Answer:
Do u need slope?
Step-by-step explanation:
The volume of a sphere of radius 3 cm is
(A)
9x cm
(B)
18.t cm
(C)
27 cm
(D)
36 cm
Answer:
3^3 = 27
27 * 3.14 = 84.78
84.78 * 4/3 = 113.04 is your answer.
Formula of volume of sphere is:
4/3 x π(3.14 or 22/7 whatever they tell you to use for pi) x r^3(your radius being cubed)
You get your radius by finding out what is half of your diameter or your given radius.
Which expression is equivalent to 4x2 - 4x – 3 in factored form?
Answer:
(2x-3)(2x+1)
Step-by-step explanation:
4x^2 - 4x - 3
we need two numbers that give 12 when multiplied and 4 when subtracted
the numbers are 6 and 2 because 6*2=12 and 6-4=4.
4x^2 - (6-2)x -3
4x^2 -6x +2x -3
take common
2x(2x -3)+1(2x-3)
take (2x-3) as common
(2x-3)(2x*1 + 1*1)
(2x-3)(2x+1)
find the particular solution y = f(t) for each differential equation.1. dy/dt = 8y and y = -2 when t = 02. dy/dt = -4y and y = 10 when t = 03. dy/dt = 16y and y = 5 when t = 04. dy/dt = -7y and y = -4 when t = 0
If 84 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets. Enter your answer as a fraction. P(win both) B
the probability that one person will win 2 prizes if that person buys 2 tickets = 0.0004048.
Let A be the event that a person wins the prize on buying one ticket and B be the event that a person wins the prize on buying two tickets. The probability that one person will win both prizes if that person buys 2 tickets is given by
P(win both) = P(A and A) + P(B)
where P(A and A) = probability of winning prize on buying one ticket and winning prize on buying another ticket
= (1/84) × (1/83) = 1/69612
[Note: the probability of winning prize on buying another ticket decreases as the total number of tickets sold decreases, thus the probability of winning both prizes will be negligible]
P(B) = probability of winning the prize on buying two tickets. Number of ways to buy 2 tickets out of 84
= 84C2 = (84 × 83) / (2 × 1) = 3486
Number of ways of choosing 2 tickets and winning both prizes = 2C2 = 1. Probability of winning both prizes on buying 2 tickets
= 1/3486
Therefore, P(win both) = P(A and A) + P(B)
= 1/69612 + 1/3486
= 0.0004048P(win both)
= 0.0004048 is the required probability.
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The graph of a logarithmic function is shown below.
On a coordinate plane, a curve starts at y = negative 2 in quadrant 4 and curves up into quadrant 1 and approaches y = 2.
What is the domain of the function?
x 0
x < 1
all real numbers
Answer:
x > 0
Step-by-step explanation:
Domain of a function is defined by the set of x-values of the graph of a function.
From the graph attached,
x-values are starting from x > 0 [Since x ≠ 0] and moves towards infinity,
Therefore, domain of the function will be,
(0, ∞) Or x > 0
Answer:
it's B on Edg
Step-by-step explanation:
I just took the test
Adam works at a bakery. He uses \( \frac{1}{8} \)of his floor supply to make bread and \( \frac{3}{4} \)of his flour supply to make other baked goods. If Adam used 21 pounds of flour, how flour did he have in his supply?
Adam uses 1/8 + 3/4 of his flour supply in total, to make the goods he needs. The LCM between 4 and 8 is 8.
So:
\(\begin{gathered} \frac{1}{8}+\frac{3}{4}= \\ \frac{1}{8}+\frac{6}{8}=\frac{7}{8} \\ \end{gathered}\)7/8 of the total is 21 pounds. Let the total be x.
\(\begin{gathered} \frac{7}{8}*x=21 \\ 7x=21*8 \\ 7x=168 \\ x=\frac{168}{7} \\ x=24 \end{gathered}\)Adam has a total of 24 pounds of flour in his supply.
Need some help in math
Answer: A all you have to do is look where the line is going
Answer:
C
Step-by-step explanation:
under a reflection in the line y = - x
a point (x, y ) → (- y, - x ) , then
(- 1, 6 ) → (- 6, - (-1) ) → (- 6, 1 )
(- 3, 2 ) → (- 2, - (- 3) ) → (- 2, 3 )
the sum of all frequencies in a frequency distribution should sum to
The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.
Frequency Distribution Table:The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.
