Answer: -19
Step-by-step explanation:
n=number
6n+1=-113
6n=-114
n=-19
differentiate xlnx from first principles
Answer:
formula for the derivative of x*lnx is equal to 1 + lnx.
Step-by-step explanation:
we need to find derivative of f(x) = x*lnx,
so we take the limiting value as x approaches x + h.
To simplify this, we set x = x + h,
and we want to take the limiting value as h approaches 0.
Now according to first derivative formula we have;
f'(x) = [tex]\lim_{h \to \zer0}[/tex]f(x+h) - f(x)]/[(x+h) - x]
[tex]\lim_{h \to \zer0}[/tex][ ln (1 + x) ] / x = 1
ln a - ln b = ln(a/b)
Using the above formulas, we have
d(xlnx)/dx = [tex]\lim_{h \to \zer0}[/tex][(x+h) ln(x+h) - xlnx]/[(x+h) - x]
= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) + h ln(x+h) - xlnx]/h
= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) - x lnx + h ln(x+h)]/h
= [tex]\lim_{h \to \zer0}\\[/tex][x(ln(x+h) - lnx) + h ln(x+h)]/h
=[tex]\lim_{h \to \zer0}[/tex][x ln [(x+h)/x] + h ln(x+h)]/h
=[tex]\lim_{h \to \zer0}[/tex][x ln (1+h/x) + h ln(x+h)]/h
=[tex]\lim_{h \to \zer0}[/tex] [x ln (1+h/x)]/h + limh→0 ln(x+h)
= [tex]\lim_{h \to \zer0}[/tex][ ln (1 + h/x) ] / (h/x) + limh→0 ln(x+h)
= 1 + lnx --- [Using limit formula [tex]\lim_{h \to \zer0}[/tex] [ ln (1 + x) ] / x = 1]
Hence, we have proved that the formula for the derivative of x*lnx is equal to 1 + lnx.
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Answer:
Step-by-step explanation:
In this section, we will determine the differentiate of xlnx using the first principle of derivatives, that is, the definition of limits. To derive the derivative of f(x) = xlnx, we take the limiting value as x approaches x + h. To simplify this, we set x = x + h, and we want to take the limiting value as h approaches 0. We will use the following formulas to prove the result:
f'(x) = limh→0[f(x+h) - f(x)]/[(x+h) - x]
limx→0 [ ln (1 + x) ] / x = 1
ln a - ln b = ln(a/b)
Using the above formulas, we have
d(xlnx)/dx = limh→0[(x+h) ln(x+h) - xlnx]/[(x+h) - x]
= limh→0[x ln(x+h) + h ln(x+h) - xlnx]/h
= limh→0[x ln(x+h) - x lnx + h ln(x+h)]/h
= limh→0[x(ln(x+h) - lnx) + h ln(x+h)]/h
= limh→0[x ln [(x+h)/x] + h ln(x+h)]/h
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Video on Converting from different bases to base 10 [+]
Convert the following base 2 numeral to a base 10 numeral and enter your answer in the box.
101011
(Remember, the above number is in Base 2!)
Base 10 numeral:
Note: Only enter your final result.
Question Help: Video Message instructor
Submit Question
101011 in base 2 is equal to 43 in base 10
For positive integer n, defined
[tex] \rm f(n) = n + \frac{16 + 5n - 3 {n}^{2} }{4n + 3 {n}^{2} } + \frac{32 + n - 3 {n}^{2} }{8n + {3n}^{2} } + \frac{48 - 3n - 3 {n}^{2} }{1 2n+3 {n}^{2} } + \cdots + \frac{25 {n} - 7n^{2} }{7 {n}^{2} } [/tex]
Then, the value of [tex] \displaystyle\rm\lim_{n \to \infty } [/tex] is equal to
Following the first term [tex]n[/tex], the [tex]k[/tex]-th term [tex]\left(k\in\{1,2,3,\ldots,n\}\right)[/tex] in [tex]f(n)[/tex] is given by
[tex]\dfrac{16k + (9-4k)n - 3n^2}{4kn + 3n^2}[/tex]
That is,
[tex]k=1 \implies \dfrac{16 + (9-4)n - 3n^2}{4n + 3n^2} = \dfrac{16 + 5n - 3n^2}{4n + 3n^2}[/tex]
[tex]k=2 \implies \dfrac{16\cdot2 + (9-8)n - 3n^2}{4\cdot2n + 3n^2} = \dfrac{32 + n - 3n^2}{8n + 3n^2}[/tex]
and so on, up to
[tex]k=n \implies \dfrac{16n + (9-4n)n - 3n^2}{4n^2 + 3n^2} = \dfrac{25n - 7n^2}{7n^2}[/tex]
We then have
[tex]\displaystyle f(n) = n + \sum_{k=1}^n \frac{16k + (9-4k)n - 3n^2}{4kn + 3n^2} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} - \frac1n \sum_{k=1}^n \frac{4kn + 3n^2}{4k + 3n} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}- \frac1n \sum_{k=1}^n n \\\\ ~~~~~~~ = \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}[/tex]
Now as [tex]n\to\infty[/tex], the right side converges to a definite integral.
