Answers
Using the Quotient Rule, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .
In the given question,
We have to differentiate the given function with respect to x.
The given function is [tex]y=\frac{x^4+1}{3x^4+4}[/tex]
We have differentiate with respect to x.
The given function is in fraction format. So solving the given expression we use Quotient Rule
According to Quotient Rule
"A method for recognizing issues where one function is divided by another is the quotient rule."
The formula of Quotient Rule is
[tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{g(x)f'(x)-g'(x)f(x)}{(g(x))^2}[/tex]....................(1)
As we see in our function then f(x) = x[tex]^4+[/tex]1 and g(x) = 3x[tex]^4+[/tex]4
Before solving the function we find the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex]
Now solving the f(x) for f'(x) with respect to x.
f(x) = x[tex]^4+[/tex]1
[tex]\frac{d}{dx}f(x)=\frac{d}{dx}(x^4+1)[/tex]
[tex]f'(x)=\frac{d}{dx}x^4+\frac{d}{dx}1[/tex]
We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.
So [tex]f'(x)=4x^{(4-1)}+0[/tex]
[tex]f'(x)=4x^3[/tex]
Now solving the g(x) for g'(x) with respect to x.
g(x) = 3x[tex]^4+[/tex]4
[tex]\frac{d}{dx}g(x)=\frac{d}{dx}(3x^4+4)[/tex]
[tex]g'(x)=3\frac{d}{dx}x^4+\frac{d}{dx}4[/tex]
We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.
[tex]g'(x)=3(4x^{(4-1)})+0[/tex]
[tex]g'(x)=3(4x^{3})[/tex]
[tex]g'(x)=12x^{3}[/tex]
Now finding the value of (g(x))[tex]^2.[/tex]
g(x) = 3x[tex]^4+[/tex]4
[tex](g(x))^4=(3x^4+4)^2[/tex]
Now using the formula of [tex](a+b)^2=a^2+2ab+b^2[/tex].
Now solving
[tex](g(x))^4=(3x^4)^2+2\times(3x^4)\times4+(4)^2[/tex]
Simplifying
[tex](g(x))^4=9x^8+24x^4+16[/tex]
Now putting the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex] in the equation (1)
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4+4)(4x^3)-(12x^3)(x^4+1)}{9x^8+24x^4+16}[/tex]
Simplifying
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4(4x^3)+4(4x^3))-((12x^3)x^4+1(12x^3))}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{(4+3)}+16x^3)-(12x^{(3+4)}+12x^3)}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{7}+16x^3)-(12x^{7}+12x^3)}{9x^8+24x^4+16}[/tex]
Now solving the bracket
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{12x^{7}+16x^3-12x^{7}-12x^3}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{16x^3-12x^3}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{4x^3}{9x^8+24x^4+16}[/tex]
Hence, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .
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Related Questions
what is the vaule of 2 × 4^2 + 5 enter the answer in the box
Answers
The value of the expression 2 x 4² + 5 will be 37
What is expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given is the following expression -
2 x 4² + 5
On solving the expression, we get -
2 x 4² + 5
2 x 4 x 4 + 5
32 + 5
37
The value of the expression 2 x 4² + 5 will be 37
Therefore, the value of the expression 2 x 4² + 5 will be 37
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f(x) = √3x
g(x) = 3x + 2
Find (4) (2). Include any restrictions on the domain.
Answers
Option A is correct. The value of function (f/g)(x) is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3.
What exactly is a function composition?In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
What is the sum of two functions?The new function obtained by performing f first and then g is the combination of two functions g and f.
Given:
f(x) = [tex]\sqrt[3]{3x}[/tex]
g(x) = 3x + 2
(f/g)(x) = [tex]\sqrt[3]{3x}[/tex]/(3x+2)
Also, the denominator should not be equal to 0.
So, 3x + 2 ≠ 0
x ≠ -2/3
Therefore, the value of function is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3. So, Option A is correct
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a - domain and range
b - intercepts
c - horizontal asymptotes
d - vertical asymptotes
e - oblique asymptotes
Answers
From given graph,
a - domain and range: (-∞, 3) ∪ (3, ∞)
b - intercepts: x = 0 and y = 0
c - horizontal asymptotes: y = 3
d - vertical asymptotes: x = 3
e - oblique asymptotes: No
In this question, we have been given a graph of a function.