The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.
Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.
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The given question is incomplete, complete question is:
What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?
The r in the simple interest formula stands for rate which best describes how to use rate in formula
Convert it to a decimal and multiply is the best way to describe rate in simple interest formula.
Define rate.The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number. An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.
Given
The r in the simple interest formula stands for rate.
Convert it to a decimal and multiply is the best way to describe rate in formula.
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if you are picking a number between 1-20 what is the probability that you will pick an even numder or a multiple of three
Answer:
The probability of an event happening is desired outcome/sample space.
For our sample space, it’s just the number of numbers: 20.
The outcome you want has some overlap: 6. 12. 18. So, we’ll subtract these as they fit both criteria.
Even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (10 numbers)
Multiples of 3: 3, 6, 9, 12, 15, 18 (6 numbers)
Pr(A or B) = Pr(A) + Pr(B) - Pr(overlap, also known as A intersect B)
Pr(even or mult. of 3) = 10/20 + 6/20 - 3/20 (the overlap)
= 13/20.
So, there is a 65% of you picking an even number or a multiple of three.
Step-by-step explanation:
Hopes this helps. <3
PLS SHOW WORK! WILL GIVE BRAINLIEST!
A bike tire has a diameter of 35 inches. If the tire rotates 10 revolutions, how far did the bike travel?
Answer:
Distance travelled = 91.61 feet
Step-by-step explanation:
Given the following data;
Diameter, d = 35 inches
Number of revolutions = 10 Rev
To find the distance travelled by the bike;
First of all, we would determine the circumference of the bike's tire, which is circular in shape.
Circumference of circle = πd
Circumference of circle = 35π
Next, we multiply by the number of revolutions to get the distance travelled.
Distance travelled = 35π * 10
Distance travelled = 350π inches
But pie, π = 3.142
Distance travelled = 350 * 3.142
Distance travelled = 1099.7 inches.
In feet;
1 inches = 0.0833 feet
1099.7 inches = x feet
Cross-multiplying, we have;
x feet = 1099.7 * 0.0833
x feet = 91.61 feet
Distance travelled = 91.61 feet
4) A firm determine demand function and total cost function: p =
550 − 0.03x and C(x) = 4x + 100, 000, where x is number of units
manufactured and sold. Find production level that maximize
profit.
To find the production level that maximizes profit, we need to determine the profit function by subtracting the cost function from the revenue function.
Given the demand function p = 550 - 0.03x and the cost function C(x) = 4x + 100,000, we can calculate the profit function, differentiate it with respect to x, and find the critical point where the derivative is zero.
The revenue function is given by R(x) = p * x, where p is the price and x is the number of units sold. In this case, the price is determined by the demand function p = 550 - 0.03x. Thus, the revenue function becomes R(x) = (550 - 0.03x) * x.
The profit function P(x) is obtained by subtracting the cost function C(x) from the revenue function R(x). Therefore, P(x) = R(x) - C(x) = (550 - 0.03x) * x - (4x + 100,000).
To maximize profit, we differentiate the profit function with respect to x, set the derivative equal to zero, and solve for x:
P'(x) = (550 - 0.03x) - 0.03x - 4 = 0.
Simplifying the equation, we get:
0.97x = 546.
Dividing both sides by 0.97, we find:
x ≈ 563.4.
Therefore, the production level that maximizes profit is approximately 563.4 units.
In conclusion, to find the production level that maximizes profit, we calculate the profit function by subtracting the cost function from the revenue function. By differentiating the profit function and setting the derivative equal to zero, we find that the production level that maximizes profit is approximately 563.4 units.
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in a certain town, in 90 minutes 1/2 inch of rain falls. It continues at the same rate for a total of 24 hours. Which of the following statements are true about the amount of rain in the 24- hour period? show your work
The statement that is true is that the amount of rain in the 24- hour period is 8 inches
Which statement is true about the amount of rain in the 24- hour period?From the question, we have the following parameters that can be used in our computation:
In 90 minutes 1/2 inch of rain falls
This means that
Rate = (1/2 inch)/90 minutes
So, we have
Rate = (1/2 inch)/(1.5 hour)
The amount of rain in the 24- hour period is
Amount = Rate * Time
So, we have
Amount = (1/2 inch)/(1.5 hour) * 24 hours
Evaluate
Amount = 8 inches
Hence, the amount of rain in the 24- hour period is 8 inches
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Explain the difference between the Addition Rule for disjoint events and the General Addition Rule.
