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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As indicated below, write the equations of the line passing through the point (2, 4) and parallel to the line whose equation is y = x. Complete your work in the space provided. Part 1: Point-Slope form of the linear equation Part 2: Slope-intercept form of the linear equation Part 3: The general form of the linear equation
Part 1
[tex]y-4=x-2[/tex]
Part 2
[tex]y=x+2[/tex]
Part 3
[tex]x-y+2=0[/tex]
Choose the correct statement.
-2 < -3
1 = -1
5 > -6
The statement 5 > -6 is the correct statement.
In this question, we have been given some mathematical statements.
We need to select the correct statement.
We know that, on the number line , numbers to the right are greater than numbers to the left.
Consider 1st statement
-2 < -3
If we see these numbers on the number line, then -2 is right to -3. This means, -2 is greater than -3.
So, above statement is False.
Consider 2nd statement
1 = -1
If we see these numbers on the number line, then we can observe that both the numbers are not equal.
So, above statement is False.
Consider 3rd statement
5 > -6
If we see these numbers on the number line, then 5 is right to -6. This means, 5 is greater than -6.
So, above statement is True.
Therefore, the statement 5 > -6 is the correct statement.
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What is the slope of the line represented by the equation y =4/5x-3?
Answer:
4/5 is the slope of the line
The 5000 that invested in Fund A returned a 3% profit. The amount that invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 5% profit?
The investment in Fund B is $2000.
To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.
If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).
For Example: If the investment is A and profit is x % then the profit is calculated by:
Profit =A×([tex]\frac{x}{100}[/tex])
Now in the given problem, let us consider the amount of investment into the Fund B be x.
Profit in Fund B=10%
Profit in Fund A is 3%.
Investment in Fund A=$5000
Total profit from both investments=3% of 5000+10% of x
[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]
Now the total investment=5000+x
The combined profit for both the Investments is 150+0.1x
But the combined profit is 5% for both investments.
profit=[tex]5\% of(5000+x)[/tex]
[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]
Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.
[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]
Thus we can conclude that she invested $2000 in the Fund B.
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Identify at least two hidden assumptions in the following argument.
I recommend giving to the Charity A because it supports so many worthwhile causes.
Which of the following are hidden assumptions for this argument? Select all that apply.
A. Giving to Charity A is better than giving to Charity B.
B. The money you give is spent on worthwhile causes.
C. Charity A does not support unworthy causes.
D. Charity A supports worthwhile causes.
Answer:
A, B, C yes
D no
Step-by-step explanation:
A. is a no-brainer. yes, that is indirectly implied.
B. this is compared to D a hidden assumption, that the money you give is guaranteed to be spent on worthwhile causes (not to mention what THAT actually means).
C. this goes combined with B. it is suggested that charity A is not engaging in unworthy causes (again, whatever that means).
D. is not hidden. that is openly said.
prove that √ 2 - 1 is irrational
Answer:
a+b/2b is an rational no. because LHS is always equal to RHS. therefore our assumption is wrong. hence , 2√2-1 is an irrational number.
Rectangle ABCD is shown on the grid.
A
(-1,4) 14
3
+2+
4
-6-5-4-312-3₁
(-3-b
B(3,3)
34
C(1-5)
X
What is the area of rectangle ABCD in square units?
O 3√17 square units
O 6√17 square units
O
17 square units
O 34 square units
well, we know it's a rectangle, so we know the opposite sides are perpendicular, so if we just get say the sides AD as its length and BA as its width, that'd give us its area, since it'll just be AD * BA.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad D(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-4}) ~\hfill AD=\sqrt{(~~ -3- (-1)~~)^2 + (~~ -4- 4~~)^2} \\\\\\ ~\hfill AD=\sqrt{( -2)^2 + ( -8)^2}\implies \boxed{AD=\sqrt{68}} \\\\\\ B(\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{4}) ~\hfill BA=\sqrt{(~~ -1- 3~~)^2 + (~~ 4- 3~~)^2}[/tex]
[tex]~\hfill BA=\sqrt{( -4)^2 + (1)^2} \implies \boxed{BA=3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Area}}{(\sqrt{68})(3)\implies (\sqrt{2^2\cdot 17})(3)}\implies (2\sqrt{17})( 3)\implies \LARGE \begin{array}{llll} 6\sqrt{17} \end{array}[/tex]
(33) MOVIES Chaz has a collection of 15 movies downloaded on his media player. He decides to download 3 more movies each month. The function M(t) = 15 + 3t counts
the number of movies M(t) he has after t months. How many movies will he have after
8 months?
Answer: 39
Step-by-step explanation: 15 is the number of movies he has already. The t in the formula stands for months. So simply plug in 8 for t because we want to know how much has has after 8 months
15+3(8)
15+24
=39
In 2019, Company A purchased a commercial building with 8 retail units for $4,200,000. In 2021, Company A decided to sell this building for $4,500,000. Interpret the change as a percentage. Round to the nearest hundredth.
