B
Step-by-step explanation:
Consider the function f(x)=x−5ln(x), 1/5≤x≤10.
The absolute maximum value is =
and this occurs at x equals =
The absolute minimum value is =
and this occurs at x equals =
f(x) = x - 5 ln(x)
Get the derivative:
f'(x) = 1 - 5/x
Find the critical points:
• f'(x) = 1 - 5/x = 0 -> 5/x = 1 -> x = 5
• f'(x) is undefined for x = 0, but that's outside the domain of f(x)
Get the second derivative:
f''(x) = 5/x ^2
Check the sign of the second derivative at the critical point x = 5:
f'' (5) = 5/5^2 = 5/25 = 1/5 > 0
Since the second derivative is positive at this point, this means x = 5 is a local minimum.
Check the value of f(x) at the critical point as well as the endpoints of the given domain:
f (5) = 5 - 5 ln(5) ≈ -3.407
f (1/5) = 1/5 - 5 ln(1/5) ≈ 1.809
f (10) = 10 - 5 ln(10) ≈ -1.513
So we have
• absolute maximum = 1/5 - 5 ln(1/5) at x = 1/5
• absolute minimum = 5 - 5 ln(5) at x = 5
The absolute maximum value is f(5)=5−5ln(5), and this occurs at x equals 5
The absolute minimum value is f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5
Given the function f(x)=x−5ln(x),
We are to find the absolute minimum and maximum value of the function
At the turning point f'(x) = x - 5ln(x)
f'(x) = 1 - 5/x
0 = 1 - 5/x
-5/x = -1
-x = -5
x = 5
Find the second derivative of the function;
f''(x) = -5/x²
Substitute the value of x = 5 into the second derivative function to have:
f''(5) = -5/5² = 1/5
Since f''(5) = 1/5 < 0, this is the local maximum and the point x = 5 is the absolute minimum
The absolute maximum value is f(5)=5−5ln(5), and this occurs at x equals 5
The absolute minimum value is f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5
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Explain how your process for solving life’s problems is similar or different from solving math problems.
Answer:
in life problem I solve in my head and not on paper. I enter life's problems calmly and carefully know I can solve them but in math I erase and cry and almost tear my paper apart. someone else can solve your math problem but not your life problem.
C
2
6.28
3
9.42
5
15.70
10
31.40
what explicit formula describes the pattern of this table
Answer:
y - 6.28 = 3.14( x - 2 )
Step-by-step explanation:
Notice that 6.28 is twice the approximate value of pi: 2(3.14), and that
9.42 is three times pi. We can deduce immediately that the slope of the line passing through (2, 6.28) and (3, 9.42) is 3.14.
Using the point-slope formula for the equation of a straight line, we get:
y - 6.28 = 3.14( x - 2 )
A roll of tissue paper towels has the given dimensions. Determine, to the nearest hundred, the volume of the roll
*see attachement for the diagram of the tissue paper
Answer:
Volume of the roll = 3,817.04 cm³
Step-by-step explanation:
The diagram of the roll of the tissue paper given is a model of two cylinders:
✔️Bigger cylinder with diameter (d) of 14 cm and height of 27 cm
✔️ Smaller/inner cylinder with diameter (d) of 4 cm and height of 27 cm
Thus:
The Volume of the roll = volume of bigger cylinder - volume of smaller cylinder
✔️Volume of bigger cylinder = πr²h
r = ½(14) = 7 cm
h = 27 cm
Volume of bigger cylinder = π*7²*27
= 4156.33 cm³
✔️Volume of smaller/inner cylinder = πr²h
r = ½(4) = 2 cm
h = 27 cm
Volume of smaller/inner cylinder = π*2²*27
= 339.29 cm³
✅The Volume of the roll = 4156.33 - 339.29 = 3,817.04 cm³
the product of a number and 5 is increased by 12 the result is 32 find the number
Answer:
4
Step-by-step explanation:
First, to get just the multiplication equation, we need to do,
32-12 = 20
20/5 = 4
The number is 4.
Now let's check our work.
4x5+12=32
The answer is 4.
The required number is 4.
Let the number be x.
Given, the product of x and 5 increased by 12 gives 32.
So in equation form,
[tex]5x+12=32\\[/tex]
Subtracting 12 from both the sides,
[tex]5x+12-12=32-12[/tex]
[tex]5x=20\\\\[/tex]
[tex]x=\dfrac{20}{5}[/tex]
Or, [tex]x=4[/tex]
Hence the required number is 4.
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A farmer would like to estimate the mean amount of
milk produced per day by his 300 cows. He selects a
random sample of 15 cows and records the amount of
milk produced in gallons) by those cows. The dotplot
shows the data. Given that all of the recorded values are integers, what is the value of the standard error of the mean?
0.765
0.792
2.267
2.346
Answer:
0.765
Step-by-step explanation:
The dot plot shows the data
x= 20,21,22,23,24,24,25,25,25,26,26,27,28,29,31
The mean x`= ∑x/n =20+21,+22,+23,+24,+24,+25,+25,+25+,26+,26+,27+,28+,29+,31/15= 376/15
=25.067
where n is the sample size= 15
The standard deviation is σ=2.96
( using calculator)
The standard error is calculated as
SE= σ/√n
SE= 2.96/√15
SE= 0.765
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.