Answer: The Addition Rule for disjoint events is the sum of the probabilities of 2 events, while the General Addition Rule says if 2 are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).
Step-by-step explanation: The Addition Rule states that for two disjoint events, the probability that one or the other occurs is the sum of the probabilities of the two events. (Book example on p. 280 about the probability that a randomly selected student is either a sophomore (A) or a junior (B) therefore P(A or B). The addition of probabilities for disjoint events is the third basic rule of probability: Rule 3: If two events A and B are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).
Answer: The Addition Rule for disjoint events is the sum of the probabilities of 2 events, while the General Addition Rule says if 2 are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).
Step-by-step explanation: hope this helps0^0
Charlotte owns two entertainment websites. Here are some details about those websites for one entire month:
Website A Website B
Number of writers 555 111111
Number of posts posted 110110110 200200200
Average number of words of post 100100100 170170170
Average likes per post 350035003500 350035003500
Average comments per post 500500500 450450450
Number of new subscribers 900090009000 20{,}00020,00020, comma, 000
Revenue \$30{,}000$30,000dollar sign, 30, comma, 000 \$75{,}000$75,000dollar sign, 75, comma, 000
Expenses \$20{,}000$20,000dollar sign, 20, comma, 000 \$47{,}000$47,000dollar sign, 47, comma, 000
Profit (Revenue-−minusExpenses) \$10{,}000$10,000dollar sign, 10, comma, 000 \$28{,}000$28,000dollar sign, 28, comma, 000
Charlotte wants to know which website produces a larger amount of content per a single writer.
1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A, Checked, Correct)
CORRECT (SELECTED)
Average number of posts per writer
(Choice B, Incorrect)
INCORRECT
Total number of words
(Choice C, Checked, Correct)
CORRECT (SELECTED)
Average number of words per writer
(Choice D, Incorrect)
INCORRECT
Average number of likes per word
2) Determine which website produces a larger amount of content per a single writer according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A, Incorrect)
INCORRECT
Yes. According to both definitions, website A produces a larger amount of content per a single writer.
(Choice B, Incorrect)
INCORRECT
Yes. According to both definitions, website B produces a larger amount of content per a single writer.
(Choice C, Checked, Correct)
CORRECT (SELECTED)
No. The definitions have opposite results.
Answer:
WOAH
Step-by-step explanation:
AWESOME EDUCATION DUDE
Answer:
1) These are the two definitions Charlotte came up with to define the quantity:
Average number of posts per writer
Average number of words per writer
2) The definitions have opposite results.
Step-by-step explanation:
Khan :)
if it takes three concrete workers 1 hour to pour 5 yd3 of concrete, and each worker makes $15 an hour, how much will it cost to pour 25 yd3?
It will cost $225 to pour 25 yd3 of concrete with 3 workers working at a rate of $15 per hour.
To determine the cost to pour 25 yd3 of concrete, you can use the following formula:
cost = (number of workers * worker rate per hour * number of hours)
In this case, the number of workers is 3, the worker rate per hour is $15, and the number of hours can be calculated by dividing the volume of concrete to be poured (25 yd3) by the rate at which the workers can pour concrete (5 yd3 per hour). Therefore, the number of hours it will take to pour 25 yd3 of concrete is 25/5=5 hours.
Plugging these values into the formula gives:
cost = (3 workers * $15/hour * 5 hours) = $<<3155=225>>225
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Kamala is reading about her favorite superhero, Captain Marvel. She would like to read at least 235 pages in one week. She has already read 25 pages. How many pages does Kamala need to read each day?
The number of pages that Kamala needs to reach each day is p ≥ 30.
What is the number of pages that Kamala needs to read?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe inequality sign that would be used is ≥. This is because the pages Kamala needs to read each day can be equal to 235 or greater than 235
25 + 7p ≥ 235
Combine similar terms: 7p ≥ 235 - 25
Add similar terms: 7p ≥ 210
Divide both sides of the equation by 7: p ≥ 210 / 7
p ≥ 30
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Based on Exercise 9, prove that τ and σ are multiplicative. That is, prove that if m and n are relatively prime, then τ(mn)=τ(m)τ(n) and σ(mn)= σ(m)σ(n).
To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).
To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.
Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).
To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).
Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.
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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.