From given graph we need to answer the following questions.
1) domain of function: (-∞, 3) ∪ (3, ∞)
the range of function : (-∞, 3) ∪ (3, ∞)
2) the intercepts:
x = 0, y = 0
3) horizontal asymptotes
A red dotted line y = 3 is a horizontal asymptotes
4) vertical asymptotes
A red dotted line x = 3 is a vertical asymptotes
5) Oblique asymptotes
The graph of function does not have any Oblique asymptotes
Therefore, from given graph,
a - domain and range: (-∞, 3) ∪ (3, ∞)
b - intercepts: x = 0 and y = 0
c - horizontal asymptotes: y = 3
d - vertical asymptotes: x = 3
e - oblique asymptotes: No
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ching and his 4 brothers set up computers at their family company. how many computers did they set up if they each set up the same number of computers?
Answers
There are '5n' computers set up if they each set up the same number of computers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ching and his 4 brothers set up computers at their family company.
Now,
Let the number of computers for each person = n
The total number of persons = 5
So, We can formulate;
⇒ The number of computers set up if they each set up the same number of computers = 5n
Thus, There are '5n' computers set up if they each set up the same number of computers.
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In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test
and their mean score is 67.7.
What is the mean score of all of these students together? Round to one decimal place.
mean of the scores of all the students.
Answers
The mean score of all the students is 79.5 and it is round off into one decimal place.
Mean
Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.
Here we need to find the mean score of all students.
In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,
=> 30 x 87.7 = 2631
Similarly, the total score for 21 students is,
=> 21 x 67.7 = 1421.7
So, the 51 students, cumulative score is
=> 2631 + 1421. 7 = 4052.7
Therefore, the mean score is calculated as,
=> 4052.7/51
=> 79.464
When we round off the value into one decimal place then we get
=> 79.5
Therefore, the mean value of all the students is 79.5.
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An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces?
Answers
The required length of the pieces is given as 20 ft, 16ft, and 14ft.
Given that,
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces is to be determined.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
according to the question,
Length of the first, second, and third be x, y and z,
According to the question,
x + y + z = 50 - - - - - - - - (1)
x = y + 4
z = y - 2
put x and z in equation 1
y + 4 + y + y - 2 = 50
3y = 50-2
y = 48/3
y = 16 ft
Now,
x = 16 + 4 = 20 ft
z = 16 - 2 = 14 ft
Thus, the required length of the pieces is given as 20 ft, 16ft, and 14ft.
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In the diagram ray MO bisects the measurement of
Answers
2x+30 = 15
X=15
You are then able to plug 15 in for the variable of X.
Ray ML
3(15)-20
45-20
= 25°
Ray MN
(15) + 10
= 25°
Or you could assume they are the same measurement as they are equal.
what fraction of the voters polled voted for eric jackson?
F. 1/26
G. 13/50
H. 13/37
J. 50/13
Answers
The fraction of the voters polled voted for Eric Jackson is 50/13. A fraction is a portion of a whole or, more broadly, any number of equal parts.
What is meant by fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction has a fraction in the integrand or denominator. The numerator of a proper fraction is smaller than the denominator.Fractions are described as parts of a whole. The total can be a single object or a group of objects.Therefore,
The fraction of the voters polled voted for Eric Jackson is 50/13
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Katelyn’s older brother borrowed money for school. He took out a loan that charges 6% simple interest. He will end up paying $720 in interest after 6 years. How much did Katelyn’s brother borrow for school?
Answers
The amount of money that Katelyn’s brother borrowed for school would be = $ 2,000.
What is interest?Interest in the amount of money that an individual pays in extra with a borrowed amount of money either from an individual or from the bank.
The formula for simple interest= Principal ×Time × Rate/100
Rate of payment= 6%
Time = 6 years
Simple interest = $720
Principal= X
From the formula above, make principal the subject of formula;
Principal = SI × 100/ T× R
= 720 × 100/ 6×6
= 72000/36
=$ 2,000
Therefore, the amount of money that Katelyn’s brother borrowed for school is $2,000.