Diet Regular
u u1 u2
n 36 36
x overbar 0.78616 lb 0.81111 lb
s 0.00444 lb 0.00752 lb
a. The test statistic, t:________
b. P-Value: ________
c. Conclusion of test
d. Construct a confidence interveral appropriate for the hypothesis test.
e. Does the confidence interval support conclusion of hypothesis test?
Answer:
Test = 17.143 ;
Pvalue = 0 ;
Reject the Null ;
(-0.028 ; - 0.022) ;
We conclude that content are different.
Step-by-step explanation:
Given that:
μ1 = μ
n1 = 36 ; n2 = 36
x1 = 0.78616 ; x2 = 0.81111
s1 = 0.04444 ; s2 = 0.00752
Test statistic :
(x1 - x2) / √(s1²/n1 + s2²/n2)
(0.78616 - 0.81111) / √(0.00444²/36 + 0.00752²/36)
- 0.02495 / 0.0014554
= 17.143
Pvalue :
Z < 17.143
Pvalue = 0
Since Pvalue < α ; Reject the Null
The confidence interval using a confidence interval calculator is (-0.028 ; - 0.022)
Since the interval does not contain Zero ; then we reject the Null and conclude that the content are different.
Which of the following angles is NOT congruent to 6?
3
2
7
1
Answer:
1
Step-by-step explanation:
We can see that 7 is equal to 6, as opposite angles are the same.
We can also see that 2 is also 6, as corresponding angles are equivalent.
Therefore, 3 is also congruent to 6, as it is equal to 2.
Hope that this helps!
is 2/5 greater than 3/7
Answer:
3/7 is greater than 2/5
Step-by-step explanation:
If you convert the fractions into decimals:
3/7=0.42
2/5=0.4
0.42 is greater than 0.4
La cantidad de automóviles que pasaron por hora por una estación de peaje en una muestra de 8 hs es
Muestra 1: 95 98 102 105 120 130 150 200
Si en la muestra 2 el número medio de autos es 130 con una varianza de 625, calcular las medidas necesarias e indicar qué muestra es más homogénea.
necesito saber como hacerlo
Answer:
198
Step-by-step explanation:
What is 147% as a simplified fraction
147/100
= 1 47/100
100 is the percent out of
and 147 is the percent.
Answer:
147/100
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 147 and 100 is 1
Divide both the numerator and denominator by the GCD
147 ÷ 1
100 ÷ 1
Reduced fraction:
147/ 100
147/100 simplified to lowest terms is 147/100.
What is the value of the expression below when x=3
Answer:
There is no image
Step-by-step explanation:
Try isolating the variable in the equation
A helicopter pad has a circumference of 47.5 yards. Find the approximate diameter of the helicopter pad. Use 3.14 for π.
Answer:
15.1 yd
Step-by-step explanation:
Since the circumference formula is C = πd, d = C/π
and in this case d = (47.5 yd) / 3.14 = 15.1 yd
The approximate diameter of the pad is 15.1 yd.
The approximate diameter of the helicopter pad is,
⇒ d = 15.12 yards
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A helicopter pad has a circumference of 47.5 yards.
Now,
We know that;
Circumference of circle = 2πr
Hence, We get;
⇒ 47.5 = 2 × 3.14 × r
⇒ 47.5 = 6.28r
⇒ r = 47.5 / 6.28
⇒ r = 7.56
Thus, the approximate diameter of the helicopter pad is,
⇒ d = 2r
⇒ d = 2 × 17.56
⇒ d = 15.12 yards
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Start at the origin, shift up 3 units
HELP ME PLEASEEEEEEEEEEEEEEEE
Single Factor ANOVA is a method we use when we want to compare a quantitative variable among more than two categories.
a. True
b. False
Answer:
The given statement is "True".
Step-by-step explanation:
A statistical analytical technique that divides the perceived aggregate unpredictability present throughout an information source even further into 2 components.
Systemic components Random componentsIf relevant information yet another category independent variable, as well as another quantifiable variable of interest, has been obtained, are using a single-way ANOVA.
Thus the above is the true answer.
A box is full of thousands of numbered tickets. We want to estimate the unknown average of all the numbers in the box. To do this, we draw 250 tickets at random. The numbers on these 250 tickets average out to 118 with a standard deviation of 53. Round your values to three decimal places. We estimate the average of all the tickets in the box to be . Attach a give-or-take value to this estimate. (That is, estimate the standard error.) For an 85% confidence interval, about how many standard errors should be added to and subtracted from the estimate
how to find the volume of this cube
2. The perimeter of a rectangular board is 24 cm. If its length is 9 cm and its width is one
third of its length, what is its width?
please answer this i follow and like and rate
Do you think this fish is a gram or kilogram ??
Solve the following system of equations using an inverse matrix. You must also indicate the inverse matrix, A^{-1},A
−1, that was used to solve the system. You may optionally write the inverse matrix with a scalar coefficient.