To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:
1. τ(mn) = τ(m)τ(n)
2. σ(mn) = σ(m)σ(n)
Let's start with property 1:
1. τ(mn) = τ(m)τ(n)
If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.
Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).
Now let's move on to property 2:
2. σ(mn) = σ(m)σ(n)
Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.
Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.
Hence, we can conclude that σ(mn) = σ(m)σ(n).
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Complete the following items. For multiple choice items, write the letter of the correct response on your paper. For all other items, show or explain your work.How many distinct real roots does the equation x⁴+3x³-4 x=0 have?
a. 1
b. 2
c. 3
d. 4
The, combining the root x = 0 from the first factor and the potential three distinct real roots from the cubic equation, we can conclude that the equation x⁴ + 3x³ - 4x = 0 has a total of 4 distinct real roots.
The correct answer is (d) 4.
To determine the number of distinct real roots of the equation x⁴ + 3x³ - 4x = 0, we need to examine the behavior and properties of the equation.
The given equation is a quartic equation (degree 4) in terms of x. A quartic equation can have a maximum of four distinct real roots. However, it is not necessary that all four roots are real.
In this case, we can attempt to factor the equation and analyze its roots. Factoring can help us determine the number of distinct real roots.
x⁴ + 3x³ - 4x = 0
We can factor out an x from each term:
x(x³ + 3x² - 4) = 0
Now, we have a product of two factors equal to zero. To satisfy this equation, either x = 0 or (x³ + 3x² - 4) = 0.
The first factor, x = 0, gives us one real root at x = 0.
To analyze the second factor, we can attempt to factor it further or use numerical methods to find its roots. However, it is evident that the equation (x³ + 3x² - 4) = 0 is a cubic equation (degree 3), and a cubic equation can have a maximum of three distinct real roots.
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What’s the answer??????
Answer: -50
Step-by-step explanation: (5-10) then multiply the answer by 10
A recipe for cookies needs 240g of flour to make enough cookies for 5 people. How much flour would you need to make cookies for 15 people?
Answer:
720g
Step-by-step explanation:
5 people = 240g
×3 x3
15 people = 720g
Please help me! I’ll mark you as the brainiest but please don’t answer if you don’t know it
Answer:
x > 7
Step-by-step explanation:
If you look at the changes in degrees, you will see it get bigger on the bottom! That means the 7 will become smaller! Your Welcome!
Answer:
the answer is B bro
Step-by-step explanation:
Money worries: A 2014 study by the reputable Gallup organization estimates that 34% of U.S. adults are worried about money. We want to know if the proportion is greater this year. We select a random sample of 100 U.S. adults this year and find that 40% are worried about money. After carrying out the hypothesis test for p0.34 compared to p>0.34. we obtain a P-value of 0.10. Which of the following interpretations of the P-value is correct? There is a 10% chance that a sample of 100 U.S. adults will have 40% or more worried about money if 34% of the population is worried about money this year. There is a 10% chance that 40 more of Use adults are worried about money this year ir 34% were wortied about money 2014 There is a 10% chance that 40% of U.S. adults are worried about money this year. There is one that 34 of U.S. acustied about this year
The interpretation of P-value correct is
"There is a 10% chance that a sample of 100 U.S. adults will have 40% or more worried about money if 34% of the population is worried about money this year
"What is P-value?
P-value is a statistical term that represents the probability of getting outcomes as extreme as or more extreme than those observed in a statistical hypothesis test.
The p-value is used to assess the null hypothesis's plausibility. The null hypothesis is a type of hypothesis that assumes that there is no statistical significance between the two variables.
P-value for given question:
In the question given,
the null hypothesis and the alternative hypothesis are as follows:
Null hypothesis:
p = 0.34
Alternative hypothesis:
p > 0.34
Where p represents the population proportion that are worried about money .The hypothesis test was performed on a sample of 100 U.S. adults this year, which found that 40% of them are worried about money. The P-value obtained from this hypothesis test is 0.10.
The correct interpretation of this P-value is
"There is a 10% chance that a sample of 100 U.S. adults will have 40% or more worried about money if 34% of the population is worried about money this year."
This implies that if the null hypothesis is correct, and the population proportion of U.S. adults worried about money is 34%,
then there is a 10% chance that a sample of 100 U.S. adults would exhibit a proportion of 40% or greater worried about money or this magnitude or greater.
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The price of a coat is reduced by 17% in a sale.
The sale price is £78.85.
What was the original price of the coat?