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The radius of a circle is 8 ft. Find its area in terms of pi
Answers
Answer:
Step-by-step explanation:
201.06ft²
Answer:
Step-by-step explanation:
The dimensions of a rectangle are 6x-7 and 3x-1. what is the area in square feet?
please help fast!!
Answers
The area of the rectangle is given by the formula below:
A = 18x^2 - 27x + 7
What is the area of the rectangle?For a rectangle of width W and length L, the area is given by the formula:
A = W*L
Here we know that the dimensions of a rectangle are 6x-7 and 3x-1, then we can define:
L = 6x - 7
W = 3x - 1
Replacing that in the area formula above we will get:
A = (6x - 7)*(3x - 1)
Now we can expand that product:
A = (6x)*(3x) + (6x)*(-1) + (-7)*(3x) + (-7)*(-1)
A = 18x^2 - 6x - 21x + 7
A = 18x^2 - 27x + 7
That is the formula for the area in terms of x.
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Schools A and B are competing in an academic contest. At the beginning of the final round, School A has 174 points and School B has 102 points. In the final round, correct answers earn 10 points and incorrect answers lose 6 points. School A gives the same number of correct and incorrect answers during the final round. School B gives no incorrect answers and the same number of correct answers as School A. The contest ends with a tie. Answer parts a and b.
Answers
Answer: C. 174 + 10x - 6x = 102 + 10x
Each school give 12 correct answers
Step-by-step explanation:
174 + 10x - 6x = 102 + 10x
x = number of correct answers AND,
x = number of incorrect answers
Solve for x:
174 - 102 = 10x + 6x -10x
72 = 6x
x = 12
Each school give 12 correct answers
A cone has a volume of 2411.52 cubic millimeters and a radius of 12 millimeters. What is its height? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The height of the cone given the volume of 2411.52 cubic millimeters and a radius of 12 millimeters is 16 millimeters.
How to find height of a cone?Volume of a cone = 2411.52 cubic millimetersRadius of the cone = 12 millimetersVolume of a cone = 1/3πr²h
2411.52 = 1/3 × 3.14 × 12 x 12 × h
2411.52 = 1/3 × 3.14 × 144h
2411.52 = 452.16h / 3
cross product7,234.56 = 452.16h
divide both sides by 452.16h = 7,234.56 / 452.16
h = 16 millimeters
In conclusion, the height of the cone is given by 16 milliliters.
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i need help with this pls
Answers
Option C: The relationship between the statement cannot be determined.
What is Conditional statement?
Two independent statements can be related to each other in a logic structure called a conditional statement.
The first statement is presented with “if,” and is referred to as the hypothesis.
The second statement is linked with “then”, and is known as the conclusion.
The notation associated with conditional statements typically uses the variable p for the hypothesis statement, and q for the conclusion.
p → q
Explanation for the answer:
The converse statement is notated as q→p (if q, then p). The original statements switch positions in the original “if-then” statement.The inverse statement assumes the opposite of each of the original statements and is notated ∼p→∼q (if not p, then not q).The contrapositive statement is a combination of the previous two. The positions of p and q of the original statement are switched, and then the opposite of each is considered: ∼q→∼p (if not q, then not p).
So, from the above we can clearly see that the both the statement 1 and statement are not start with "if" and "then".
Therefore, their relationship cannot be determined.
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What is 43+5673+20(1)
Answers
Answer:
5736
Step-by-step explanation:
calculator
Answer: 5736
Step-by-step explanation:
Solve for r.
r/3 + 16 = 19
Answers
Answer:
r = 9
Step-by-step explanation:
Hello!
Solve for r by isolating the variable.
Solve for r[tex]\frac r3 + 16 = 19[/tex] Subtract 16 from both sides[tex]\frac r3 = 3[/tex] Multiply both sides by 3[tex]r = 9[/tex]The value of r is 9.
A boy paid $11
for a bottle with a cork.
A bottle costs $10
more than a cork.
How much does a cork cost?
Answers
Step-by-step explanation:
A boy paid $11 for a bottle with a cork. A bottle costs $10 more than a cork. How much does a cork cost?
cork: c
bottle: 10c
c + 10c = 11
11c = 11
c = $1
A cork costs $1
K
Choose the measurement closest to 30 km: 10 mi, 20 mi or 30 mi.
Choose the correct answer below.
