Use calculus to find the absolute maximum and minimum values of the function. f(x) = 5x − 10 cos(x), −2 ≤ x ≤ 0 (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
Answer:
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Answer:
The absolute maximum is about -5.84 at x = -2.
And the absolute minimum is about -11.28 at x = -π/6.
Step-by-step explanation:
We want to find the absolute maximum and minimum values of the function:
[tex]\displaystyle f(x) = 5x-10\cos x\text{ for } -2\leq x\leq 0[/tex]
First, we should evaluate the endpoints of the interval:
[tex]\displaystyle f(-2) = 5(-2) - 10\cos (-2) \approx -5.8385[/tex]
And:
[tex]f(0) = 5(0) -10\cos (0) = -10[/tex]
Recall that extrema of a function occurs at its critical points. The critical points of a function are whenever its derivative is zero or undefined.
So, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ 5x - 10\cos x\right][/tex]
Differentiate:
[tex]\displaystyle f'(x) = 5 + 10\sin x[/tex]
Set the function equal to zero:
[tex]\displaystyle 0 = 5+10\sin x[/tex]
And solve for x:
[tex]\displaystyle \sin x = -\frac{1}{2}[/tex]
Using the unit circle, our solutions are:
[tex]\displaystyle x = \frac{7\pi}{6} + 2n\pi\text{ or } \frac{11\pi}{6} + 2n\pi \text{ where } n\in \mathbb{Z}[/tex]
There is only one solution in the interval [-2, 0]:
[tex]\displaystyle x = \frac{11\pi}{6} - 2\pi = -\frac{\pi}{6}\approx -0.5236[/tex]
Thus, we only have one critical point on the interval.
Substituting this back into the function yields:
[tex]\displaystyle\begin{aligned} f\left(-\frac{\pi}{6}\right) &= 5\left(-\frac{\pi}{6}\right) - 10\cos \left(-\frac{\pi}{6}\right) \\ \\ &=-\frac{5\pi}{6} - 5\sqrt{3}\\ \\ &\approx -11.2782 \end{aligned}[/tex]
In conclusion, the absolute maximum value of f on the interval [-2, 0] is about -5.8385 at x = -2 and the absolute minimum value of f is about -11.2782 at x = -π/6.
We can see this from the graph below as well.
Rewrite the following expanded notation in standard form. 600,000 + 80,000 + 1,000 + 400 + 70 + 5
Answer:
this is the answer
681,474
Avery made 6 litres of hot chocolate for the 4th annual bonfire with his family. If
each cup holds of a litre of liquid, how many cups can Avery fill?
Answer:
Avery can hold 6 cups
Step-by-step explanation:
so you have a 6 litre of hot chocolate and for every cup you remove 1 litre of hot chocolate wich makes you get 6 cups of hot chocolate
What is the percent discount if a 12,500 car is now on special for 10,250?
Answer:
Step-by-step explanation:
the answer is 2250 percent is = 22.5
Answer:
18% discount
Step-by-step explanation:
Percent discount is found by the following formula:
[tex]\frac{original-discount}{original}[/tex]
In this scenario, the original is 12500 and the discount, or special is 10250.
We can plug this into the formula to get
[tex]\frac{12500-10250}{12500}[/tex]
We can simplify the numerator by subtracting, and we get that answer as 2250.
We get the remainder of the answer as 2250 divided by 12500. We divide that, and get the answer as 0.18, which can be rewritten as 18%.
Match each equation to its graph.
1. y= x-2
2. y= -2x
3. x= -2
4. y= -2
The equation of the graph is : x = -2
What is a graph?A graph is a pictorial representation of the locus of a certain point.
How to draw a graph?A graph can be drawn by picking some fixed points from the locus of the point.
Here, the straight line passes through the points are : (-2,1); (-2,2); (-2,-5);(-2,-5).
Hence, the straight line is to be parallel to the x-axis and the equation of the graph is x= -2.
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3.3.C-1
If one tablet of calcium pantothenate contains 0.5 gram, how much is contained in
n 2 1/4 tablets? How many tablets are needed to make up 2.3 grams?
A fraction calcium pantothenate contains 0.5 gram of a tablet 5 tablets to make up 2.3 grams.
To calculate the amount of calcium pantothenate contained in a given number of tablets, use the given information that one tablet contains 0.5 grams.
Amount in n 2 1/4 tablets:
To calculate the amount of calcium pantothenate in n 2 1/4 tablets, we need to calculate the total amount for each part (whole tablets and the fraction of a tablet) and then sum them up.
