state the rule of differentiation for the logarithmic function f(x). how does it differ from the derivative formula for ?
Answers
The main difference between these two derivative formulas is the presence of the variable x in the denominator of the natural logarithmic function's derivative formula. This is due to the fact that the natural logarithmic function is the inverse function of the exponential function, and therefore their derivative formulas are related in this way.
The rule for differentiating the natural logarithmic function f(x) = ln(x) is:
f'(x) = 1/x
This means that the derivative of the natural logarithmic function with respect to x is equal to the reciprocal of x.
The rule for differentiating the exponential function g(x) = e^x is:
g'(x) = e^x
This means that the derivative of the exponential function with respect to x is equal to the function itself.
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Related Questions
find the yy -component of vector a⃗ a→ = (5.0 m/s2m/s2 , −y−y -direction).
Answers
The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.
Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s² Answer: 0 m/s².
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The yy-component of vector a⃗ a→ is -y-direction.
Explanation:The yy-component of a vector represents the magnitude of the vector in the y-direction.
In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).
Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.
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Use a net to find the surface area of the prism. 7 cm 10 cm 5 cm
Answers
The surface eof the prism is 6254900
the perimeter of a rectangular field is is 84m.If the width of the rectangle is 6m less than the length,then find the dimensions?please friends help!!!!!!!!
Answers
Answer:
24
**Solving Steps**
2 x (2 x X - 6) = 84
4x-12=84
84+12=96
96/4 = 24
Hope it helps.
Can someone PLEASE HELLPP MEE
Answers
2 1/2 divided by 1 7/8
SHOW YOUR WORK and if you do i'll give you brainiest :)
Answers
Answer:
1.33
Step-by-step explanation:
2 1/2=2.5
1 7/8=1.87
=1.33
For f(x) = -7x + 14, evaluate f(3)
Answers
Answer:
f(3) = -7
Step-by-step explanation:
f(3) = -7(3) + 14
f(3) = -21 + 14
f(3) = -7
Determine the maximum deflection of the simply supported beam. E= 200 GPa and.i = 39,9 (10^6) M^4
Answers
The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.
The maximum deflection of the simply supported beam is given by:
Maximum deflection = (5PL^3)/(384EI)
where P is the load applied to the beam, L is the length of the beam, E is the Young's Modulus of the beam material, and I is the moment of inertia of the beam.
Substituting the given values into the equation, we get:
Maximum deflection = (5*P*L^3)/(384*200*10^9*39.9*10^6)
= (5*P*L^3)/(1536.3*10^15)
= (5*P*L^3)/1536.3*10^15 m
The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.
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Why did the National Assembly break away from the Estates General?
Answers
After Louis XVI's failed attempts to sabotage the Assembly and to keep the three estates separate, the Estates-General ceased to exist, becoming the National Assembly. It renamed itself the National Constituent Assembly on July 9 and began to function as a governing body and constitution-drafter.
National assembly
The National Assembly was the first revolutionary government of the French Revolution and existed from June 14th to July 9th in 1789. The National Assembly was created amidst the turmoil of the Estates-General that Louis XVI called in 1789 to deal with the looming economic crisis in France.
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In regression, what we want to establish is the exact numerical relationship between the two variables so that, for any given profit centre, we can try to forecast profit based on some causal value.
Select one:
True/False
Whereas time-series and causal models rely on quantitative data, qualitative models attempt to incorporate judgmental or subjective factors into the forecasting model.
Select one:
True/False
Answers
In regression, what we want to establish is the exact numerical relationship between the two variables so that, for any given profit centre, we can try to forecast profit based on some causal value. This statement is true.
Regression is a statistical tool that is utilized to establish the relationship between two variables. It examines whether there is a cause-and-effect connection between the two variables. It is commonly used in econometrics and finance to forecast and predict the future of a product or a business. The relationship between two variables is represented graphically on a scatter plot with regression analysis. Whereas time-series and causal models rely on quantitative data, qualitative models attempt to incorporate judgmental or subjective factors into the forecasting model. This statement is false. Qualitative methods, also known as judgmental techniques, rely on expert opinion and subjective information to make forecasts. Whereas time-series and causal models rely on quantitative data, qualitative models attempt to incorporate judgmental or subjective factors into the forecasting model.