20 mi
30 mi
10 Ini
O
O
O 10
Answers
Answer:
20 miles
Step-by-step explanation:
1.6km is equivalent to 1 mile
so 30km / 1.6 = 18.75 miles
therefore 20 miles is the closest to 30km
A cube shaped aquarium with a side length of 1.2 meters is full of liquid. A fish swims in the container. What is the probability that the fish is at most 0.5 meters away from the center of the container?
Answers
The probability that the fish is at most 0.5 meters away from the center of the container, considering the volume of the cube, is given as follows:
0.0723 = 7.23%.
What is the volume of a cube?The volume of a cube of side length s is given by the side length cubed, that is:
V = s³.
The cube in this problem has a side length of 1.2 meters, hence the volume is given as follows:
V = 1.2³ = 1.728 cubic meters.
Considering only the inner 0.5 meters of the cube, the volume is given as follows:
V = 0.5³ = 0.125 cubic meters.
A probability is given by the division of the number of desired outcomes by the number of total outcomes, hence:
p = 0.125/1.728 = 0.0723 = 7.23%.
(desired volume is of 0.125 m³, total is of 1.728 m³).
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Pass journal entries using the perpetual system of inventory-
Purchased 1000 units of shoes from Indiana International at $300 each on account
Sold 200 units to Ceridian Corporation at $500 each on account
Sold 500 units to Semed Inc. at 550 each on cash
Paid cash in full to Indiana International
Purchased 800 units of shoes from CITS at $450 each on cash
Sold 100 units to Deeman Corp at $600 each on cash
Answers
The passage of journal entries to record the transactions, using the perpetual system of inventory with the First-in, First-out (FIFO) method, is as follows:
Journal Entries:Account Titles Debit Credit
Inventory $300,000
Accounts Payable (Indiana International) $300,000
To record the purchase of 1000 units of shoes at $300 each.Accounts Receivable
(Ceridian Corporation) $100,000
Sales Revenue $100,000
To record the sale of 200 units at $500 each on account.Cost of goods sold $60,000
Inventory $60,000
To record the cost of 200 units sold.Cash $275,000
Sales Revenue $275,000
To record the sale of 500 units at $550 each.Cost of goods sold $150,000
Inventory $150,000
To record the cost of 500 units sold.Accounts Payable
(Indiana International) $300,000
Cash $300,000
To record the cash payment on account.Inventory $360,000
Cash $360,000
To record the purchase of 800 units at $450 each.Cash $60,000
Sales Revenue $60,000
To record the sale of 100 units at $600 each.Cost of goods sold $30,000
Inventory $30,000
To record the cost of 100 units sold.Transaction Analysis:Inventory $300,000 Accounts Payable (Indiana International) $300,000
Accounts Receivable (Ceridian Corporation) $100,000 Sales Revenue $100,000
Cost of goods sold $60,000 Inventory $60,000
Cash $275,000 Sales Revenue $275,000
Cost of goods sold $150,000 Inventory $150,000
Accounts Payable (Indiana International) $300,000 Cash $300,000
Inventory $360,000 Cash $360,000
Cash $60,000 Sales Revenue $60,000
Cost of goods sold $30,000 Inventory $30,000
Thus, with the perpetual system using FIFO, inventory movements are recorded in the Inventory account as they occur and not at the period's end.
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If using the method of completing the square to solve the quadratic equation
x² - 13x +31 = 0, which number would have to be added to "complete the
square"?
Answers
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 13x + 31 = 0
(x - 13/2)² + (293/4) = 0
The number added to complete the square is 293/4.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² - 13x + 31 = 0
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0
(x - 13/2)² + 169/4 + 31 = 0
(x - 13/2)² + (293/4) = 0
Thus
The number added to complete the square is 293/4.
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HELP PLEASE ASAP 30 POINTS PLUS BRAINLEST Find the sum of (8.7 x 10^6) and (5.5 x 10^5). Write the final answer in scientific notation.
14.2 x 10^11
1.42 x 10^10
9.25 x 10^6
9.25 x 10^5
Answers
Many Texas cities have experienced substantial growth in population over the last 20 years. The growth of Houston, Texas, since 2015 is shown in the scatterplot. A least-squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by Population = 0.025 (year) + 2.01.