Amount in n whole tablets: n tablets × 0.5 grams/tablet
Amount in 1/4 tablet: (1/4)× 0.5 grams
So, the total amount in n 2 1/4 tablets would be:
Total amount = n ×0.5 + (1/4) ×0.5 grams
Tablets needed to make up 2.3 grams:
To calculate the number of tablets needed to make up 2.3 grams of calcium pantothenate, set up a proportion using the given tablet amount (0.5 grams/tablet).
Let x be the number of tablets needed.
0.5 grams/tablet = 2.3 grams / x tablets
Cross-multiply:
0.5 × x = 2.3
x = 2.3 / 0.5
x = 4.6
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WHAT IS THE ANSWER TO 9-3:3= ?
I NEEDD HELP I ONLY GOT 2 MIN I WILL GIVE BRAINLY
Answer: 8
Hope this help :)
the cost of 2 pairs of trousers and 3 shirts is $825 it shirt cost $50 less than the trouser. find the cost of each shirt and trouser
Answer:
a pair of trousers cost = x = 195 $
one shirt costs = x - 50 = 145 $
Step-by-step explanation:
let the cost of trouser be x.cost of shirt = (x - 50)2 pairs of trousers cost = 2x 3 shirts cost = 3(x - 50)= 3x- 150
2 trousers and 3 shirts cost = 825
=> 2x + 3x - 150 = 825
=> 5x = 975
x = 195
a pair of trousers cost = x = 195 $
a pair of trousers cost = x = 195 $ one shirt costs = x - 50 = 145 $
What is the circumference of the circle in terms of [tex]\pi[/tex]?
a. 900[tex]\pi[/tex] in.
b. 90[tex]\pi[/tex] in.
c. 60[tex]\pi[/tex] in.
d. 30[tex]\pi[/tex] in.
Answer:
[tex]c. \: 60\pi \: in.[/tex]Step-by-step explanation:
Given,
Radius = 30 in
So,
Circumference
[tex] = 2\pi r[/tex]
[tex] = 2 \times \pi \times 30in.[/tex]
[tex] = 60\pi \: in.(ans)[/tex]
[tex] \sf \: r \: = 30 \: in. \\ \sf \: C \: = 2\pi r \\ \\ \sf \: C \: = 2\pi(30) \\ \sf \: C = 2 \times 30\pi \\ \sf \: C = \boxed{\underline{ \bf c. \: 60\pi \: in.}}[/tex]
Classify the following triangle 120 degrees
options
a. acute
b.Scalene
c.isosceles
d.obtuse
e.right
f. equilateral
Answer:
I think it is Obtuse.
Step-by-step explanation:
120 Degrees - Obtuse
Karl wants to raise money for charity. He designs a game for people to play.
Karl uses a ten sided dice for the game. The dice is numbered 1 to 10.
Each person will roll the dice once. A person wins the game if the dice lands on a multiple of 4.
Ali plays the game once,
a) Work out the probability that Ali will win the game.
(2 m
Answer:
0.2 = 20% probability that Ali will win the game.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
The 10 sides that the dice can land, which means that [tex]T = 10[/tex]
Desired outcomes:
Sides that are multiple of 4, that is, side 4 and side 8, so [tex]D = 2[/tex]
Work out the probability that Ali will win the game.
[tex]p = \frac{D}{T} = \frac{2}{10} = 0.2[/tex]
0.2 = 20% probability that Ali will win the game.
Plsss HELP!!!
*image included
the first four terms of a sequence are shown below:
7,4,1,-2
which of the following functions best defines this sequence?
A) f(1)=7, f(n+1)= f(n)+3; for n>= 1
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
C) f(1)=7, f(n+1)= f(n)-4; for n >= 1
D) f(1)=7, f(n+1)= f(n)+4; for n >= 1
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Answer:
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
Step-by-step explanation:
The first term of the sequence is 7 and the next (4) is found by adding -3 to that: 4 = 7-3. This is described in answer choice B.
An experiment to investigate the survival time in hours of an electronic component consists of placing the parts in a test cell and running them under elevated temperature conditions. Six samples were tested with the following resulting failure times (in hours): 34, 40, 46, 49, 61, 64. (a)Calculate the sample mean and sample standard deviation of the failure time. (b)Determine the range of the true mean at 90% confidence level. (c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time
Answer:
a) The sample mean is of 49 and the sample standard deviation is of 11.7.
b) The range of the true mean at 90% confidence level is of 9.62 hours.
c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Step-by-step explanation:
Question a:
Sample mean:
[tex]\overline{x} = \frac{34+40+46+49+61+64}{6} = 49[/tex]
Sample standard deviation:
[tex]s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7[/tex]
The sample mean is of 49 and the sample standard deviation is of 11.7.
b)Determine the range of the true mean at 90% confidence level.