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Which is the equation of the line with slope 5 that contains point (-2, -3)?
A. y+2=5(x-3)
B. y+3=5(x+2)
C. y-3=5(x-2)
D. y-2=5(x-3)
Answers
Answer:
y+3=5(x+2)
Step-by-step explanation
1.y+3=5(x+2)
2.y+3=5x+10
Substitute
3.-3+3=5(-2)+10
4.0=-10+10
5.0=0
What quadrant is the solution?1.) quadrant III2.) quadrant II3.) quadrant IV4.) quadrant I
Answers
We have the following:
The solution of a system of equations is the value or values that make all the equations in the system valid. The graphs of the equations in the system tell you how many solutions there are for that system.
If the graphs of the equations intersect, then there is a solution that is valid for both equations.
The lines intersect in the first quadrant, therefore the correct answer is 4.) Quadrant I
A reservoir is in the shape of a circle of radius 2000 m. The water levels drops 2 cm over a period of a week. At what rate is the lake losing water? ______ cubic meters per hour
Answers
The reservoir is losing water at a rate of approximately 1,495.9 cubic meters per hour. The water level dropped by 2 cm over a period of one week.
Given that,
Reservoir shape: Circle with a radius of 2000 m
Water level drop: 2 cm over a period of one week
Conversion: 2 cm which is equivalent to 0.02 m
Volume calculation: V = πr²h
To find the rate at which the lake is losing water in cubic meters per hour, Convert the given measurements into a consistent unit of measure.
First, let's convert the drop in water level from centimetres to meters.
Since, 1 = 100 centimeters,
The drop in water level is 2 cm ÷ 100 = 0.02 meters.
Since the reservoir is in the shape of a circle,
Calculate the volume of the water lost using the formula for the volume of a cylinder:
V = πr²h,
Where,
V is the volume,
π is a mathematical constant (approximately 3.14159),
r is the radius,
h is the height (or drop in water level).
Substituting the given values,
V = 3.14159 x (2000)² x 0.02
V = 251,327.41 cubic meters (rounded to two decimal places).
Since the water level drops over a period of one week,
Convert this to hours:
There are 7 days x 24 hours = 168 hours in a week.
Finally, to find the rate at which the lake is losing water,
Divide the volume lost by the time duration:
251,327.41 cubic meters / 168 hours = 1,495.9 cubic meters per hour (rounded to two decimal places).
Hence,
The reservoir is losing water at a rate of approximately 1,495.9 cubic meters per hour.
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Jeannie got a new pair of eye glasses. She was able to pay $15 at the
time she received her glasses. She will pay $12 each month on the
balance. The original cost of the glasses was $87.
a. Write an equation to determine how many months it will take
Jeannie to pay for her glasses?
Answers
Answer:
Equation A. 12x=87
what decimal number corresponds to the binary number 11111111?
Answers
The decimal number that corresponds to the binary number 11111111 is 255.
What is decimal number?The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.
Here,
In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.
For 11111111, the calculation would be:
=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
=255
The decimal equivalent of the binary number 11111111 is 255.
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name the property of real numbers illustrated by each equation
Answers
The property of real numbers illustrated by each equation depends on the specific equation. However, some common properties of real numbers include the commutative property, associative property, distributive property, identity property, and inverse property.
The property of real numbers illustrated by each equation depends on the specific equation. However, there are several properties of real numbers that can be applied to equations:
commutative property: This property states that the order of addition or multiplication does not affect the result. For example, a + b = b + a and a * b = b * a.associative property: This property states that the grouping of numbers in addition or multiplication does not affect the result. For example, (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c).distributive property: This property states that multiplication distributes over addition. For example, a * (b + c) = (a * b) + (a * c).identity property: This property states that there exist unique elements called identity elements for addition and multiplication. For addition, the identity element is 0, and for multiplication, the identity element is 1. For example, a + 0 = a and a * 1 = a.inverse property: This property states that every real number has an additive inverse and a multiplicative inverse. The additive inverse of a number a is -a, and the multiplicative inverse of a non-zero number a is 1/a. For example, a + (-a) = 0 and a * (1/a) = 1.Learn more:About property of real numbers here:
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I need help on this and the first person who answer correctly gets a BRANLIST
Answers
Answer:
135 degrees
Step-by-step explanation:
A triangle is 180 degrees and because the triangle has a 90 degree and an 45, it would add up to 135 and 180 minus 135 is 45.