The change as a percentage is 6.7 %
How to calculate the percentage change ?The price of the building in the year 2021 is $4,200,00
The price of the building in 2021 is $4,500,000
Therefore the percentage change can be calculated as follows
= 4,500,000 - 4,200,000/4,500,000 × 100
= 300,000/4,500,000 × 100
= 0.066 × 100
= 6.7 %
Hence the percentage change is 6.7%
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Simplifiy the expression 1/2 cubed - 6 divide √64
Answer:-0.625
Step-by-step explanation:
Scott rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 92 cents for each mile driven. Scott had to pay $150.55 when he returned the truck. For how many miles did he drive the truck?
I need to find how many miles
Answer:
143 miles
Step-by-step explanation:
Let x = number of miles
Let y = total cost
150.55 = .92x + 18.99 Multiply all the way through by 100 to clear the decimal
15055 = 92x + 1899 Subtract 1899 from both sides
13156 = 92x Divide both sides by 92
143 = x
Use an integer to describe the
situations.
6 meters
above sea level
sea level
An integer to describe 6 meters above the sea level would be [tex]+6[/tex] meters.
As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".
We assume that sea level is the datum line and anything above that would be positive and below that would be negative.
So 6 meters above the sea level can be described as [tex]=6meters[/tex].
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A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 14 feet less than 3 times the height. Find the width and the height if the carpenter expects
to use 28 feet of lumber to make it.
Width:
feet
Height:
feet
Question Help: Video
Answer:
w= 3 feet
h= 5 feet
Step-by-step explanation:
H=height; W=width=2H-7ft
W=2H-7ft
2H+4W=22ft Substitute for W
2H+4(2H-7ft)=22ft
2H+8H-28ft=22ft Add 28 ft to each side.
10H=50ft
H=5 ft ANSWER 1: The bookshelf is 5 feet high.
W=2H-7ft=2(5ft)-7ft=10ft-7ft=3ft
ANSWER 2: the bookshelf is 3 feet wide.
CHECK:
2H+4W=22ft
2(5ft)+4(3ft)=22ft
10ft+12ft=22ft
22ft=22ft
Hope this helps!
What is the simplified form of (-5+21) -(5-31)?
A
-10-i
B
-10+5i
- i
5i
WILL GIVE BRIANLIEST
Evaluate the left hand side to find the value of a in the equation in simplest form.
The value of a in the equation in the simplest form will be 17 / 6.
We are given an equation:
x³ / x^(1/6) = x^(a)
We need to evaluate the left hand side to find the value of a in the equation in simplest form.
We know that:
x^ (a) / x^ (b) = x^ ( a - b)
Using this, we get that:
x^ (3 - 1/6) = x^ (a)
x^ (17/6) = x^ (a)
By comparing the bases, we get the value of a as:
a = 17 / 6.
Therefore, the value of a in the equation in the simplest form will be 17 / 6.
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Janayea wanted to change 0.079 to a percent. She changed it to 79%. Which statement is true?
A) Janayea Is Correct?
B) Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.
C) Janayea should have moved the decimal point of 0.079 two places to the right to get 7.9%.
Answer:
Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.
solve for x please
4 / x • 26 / 2
Answer:
x = 3.25
Step-by-step explanation:
Use the Rule of 3 to solve this
Work in picture
A sloth travels about 7 feet every minute. Generate the set of ordered pairs for the ratio relationship between the total distance traveled y and the number of minutes x for a total of 1, 2, 3, and 4 minutes.
Answer:
(1, 7)
(2, 14)
(3, 21)
(4, 28)
Step-by-step explanation:
find the quotient 17 ÷ 6 8/10
The ratio of EQUATION the outcome is (17/6)/(8/10) = 3.5416667.
What in mathematics is a quotient?The quotient is the result of dividing two numbers by each other. As in the case of 8 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4.
based on the available facts;
Divide: 17/6 : 8/10
= 17/6· 10/8
= 17 · 10/6 · 8
= 170/48
= 85/ 24
= 85/24
When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal value. Finding the reciprocal of the second fraction is the first sub-step. For example, the reciprocal of 8/10 is 10/8. Multiply the two numerators after that. Multiply the two denominators after that. The intermediate step that comes after canceling by a common factor of 2 yields 85/24.
Therefore, eight tenths of seventeen sixths equal eighty-five twenty-fourths.
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The Burger Joint expects to serve 250 hamburgers on Saturday evening. Each hamburger weighs 6
ounces before it is cooked. The chef orders ground beef in bulk by the pound from Outwest Meats,
ready to be formed into hamburger patties by the kitchen staff. How much ground beef will the chef
need to order to prepare for Saturday?