We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0.150
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. So
[tex]M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62[/tex]
The range of the true mean at 90% confidence level is of 9.62 hours.
(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.
This is the confidence interval, so:
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.
The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.
The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
How far will fiona jog (in feet)
Answer:
1780 ft
Step-by-step explanation:
We need to find the perimeter of the rectangle, given by
P= 2(l+w) where l is the length and w is the width
The units need to be the same
Change 230 yds to ft
230 yd * 3 ft/ y = 690 ft
P = 2(690+200)
P = 2(890)
P =1780
The total number of vertices adjacent to the vertex is called?
Answer:
The degree of vertex is the total number of vertices adjacent to the vertex .
The total number of vertices adjacent to the vertex is called degree of the vertex.
What is vertex?" Vertex is defined as when two adjacent side meet at one point."
According to the question,
The degree of a vertex is always as the total number of adjacent side to the vertex.
If adjacent sides far away from each other degree is more.
If adjacent sides near to each other degree is less.
Hence, the total number of vertices adjacent to the vertex is called degree of the vertex.
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the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?
Answer:
The coefficient of the squared term is 1/25.
Step-by-step explanation:
We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.
And we want to determine the coefficient of the squared term of the equation.
Since we are given the vertex, we can use the vertex form of the quadratic:
[tex]\displaystyle y = a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.
Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:
[tex]\displaystyle y = a(x-2)^2-4[/tex]
y = -3 when x = -3. Solve for a:
[tex]\displaystyle (-3) = a((-3)-2)^2-4[/tex]
Simplify:
[tex]\displaystyle 1 = a(-5)^2\Rightarrow a = \frac{1}{25}[/tex]
Therefore, our function in vertex form is:
[tex]\displaystyle f(x) = \frac{1}{25}\left(x-2)^2-4[/tex]
Hence, the coefficient of the squared term is 1/25.
Answer:
-5
Step-by-step explanation:
from a p e x
Can anyone help with problem 5?
Answer:
Other leg: 25 cm
Hypotenuse: 25√2 cm
Step-by-step explanation:
Hi there!
We are given a 45°-45°-90° triangle, and one leg (a side that makes up the right triangle) measures 25 cm
We want to find the length of the other sides
First, let's find the length of the other leg
A 45°-45°90° triangle is actually an isosceles triangle, and if it was to be drawn, the base angles are 45 and 45 degrees
That means the legs of the right triangle are actually the legs in the isosceles triangle as well
So the other leg is also 25 cm
Now, let's find the length of the hypotenuse, which is the side OPPOSITE from the 90° angle
You can solve for the other side using Pythagorean Theorem if you wish, however, there is a shortcut to finding the hypotenuse
In a 45°-45°-90° triangle, if the length of the legs are a, then the hypotenuse is a√2 cm
So that means the length of the hypotenuse in this case is 25√2 cm
Hope this helps!
39.948859° What is the measurement in degrees, minutes, and seconds?
Answer:
try to calculate
here some examples
Step-by-step explanation:
Decimal Degrees to Degrees, Minutes, Seconds Calculator
Enter decimal degrees to convert to minutes and seconds. See the formulas below to see how it’s done.
Angle:
Decimal:
47.31
°
degrees, minutes, seconds to decimal
Degrees, Minutes, & Seconds:
47° 18′ 36″
I hope it helps
This table shows the ratio of number of people to liters of Find the missing values in the ratio table
ginger ale needed.
A=
People
Ginger Ale
Answer:
A= 2 B= 6
Step-by-step explanation:
Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech and 40% attended both events. If a randomly selected delegate is known to have attended the dinner speech, the probability that he also attended the breakfast forum is
Answer:
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Attended the dinner speech.
Event B: Attended the breakfast forum.
70% attended the dinner speech
This means that [tex]P(A) = 0.7[/tex]
40% attended both events.