(1) An architect firm uses an average of 60 boxes of copier paper a day. The fim operates 280 days a year. Storage and handling costs for the paper are $30 a year per box, and its costs approximately $60 to order and receive a shipment of paper. (a) What quantity order size would minimize the total annual inventory cost? (b) Determine the minimum total annual inventory cost. (c) The office manager is currently using an order size of 300 boxes. The partners of the firm expect the office to be managed "in a cost-efficient manner." Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes):
Answers
Part a: What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost
The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)
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2. Valerie paid \( \$ 170 \) for an item that was originally priced at \( \$ 550 \). What percent of the original price did Valerie pay? Round your answer to the nearest tenth of a percent
Answers
Valerie paid approximately 30.9% of the original price.
Here, we have,
To find the percentage of the original price that Valerie paid, we can use the formula:
Percentage = (Amount Paid / Original Price) * 100
Given that
Valerie paid $170 for an item originally priced at $550, we can substitute these values into the formula:
Percentage = (170 / 550) * 100
To calculate the percentage, we can divide the amount paid by the original price and then multiply by 100:
Percentage = (170 / 550) * 100
Calculating this expression gives us:
Percentage = 30.90909090909091
Rounding this to the nearest tenth of a percent, we get:
Percentage ≈ 30.9%
Therefore, Valerie paid approximately 30.9% of the original price.
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the concentration of a drug in a patient's bloodstream is monitored over 10-minute intervals for two hours. t (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 c (mg) 0 2 17 37 55 72 89 103 111 113 113 103 68 a.) how fast is the concentration of the drug changing at 50 minutes? 1.7 mg/min b.) how fast is the concentration of the drug changing at 85 minutes? 1 mg/min c.) is the drug's concentration increasing or decreasing at 115 minutes? decreasing
Answers
a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.
b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.
c) The drug's concentration is decreasing at 115 minutes.
a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.
f'(x) = (f(x+h) - f(x-h))/2 × h ....(1)
As per the question, we have h = 10 and x = 50
Substitute the values of h = 10 and x = 50 in (1),
f'(40) = (f(50+10) - f(50-10))/2 × 10
f'(40) = (89-55)/20
f'(40) = 1.7 mg/min
b) For the rate of change of concentration at 85 minutes:
Here, f(80) = 111 mg and f(90) = 113.
The concentration at 90 minutes is 113 mg.
Rate of change = (f(90) - f(80)) / h
= (113 - 111) /10
= 2 / 10
= 0.2 mg/min
c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.
Therefore, the drug's concentration is decreasing at 115 minutes.
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Acellus weekly time card please help
Answers
i think im not sure if i did it right
PLEASE HELP The quotient of seven more than three times a number m The number 27 less than n?
Answers
It's (3m + 7) ÷ (n - 27)
Seven more than three times a number m": This can be expressed as 3m + 7.
The number 27 less than n": This can be expressed as n - 27.
The Quotient
(3m + 7) ÷ (n - 27)
A fish is swimming at a constant rate towards the ocean floor. The equation y = -5x – 9 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming. Which statement best describes the depth of the fish, given this equation? Answer
Answers
The statement best describes the depth of the fish is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second
How to determine the statement that best describes the depth of the fish?
In order to know which statement best describes the depth of the fish, we have to first understand what the equation means:
Given: the equation y = -5x – 9
This can be likened to the equation of a straight line, which is of the form y =mx +c,
where m is the slope and c is the y-intercept
Comparing the given equation with the equation of a line :
y = -5x – 9
Slope(m) = -5 and y-intercept(c) = -9
The y-intercept represents the starting while the slope is the rate of descend
Therefore, what this means is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second.
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A recipe calls for 1/2 cup of flour for every 8 teaspoons of milk.How much flour should be used for 4 teaspoons of milk?