Answer:150 ounces
Step-by-step explanation:
Divide the fractions. ½÷⅞
Answer:1/2 / 7/8 = 8/14 = 4/7
Step-by-step explanation: switch the numbers on the second fraction and multiply. 1 * 8 = 8 2 * 7 = 14, 8/14 simplify: 4/7
whats the answer
to 0.75(8+e)=2-1.25e
The value of e from the given equation is -1.78
Linear functionsLinear functions are function that has a leading degree of 1
Given the expression below;
0.75(8+e)=2-1.25e
Expand to have;
0.75(8) + 0.75e = 2-1.25e
6 + 0.75e = 2 - 1.5e
6-2 = -1.5e - 0.75e
4 = -2.25e
e = 4/-2.25
e = -1.78
Hence the value of e from the given equation is -1.78
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Is this argument inductive or deductive?
"Whenever I get off at Valencia rather than McBean, I get to campus faster. So Valencia must be
the faster route to school."
Answer:
Step-by-step explanation:
Indutivo
Solve For x
[tex] \tt \red{4x + 2 = -8}[/tex]
Thank uh ~
Answer:
The answer will be -5/2.
Step-by-step explanation:
[tex]4x + 2 = - 8 \\ subtracting \: 2 \: from \: each \: sides \: we \: get \\ 4x + 2 - 2 = - 8 - 2 \\ 4x = - 10 \\ diving \: both \: sides \: by \: 4 \: we \: get \\ \frac{4x}{4} = \frac{ - 10}{4} \\ x = \frac{ - 5 \times 2}{2 \times 2} \\ x = \frac{ - 5}{2} [/tex]
A researcher who is interested in the behavior of chimps believes that temperature is related to aggression in this species of animal. She goes out to her local zoo during a particular weekend and adjusts the temperature of their climate-controlled habitat to 50-degrees, 70-degrees and 90-degrees Fahrenheit over the course of three days, noting the number of aggressive acts she observes at each temperature level.
A) What is the independent variable?
B) What is the dependent variable?
C) Is the dependent variable discrete or continuous?
D) What scale of measurement (nominal, ordinal, interval or ratio) is used to measure the dependent variable? What research method is being used (experimental or observational), and why?
The experimental research conducted by the scientist takes into account the following factors:
a)The change in temperature is the independent variable.
b) The effect of temperature on the chimp's act of aggression is the dependent variable.
c)The dependent variable is continuous.
d)The scale of measurement used to measure the dependent variable is interval.
e) The research method being used here is experimental.
In the above experiment the researcher wants to see the change in the aggression of the chimp when there is a change in temperature in the zoo.
In this experiment there are two variables that are being used, independent and dependent.The independent variable is the change in temperature as it is regulated by the researcher.The dependent variable is the change in the aggressive nature of the chimps, as the change in nature is directly affected by the change in temperature. The dependent variable(mood of the chimp) is continuous, as the value cannot be defined separately.Since the data is not discreet but continuous , the scale of measurement used is interval.The research method being used is experimental , because the researcher is controlling the variable temperature to see the effect of the temperature change on the chimps. So the researcher is directly experimenting on the chimps by changing an external factor. So the experiment is not observational.To learn more about research experiment and variables:
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Find the circumference and area of a circle with radius 7 cm. Express your answer in terms of π.
Answer:
Circumference = 2πr=2×
7
22
×7=44 cm
Area = πr
2
=
7
22
×7×7=154 cm
2
Answer:
With a circle with radius 7 cm, the circumference of given circle is 14π (cm) and the area is 49π (cm²).
Step-by-step explanation:
Given: radius = 7 cm
Circumference of a circle: C = 2πr
C = 2πr
Substitute given value radius.
C = 2π(7)
Multiply 7 and 2.
C = 14π cm.
Area of a circle: A = πr²
A = πr²
Substitute given value radius.
A = π(7)²
Square the 7.
A = 49π cm²
The sales tax in Jorge's state is 7%. Jorge bought a Ford Mustang having a sales tax of $1,928.22. What was the cost of the car?
The cost of the car is $27,546
How to calculate the cost of the car ?The sales tax is 7%
Jorge bought a ford mustang having a sales tax of $1,928.22
Therefore the cost of the car can be calculated as follows
1928.22÷ 7/100
= 1928.22/0.07
= 27,546
Hence the cost of the car is $27,546
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Thunder from a bolt of lightning travels 1/10 mile in 1/2 second. At this rate, how many miles can it travel in one second?
Answer:
1/5 mile
Step-by-step explanation:
1/10 mile in 1/2 second
This can be written as a ratio:
1/10 mile : 1/2 second
We need the ratio in terms of 1 second, so multiply both numbers in the ratio be 2.
2 × 1/10 mile : 2 × 1/2 second =
= 2/10 mile : 1 second
= 1/5 mile : 1 second
Answer: 1/5 mile
PLEASE ANSWER AND will report if your answer is wrong/incorrect
6 less the quantity 9 times a number
hi
with " x' a number then :
6 -9X