled $268, how many students attended the show?
Answer:I think it is 226
Step-by-step explanation:
85/2= 42.5 then 268 - 42.5= 225.5 then round it and you get 226