[tex]\displaystyle \lim_{n\to\infty} f(n) = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} \\\\ ~~~~~~~~~~~~~ \,= \int_0^1 \frac{16x + 9}{4x + 3} \, dx[/tex]
Wrap up by substituting [tex]x\mapsto\frac{x-3}4[/tex].
[tex]\displaystyle \lim_{n\to\infty} f(n) = \frac14 \int_0^1 \frac{16x + 9}{4x + 3} \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \frac{4x - 3}x \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \left(4 - \frac3x\right) \, dx \\\\ ~~~~~~~~~~~~~\, = \left. \frac14 (4x - 3\ln|x|) \right\vert_3^7\\\\ ~~~~~~~~~~~~~\, = \boxed{4 + \frac34 \ln\left(\frac37\right)}[/tex]
For the third week of July, Barbara Watson worked 55.50 hours. Barbara earns $10.40 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
The highest point in a country has an elevation of 14,291 feet. The lowest point in a country is at 508 fest below sea level. How much higher is the highest point then the lowest point?
The highest point is ____ ft. higher than the lowest point
( the answer is not 13,783 )
The highest point is 14799 ft. higher than the lowest point.
How to calculate the value?From the information, the highest point in a country has an elevation of 14,291 feet. The lowest point in a country is at 508 fest below sea level.
The difference between the points will be:
= 14291 - (-508)
= 14291 + 508
= 14799 feet
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please help
maths geometry
Step-by-step explanation:
(1)
FP = FN
makes the triangle FNP an isoceles triangle (both legs have the same length). and that means both angles of these equal legs with the third side (PN) must be equal.
therefore, the angle N = P2 = 56°.
and we know that the angle P = P1 + P2 = 68 + 56 = 124°.
LE = LM
makes the triangle ELM an isoceles triangle. because of that, both angles of these 2 legs with the third side (ME) are equal.
therefore, M1 = E1 = 62°.
the fact that the sum of all angles in a triangle is always 180° gives us the angle L
180 = 62 + 62 + angle L = 124 + angle L
56° = angle L
because angles L and P are supplementary (that means together they have 180°, which is true as 124 + 56 = 180), it means that LM || PN. as this pair of supplementary angles means that their connecting line LP is intersecting the lines LM and PN at the same angles, which makes LM parallel to PN.
and as angle N = angle L (56°), this also proves that MN is parallel to LP (as now the line PN intersects LP and MN at the same angles and N and P are supplementary angles).
(2)
with the proof in (1) that we have 2 sets of parallel sidelines (LP || MN, LM || PN), this makes LMNP per basic definition a parallelogram.
A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. Outline the feasible region that can be used to find the number of batches of bread and muffins that should be made to maximize profits? Use the color RED to indicate the feasible region!
Step-by-step explanation:
let the number of wholewheat bread batches be x
let the number of muffin batches be y
prep condition: 4x + (1/2)y ≤ 16 or 8x + y ≤ 32
baking condition : 1x + (1/2)y ≤ 10 or 2x + y ≤ 20
graph each of those in the first quadrant shading in the region below each one.
Final shading is the region satisfying both conditions.
profit = 35x + 10y
allow this line to "slide" away from the origin as far as you can.
It should be clear that the farthest we can go is the intersection of
8x+y = 32 and
2x + y = 20 or the x and y intercepts of our two boundary lines.
subtract them as they are:
6x = 12
x = 2
then in our head , y = 16
max profit = 2(35) + 10(16) = 230
Just to make sure, I will test the intercepts of our intersecting region, namely (4,0) and (0,20)
for (4,0) profit = 4(35)+1 = 140
for (0,32) profit = 0 + 10(20) = 200
so max profit is 230 when x=2 and y=16
(notice all the prep time and baking time is utelized)
michael read 135 pages in 90 minutes. select all of the rates that have the same constant rate of change as michael's rate.