Based on the residual plot, is a linear model suitable for modeling the population growth of Houston?
A linear model is suitable because a pattern is evident in the residual plot.
A linear model is not suitable because the residuals do not cluster around zero.
A linear model is not suitable because the residual plot shows a curved pattern.
A linear model is suitable because the residuals seem to be randomly scattered.
Answers
Based on the given residual plot, as regards the linear model, we can say that; A linear model is not suitable because the residual plot shows a curved pattern.
What is a residual Plot?
A residual plot is a plot that shows the difference between the observed response and the fitted response values.
The ideal residual plot is usually called the null residual plot, and it shows a random scatter of points that form an approximately constant width band around the identity line.
When it comes to finding out if a linear model will be suitable, we can say that the points will form a pattern when the model function is not correct.
Now, you might be able to transform variables or even add polynomial and interaction terms in order to remove the pattern.
Now, looking at the given graph, we can say that a linear model is not suitable because from the definitions above, we can see that the residual plot shows a curved pattern.
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Ingia went to the farmers market to get ingredients. Determine the price per item of each vegetable.
4.1 6 onions for $1.80
12 mushrooms for $3 4.3 5 peppers for $5.50
4.2
Answers
$0.30 per onion (1.80 divide 6= 0.30)
$0.29 per mushroom (3.45 divide 12 = 0.28975)
$1.10 per pepper (5.50 divide 5= 1.10)
** it is a bit unclear the numbers you wrote on the question so I’m assuming this is what you meant; if it isn’t reply to this and rewrite the question**
Professional tennis player Serena Williams has a career win record of 81%. If we took a simple random sample of 65 of her matches, what is the probability that at least 55 would be wins?
Answers
Answer:
The probability is 81%
Step-by-step explanation:
(6, y) and (-8, 4); slope: 1/7
Answers
For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.
What is the slope of a line?
A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula
[tex]Slope(m)=\frac{d - b}{ c - a}[/tex]
The given points are (6, y) and (-8, 4).
and the slope of the line is given as m = 7.
By using the slope of a line formula, we get
[tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]
Hence, the value of y is 10.
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Find D subscript x y if
y = e^(-1/x^2)
Hint: remember the definition of derivative of natural log and use chain rule
Answers
The derivative of the natural log function y = e^(-1/x^2) is
2x^(-3)e^(-1/x^2)How to solve for the derivativeThe given function is
y = e^(-1/x^2)
The given function is rearranged as
y = e^(-1/x^2) = e^u such that u = (-1/x^2)
Applying chain rule
y = e^u
y' with respect to u = e^u
u = (-1/x^2) = -x^(-2)
u' with respect to x = 2x^(-3)
(y' with respect to u) * (u' with respect to x)
= e^u * 2x^(-3)
plugging in the value of u
= e^(-1/x^2) * 2x^(-3)
= 2x^(-3)e^(-1/x^2)
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If you buy stock for $36.20 per share and sell that stock for $37.90 per share, what was your
return on investment?
Answers
Answer:
$1.70 per share
Step-by-step explanation:
37.90-36.20=1.70
△MNP≅△QST.
What is m∠S?
Enter your answer in the box.
Answers
Answer:
78°
Step-by-step explanation:
∠M=∠Q
∠N=∠S
∠P=∠T
Answer:
m∠S =78°---------------------
Given
Two congruent triangles △MNP≅△QSTWe know that corresponding angles of congruent triangles are congruent (vertices in same order as name of triangle):
∠M ≅ ∠Q, ∠N ≅ ∠S, ∠P ≅ ∠TAngle S corresponds to angle N, hence their values are equal:
m∠S = m∠N = 78°Given p(x)=x+7/3, if p(x)=13 find x
Answers
x = 32
Step-by-step explanation:
[tex]{ \tt{p(x) = \frac{x + 7}{3} }}[/tex]
If p(x) = 13, then
[tex]{ \tt{13 = \frac{x + 7}{3}}} [/tex]
[tex]{ \tt{13 \times 3 = x + 7}}[/tex]
[tex]{ \tt{39 = x + 7}}[/tex]
[tex]{ \tt{39 - 7 = x}}[/tex]
[tex]{ \red{ \boxed{ \blue{ \sf{x = 32}}}}}[/tex]