This means that [tex]P(A \cap B) = 0.4[/tex]
The probability that he also attended the breakfast forum is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
how many itegers from 15 to 85, inclusive are multibles of 8
Answer:
9 multiples
Step-by-step explanation:
16,24,32,40,48,56,64,72,80
9
Question 14 please show ALL STEPS
List of possible integral roots = 1, -1, 2, -2, 3, -3, 6, -6
List of corresponding remainders = 0, -16, -4, 0, 0, 96, 600, 1764
Check out the table below for a more organized way to represent the answer. The x values are the possible roots while the P(x) values are the corresponding remainders.
====================================================
Explanation:
We'll use the rational root theorem. This says that the factors of the last term divide over the factors of the first coefficient to get the list of all possible rational roots.
We'll be dividing factors of 6 over factors of 1. We'll do the plus and minus version of each. Since we're dividing over +1 or -1, this means that we're basically just looking at the plus minus of the factors of 6.
Those factors are: 1, -1, 2, -2, 3, -3, 6, -6
This is the list of possible integral roots.
Basically we list 1,2,3,6 with the negative versions of each value thrown in as well.
---------------------------------
From there, you plug each value into the P(x) function
If we plugged in x = 1, then,
P(x) = x^4 - 3x^3 - 3x^2 + 11x - 6
P(1) = (1)^4 - 3(1)^3 - 3(1)^2 + 11(1) - 6
P(1) = 1 - 3 - 3 + 11 - 6
P(1) = 0
This shows that x = 1 is a root, since we get a remainder 0. Do the same for the other possible rational roots listed above. You should find (through trial and error) that x = -2 and x = 3 are the other two roots.
for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?
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Answer:
21
Step-by-step explanation:
The number who bought expensive tickets is 3/5 of the number who bought cheap tickets.
(3/5)(35) = 21
21 people bought the more expensive ticket.
Answer:
21 people
Step-by-step explanation:
$9.75 $14.50
5 people to 3 people
35 people to ? people
consider the proportions: 5/3 = 35/?
we need the equivalent fraction of 5/3 that has 35 on the denominator
so 5/3 = (5/3)(7/7) because 7/7 =1, and 5*3 =35
5/3 = 5*7/3*7 = 35/21
Change these percentages to decimals.
30%
45%
60%
5%
1%
55%
80%
10%
Hi can someone answer this question please thank you
Answer:
25
Step-by-step explanation:
5:20
We want to get the second number to 100
100/20 = 5
Multiply each term by 5
5*5 : 20*5
25 : 100
x is 25
Given that,
→ 5 : 20 :: x : 100
Then we have to,
find the second number to 100.
→ 100/20
→ 5
Now multiply each term by 5 in 5:20,
→ 5 × 5 : 20 × 5
→ 25 : 100
→ x = 25
Now these ratio will be,
→ 5 : 20 :: 25 : 100
Hence, the value of x is 25.
Plan production for the next year. The demand forecast is: spring, 20,600; summer, 9,400; fall, 15,400; winter, 18,400. At the beginning of spring, you have 69 workers and 1,030 units in inventory. The union contract specifies that you may lay off workers only once a year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall, respectively. If demand exceeds supply, use overtime in spring only, which means that backorders could occur in winter. You are given these costs: hiring, $130 per new worker; layoff, $260 per worker laid off; holding, $21 per unit-quarter; backorder cost, $9 per unit; regular time labor, $11 per hour; overtime, $17 per hour. Productivity is 0.5 unit per worker hour, eight hours per day, 50 days per quarter.
Find the total cost of this plan. Note: Hiring expense occurs at beginning of Fall. (Leave no cells blank - be certain to enter "O" wherever required.) Fall 15,400 Winter 18,400 15,400 30,800 77 18,400 36,800 77 Spring Summer Forecast 20,600 9,400 Beginning inventory I 1,030 Production required 9,400 Production hours required 39,140 18,800 Regular workforce 69 47 Regular production Overtime hours Overtime production Total production Ending inventory Ending backorders Workers hired Workers laid off Spring Summer Fall Winter Straight time Overtime Inventory Backorder Hiring Layoff Total Total cost
please help, it’s urgent !!!
Answer:
1. purple graph
2. orange graph
3. green graph
4. blue graph
how do we write a set in set- builder method?
Answer:
(×:x is a natural number up to 10) just an example
√12 + √10 − √2) is
(a) A positive rational number
(b) Equal to zero
(c) An irrational number
(d) A negative integer
Hello!
[tex] \bf \sqrt{12} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} \times 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} } \sqrt{ 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \boxed{ 2 \sqrt{3} + \sqrt{10} - \sqrt{2}} [/tex]
Answer: (c) An irrational number
Good luck! :)