#1) 180 pages in 2 hours?
#2) 60 pages in 30 minutes?
#3) 108 pages in 2 1/2 hours?
#4) 150 pages in 1 hour?
#5) 225 pages in 150 minutes?
#6) 210 pages in 2 hour 2 minutes?
Answer:
#1) & #5) are the rates that have the same constant rate of change as Micheal's rate.
A company makes steel rods shaped like cylinders. Each rod has a radius of 3 centimeters and a height of 40 centimeters. If the company used 48,607.2 cm³
of steel, how many rods did it make?
Use 3.14 for, and do not round your answer.
Answer:
heheghgcfyhcggh I am a bit of a bit of a bit of a bit of a bit of a bit of a bit
Which mixed number is equivalent to the improper fraction?
2/
OA. 22
O B. 22
7
O C. 11/1/2
O D. 32
Answer:
answer should be A. 2⅖
Step-by-step explanation:
you can find out by turning it into an improper fraction: =5×2+2/5
=10+2/5
=12/5
What is the area, in square feet, of a rectangle whose width is 6 feet and whose length is 2 feet more
than three times its width?
Answer:
120
Step-by-step explanation:
l = (w*3)+2
w = 6
area = ((6*3)+2) * 6
((18) + 2) * 6
20 * 6
120
Find the distance between X(-2,4) and Y(6,1)
Answer:
Exact Distance = [tex]\boldsymbol{\sqrt{73}}[/tex] units
Approximate Distance = 8.544 units
====================================================
Explanation:
I'll relabel the points as A and B, and I'll be using the distance formula.
[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (6,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-6)^2 + (4-1)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\[/tex]
The exact distance is [tex]\sqrt{73}[/tex] units.
The approximate distance is roughly 8.544 units.
Round the approximate value however your teacher instructs.
The table lists how poverty level income
cutoffs (in dollars) for a family of four have
changed over time. Use the midpoint
formula to approximate the poverty level
cutoff in 1987 to the nearest dollar.
The poverty level cutoff in 1987 was dollars.
(Round to the nearest dollar as needed.)
Year
1970
1980
1990
2000
Points: 0 of 1
Income (in dollars)
3703
8234
13575
17371
Midpoint formula : -
Midpoint calculation
The midpoint formula is a method used to locate the midway point between two coordinates on a graph. The midpoint of a line segment with endpoints A and B is the point that is precisely between A and B, that is, it is placed at the same distance from A and B, as shown in the illustration below.
The midpoint formula can be utilized when two points on a graph in the coordinate plane are known. The midpoint M of two points (x1, y1) and (x2, y2) is:
Notice that the midpoint formula includes calculating an average of the x- and y-values of two coordinates. The midway formula may be simpler to recall as a result. The sum of two number is equal to multiplying a number by 2. In a coordinate system, a line segment's midpoint is defined as the point midway between two points in the vertical and horizontal directions. This value is equivalent to the line segment's average x- and y-coordinates. It should be rather simple to recall the midway formula if you keep this in mind.
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Explain why this is not true. WILL GIVE BRAINLIEST
Answer:
x(assuming x = 1) + 3 is not less than a negative number(-2).-5 + 3 is 2, so that should be put as equal.-2 is equal to -2.2 is greater than -2 on a scale of positive to negative.PLEASE HELP
5|12-r|>15
Step-by-step explanation:
5.|12 - r| > 15
|12 - r| > 15/5
|12 - r| > 3
12 - r < -3 or 12 - r > 3
-r < -3 - 12 or -r > 3 - 12
-r < -15 or -r > -9
r > 15 or r < 9
Percent change from 10,000 to 10,200
when a pipe constricts as shown in the figure below, the velocity v of fluid flowing through the pipe is inversely proportional to the pipes cross sectional area a. suppose water flows through a section of pipe of area 10 cm^2 at a velocity of 4 m/s. if the pipe constricts to an area of 2.5 cm^2, what will its velocity be in this section of pipe
Answer:
A because of the way the pipe is designed
If m∠NOL=54° then m∠FOG=__
8. A fever is generally considered to be a body temperature greater than
100°F. Your friend has a temperature of 37°C. Does your friend have a
fever when the temperature increases by 1°F? 1°C?
The friend doesn't have a fever when the temperature increases by 1°C.
How to convert the temperature?To convert Celcius to Fahrenheit,we have to multiply by 1.8 and add 32°.
This will be:
37°C = (37 × 1.8) + 32
= 98.6
When we add 1°, we will get 99.6.