Answers
Answer:
I think it's probably 1/4
Step-by-step explanation: It's probably 1/4 since you are really only taking away both of the ones and then dividing 2 and 8 that equals 4 so then you add the only 1 of the the ones and then you get 1/4
Four friends want to take a vacation together, so each one gets a prat-time job. Each person has 6 weeks to save $750 for the vacation. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $750 for vacation? Friend A: Works 20 hours per week at $6.95 per hour. Friend B: Works 25 hours per week at $5.85 per hour. Friend C: Works 15 hours per week at $8.25 per hour. Friend D: Works 11 hours per week at $10.80 per hour.
Answers
Answer:
Only Friend A and Friend B met the target of saving $750 for their vacation
Step-by-step explanation:
From the question, we are to find out who achieved their goal of saving $750 in 6 weeks. We would analyse the options we were given
Friend A: Works 20 hours per week at $6.95 per hour.
1 week = 20 hours
6 weeks = 20 × 6
= 120 hours
The friend each $6.95 per hours earns, the amount earned in 6 weeks =
120 hours × $6.95
= $834
Friend A met the target
Friend B: Works 25 hours per week at $5.85 per hour.
1 week = 20 hours
6 weeks = 25 × 6
= 150hours
The friend each $5.85 per hours earns, the amount earned in 6 weeks =
150 hours × $5.85
= $877.5
Friend B met the target of saving $750.
Friend C: Works 15 hours per week at $8.25 per hour.
1 week = 15 hours
6 weeks = 15 × 6
= 90hours
The friend each $8.25 per hour earns, the amount earned in 6 weeks =
90 hours × $8.25
= $742.5
Friend D did not meet the target of saving $750
Friend D: Works 11 hours per week at $10.80 per hour.
1 week = 11 hours
6 weeks = 11 × 6
= 66 hours
The friend each $10.80 per hour earns, the amount earned in 6 weeks =
66 hours × $10.80
= $712.8
Friend D did not meet the target of saving $750
Therefore, from the above calculation, only Friend A and Friend B met the target of saving $750 for their vacation.
Determine the SHADED AREA Below:
Answers
Answer:
120 square inch..
Step-by-step explanation:
first ,Area of square
subtracting Area of triangle
2. If m arc VW - 62" and marc YZ -25°, then what is the
measure of
Answers
Add the two arcs to get 87. All circles have a circumference of 360. 360-87=273. The two angles are vertical angles so they are congruent and have the same number. 273/2 is 136.5
The temperature dropped 25 degrees over 8 hours. How much did the temperature drop per hour?
Answers
Answer:
3.125 degrees per hour
Step-by-step explanation:
It’s 25 degrees over 8 hours.
A unit rate problem since we are to find the unit rate or “per hour”
25/8 = 3 1/8
3 1/8 or 3.125 both works
-4
-3
-2
-1
0
1
1
2
3
4
b.
12
5
0
-3
-4.
у
-30
5 12
Answers
Answer:
Linear Regression: y = 0x + 2.67
Quadratic Regression: y = 1x^2 + 0x - 4
Step-by-step explanation:
USE STATS CALCULATOR
If FH and IK are parallel lines and mIJL = 65°, what is mFGJ?
Answers
Answer:
m FGJ = m IJL
( they are pair of corresponding angles )
so, FGJ = 65°
when robin correctly calculates intresult ^= 2, what value does she get
Answers
The value that Robin gets when she correctly calculates intresult ^= 2 is dependent on the initial value of intresult.
If intresult is initially set to a positive integer, the expression intresult ^= 2 is equivalent to performing a bitwise XOR operation between intresult and 2. The result will be the value obtained by XORing the binary representations of intresult and 2.
If the binary representation of intresult has a 1 in the second least significant bit and the rest of the bits are 0, then the result will have a 1 in the second least significant bit and the rest of the bits will be 0. Otherwise, if the binary representation of intresult has a 0 in the second least significant bit, the result will have a 1 in the second least significant bit and the rest of the bits will remain unchanged.
In summary, the specific value obtained when Robin correctly calculates intresult ^= 2 depends on the initial value of intresult and the binary representation of that value.
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