−3x−2y=−8
−6x−5y=−7
A1=[ ? ] x= ? y=?
Answer:
x-intercept(s):
(
−
8
3
,
0
)
y-intercept(s):
(
0
,
−
4
)
Step-by-step explanation:
The x-intercepts are (83, 0), and the y-intercepts are (0, 4). Matrixes, like numbers, have reciprocals. In the world of matrices, this reciprocal is known as a "inverse matrix."
What is the inverse matrix?The concept of a matrix's inverse is a multidimensional generalization of the concept of a number's reciprocal: just as the product of a number and its inverse equals one, the product of an identity matrix and a square matrix equals one.
A A-1 = A-1 A = I because the identity matrix I is the inverse of a matrix. An invertible matrix is one that has a non-zero determinant and can have its inverse determined. Finding the inverse of a 2x3 matrix is impossible because it is not a square matrix.
Response: (8 3, 0) are the x-intercepts.
(0, 4 ) are the y-intercepts.
Therefore,
-3 x-2 y=-8
Add 2 y to both sides
-3 x-2 y+2 y = -8+2 y
Simplify
[tex]$$-3 x=-8+2 y$$[/tex]
Divide both sides by -3
[tex]$$\frac{-3 x}{-3}=-\frac{8}{-3}+\frac{2 y}{-3}$$[/tex]
Simplify
[tex]$$x=-\frac{-8+2 y}{3}$$[/tex]
Response: (8 3, 0) are the x-intercepts.
(0, 4 ) are the y-intercepts.
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I need help can someone help
Answer:
yes i can but will have to get back to you in about half a hour just doing maths atm with the teacher
Step-by-step explanation:
Tala drives 8 miles to work each day. how many miles does she drive to work in 83 days?
Answer: 664
Step-by-step explanation:
Take the amount of days, and multiply it by the miles per day
so
8 x 83 = 664 miles
Hope this helps!! (^_^)
SOMEONE HELP PLEASE!! Dawn was driving at a steady speed of 67 mph for 10 minutes. How far did she travel in that time?
Answer:
distance = 11.1666 miles (round to 11.1667)
11.1667 mi
How I solved it:
Well, I knew that in one hour, she would go 67 miles.
I then divided the hour into 6 sections (10 min, 20 min, 30, 40, 50 and 60)
So, we divide 67/6
and our answer is 11.1666 (round to 11.1667)
A culture of bacteria grows in a lab according to the model B = 600e^(kt) where t is the measured in hours. The culture reaches a size of 750 after 6 hours. Find the value of k.
NO LINKS!!!!!!
9514 1404 393
Answer:
k ≈ 0.03719
Step-by-step explanation:
Fill in the given numbers and solve for k.
750 = 600e^(6k)
1.25 = e^(6k)
ln(1.25) = 6k . . . . . take the natural log
k = ln(1.25)/6 . . . . . divide by 6
k ≈ 0.03719
64
41
Solve for <1.
« 1 = [?]
720
35°
Answer:
[tex] \displaystyle \angle1 = {73}^{ \circ} [/tex]
Step-by-step explanation:
remember that,
the sum of the interior angles of a triangle is 180°
Thus our equation is
[tex] \displaystyle \angle1 + {72}^{ \circ} + {35}^{ \circ} = {180}^{ \circ} [/tex]
simplify addition:
[tex] \displaystyle \angle1 + {107}^{ \circ} = {180}^{ \circ} [/tex]
cancel 107° from both sides:
[tex] \displaystyle \angle1 = {73}^{ \circ} [/tex]
Step-by-step explanation:
Answer:
Solution given:
<1+72+35°=180°[ interior angle of a triangle is 180]
<1=180-107
<1=73 °
1. Jake is filling up the fish tank below completely with water. How many
cubic feet of water will he need?
A student drops a penny of a house that is 16 feet tall if the equation of height as a function is h(t)= -16t2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the penny to hit the ground
Answer:
Step-by-step explanation:
the correct answer is 1 second
The time it will take for the penny to hit the ground is 1 second.
What is a linear equation?A linear equation has one or two variables.No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
Calculation:-
Given initial feight= 16 feet
h(t)= -16t2 + initial height
for 1 second
⇒ h(1)= -16(1)2 +16
⇒ h = -32 +16
⇒ h = -16 ( 16 feet downward i.e penny will tough the ground)
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HELPP ASAP DONT SEND A FILE PLS DESCRIBE THE TRANSFORMATION RULE FOR ROTATIONS !!! Only ANSWER IF YOU KNOW I NEED THE ANSWR FOR 1 and 3
Answer:
Step-by-step explanation:
I will not give the answer but the rules are:
90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...
180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...
270 Degree Rotation.
Hope at least that helps.
In her first basketball game, Charlotte scored 21 points. In the next game, she scored 15
points. By what percent did her score decrease?
ASAP
Answer:
28.57%
Step-by-step explanation:
Find the percent decrease by dividing the change in the number of points by the original number of points, then multiplying it by 100:
((21 - 15) / 21) x 100
(6 / 21) x 100
= 28.57
So, her score decreased by approximately 28.57%