Therefore, the friend doesn't have a fever when the temperature increases by 1°C.
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1 fluid oz = ______
please answer asap
Find n(S ∩ T) given that n(S)=6, n(T)=9 and n(S ∪ T)=15.
Answer:
0
Step-by-step explanation:
[tex]n(S \cup T)=n(S)+n(T)-n(S \cap T) \\ \\ 15=15-n(S \cap T) \\ \\ n(S \cap T)=0[/tex]
Simplify 7+5c+4d-8c+d
Step-by-step explanation:
if there is no typo the expression is :
7 + 5c + 4d - 8c + d
to simplify combine all terms with the same variable and exponent of that variable.
so, this is
7 + (5c - 8c) + (4d + d) = 7 - 3c + 5d
Answer:
-3c+5d+7
Step-by-step explanation:
Vertical asymptotes at x=−1 and x=4 , x -intercepts at (−5,0) and (2,0) , horizontal asymptote at y=−4
solve for f(x)
Answer is f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]
vertical asymptote, the denominator must be contained (x−5)
and for zeros the numerator must be contained (x−2)
then we get,
So far f(x)= f(x)= [tex]\frac{ (x - 2)}{x - 5}[/tex]
For slant asymptote, quotient of numerator divided by denominator must be (x+4)
Therefore:
f(x)= [tex]\frac{(x + 4) (x - 2)}{x - 5}[/tex]
after solving this equation we get,
So f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]
A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.
In Mathematics, a slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.
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At Skyrocket Amusement Park, 30% of the rides are roller coasters. There are a total of 18 roller coasters. How many rides are there at Skyrocket Amusement Park in all?
Answer: 60 rides
Step-by-step explanation:
18/30% = (as fraction) 180/3
= 60
Multiply.
4.62 x 10^6=???
Answer:
[tex]=4620000x[/tex]
Step-by-step explanation:
[tex]=1000000\cdot \:4.62x[/tex]
[tex]=4620000x[/tex]
Answer:
4620000
Step-by-step explanation:
4.62x10^6
1000000x4.62
Jason has $200 Karen has 7/8 as much money as him how much money does Karen have
Answer:
175
Step-by-step explanation:
because 7/8 of 200 is 175
Suppose there are 17 jelly beans in a box—2 red, 4 blue, 4 white, and 7 green.
What part of the jelly beans is blue? Express your answer in each of the forms requested.
As a fraction ____
Hint: To enter a fraction, use the forward slash button on the keyboard.
As a decimal rounded to the nearest ten-thousandth (four decimal places). _______
As a percentage rounded to the nearest hundredth (two decimal places) ______
Answer: 4/17
0.2353
0.24
Step-by-step explanation:
4 blue jelly beans. 17 total jelly beans.
4/17=0.235294
0.235294=0.2353
0.2353=0.24
Which of the following is correct?
Group of answer choices
10 mg = 0.001 gm
1L = 1000 mL
1 mcg = 0.1 mg
1000L = 1 mL
Answer: 1L = 1000 mL
Step-by-step explanation:
1. 1 milligram (mg) is equal to 0.001 gram (gm), so 10mg = 0.01. The first choice is incorrect
2. 1 liter (L) = 1000 milliliter (mL) so the second choice is correct
3. 1 microgram (mcg) is equal to 0.001 milligram (mg), so the third choice is incorrect.
4. 1 liter (L) = 1000 milliliter (mL), so the fourth choice is evidently incorrect. (1000 L would be 1,000,000 mL)
Rewrite the expression [tex]\sqrt (4x)}[/tex] using rational exponents
The expression √4x using rational exponents ( 4x )^{\frac{1}{2} } .
What is rational exponents?
Expressions having exponents that are rational values are known as rational exponents (also known as fractional exponents) (as opposed to integers ). It is beneficial to give rational exponents serious consideration even though all the standard exponent criteria still apply.What is Integer Exponents?
In mathematics, exponents that should be integers are known as integer exponents. It may be an integer that is either positive or negative. It specifies how many times the base number should be multiplied by itself using positive integer exponents.√4x
use [tex]\sqrt[n]{a^{x} } = a^{x/n}[/tex]
to rewrite
√4x = [tex]( 4x )^{\frac{1}{2} }[/tex]
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Austin buys cookies and oranges at the store.
He pays a total of $34.18.
He pays a total of $6.86 for the cookies.
He buys 4 bags of oranges that each cost the same amount.
How much does each bag of oranges cos
Answer:...
Step-by-step explanation:
Answer:
Step-by-step explanation:
444