Give your answer in pounds (£).
The required original price of the coat is given as £95.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95
Hence, the cost of the coat before the sale is £95.
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Which of the following parts does not belong to a theoretical:
A. The hypotheses corresponding to the model
B. The operationalization of the used constructs of the model
C. A logical explanation of the relationship within a model
D. A graphical respresentation of the model
The operationalization of the used constructs of the model is not typically considered a part of the theoretical aspects of a model. The correct option is (B).
Operationalization refers to the process of defining and measuring the variables or constructs in a study. It involves turning abstract concepts into observable and measurable variables.
On the other hand, the theoretical parts of a model typically include:
A. The hypotheses corresponding to the model: This refers to the specific statements or predictions derived from the theoretical framework of the model.
Hypotheses provide testable expectations about the relationships between variables in the model.
C. A logical explanation of the relationship within a model: This involves providing a theoretical rationale or logical explanation for the expected relationships between variables in the model.
It is the theoretical framework that underlies the model and helps in understanding the underlying mechanisms or processes.
D. A graphical representation of the model: Graphical representation, such as diagrams or visual models, can be used to depict the structure or relationships within a model. It helps in visualizing the connections between variables and understanding the overall framework.
Therefore, B. The operationalization of the used constructs of the model does not belong to the theoretical parts of a model.
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(05.05) Which of the following inequalities matches the graph? (1 point)
Answer: Choice A. \(x \le -7\)
=====================================================
Explanation:
Every point in the shaded region has an x coordinate that is equal to -7 or smaller.
Example points include
(-8, 0)(-10, 2)(-9, -5)The y coordinate does not matter. All that matters is the x coordinate. The boundary line is the equation x = -7, representing all points that have x coordinate of -7. The solid boundary line says to the reader "any point on this boundary line is part of the shaded region solution set". This inclusion is due to the "or equal to" of the inequality sign.
the _____ of a trapezoid is a segment whose endpoints are the midpoints of its legs.
Answer:
The segment that connects the midpoints of the legs of a trapezoid is called the median of the trapezoid.
Step-by-step explanation:
what is the slope of T(4, 2), V(4, -3)
Answer:
m= slope - - = +. formula is m=y2-y1
Answer:(-5/0) (y,x) (rise/run)
Step-by-step explanation:
Assuming that those are two points, the slope is -5/0.
(y1-y2) Rise
over over
(x1-x2) Run
Let F(x) = f(x ^ 9) and G(x) = (f(x)) ^ 9 You also know that a ^ 8 = 5 , f(a) = 2; f^ prime (a)=15, f^ prime (a^ 9 )=6
Solution
- The solution steps are given below;
Question 1
\(\begin{gathered} F(x)=f(x^9) \\ \text{ Let }x^9=u \\ F(u)=f(u) \\ F^{\prime}(u)=\frac{d}{du}F(u)=f^{\prime}(u) \\ \\ \frac{du}{dx}=\frac{d}{dx}(x^9)=9x^8 \\ \\ F^{\prime}(x)=\frac{d}{du}F(u)\times\frac{du}{dx} \\ \\ F^{\prime}(x)=f^{\prime}(u)\times9x^8 \\ \\ F^{\prime}(x)=f^{\prime}(x^9)\times9x^8 \\ \\ \text{ Thus, put }x=a \\ \\ F^{\prime}(a)=f^{\prime}(a^9)\times9a^8 \\ \text{ But we have been given:} \\ f^{\prime}(a^9)=6 \\ a^8=5 \\ \\ \therefore F^{\prime}(a)=5\times6=30 \end{gathered}\)Question 2:
\(\begin{gathered} G(x)=(f(x))^9 \\ \text{ Let }u=f(x) \\ \frac{d}{dx}u=u^{\prime}=f^{\prime}(x) \\ \\ G(u)=u^9 \\ \frac{d}{du}G(u)=G^{\prime}(u)=9u^8 \\ \\ \frac{d}{du}G(u)\times\frac{d}{dx}u=f^{\prime}(x)\times9u^8 \\ \\ G^{\prime}(x)=f^{\prime}(x)\times9(f(x))^8 \\ \\ put\text{ }x=a \\ \\ G^{\prime}(a)=f^{\prime}(a)\times9(f(a))^8 \\ \text{ We know that:} \\ f^{\prime}(a)=15 \\ f(a)=2 \\ \\ \text{ Thus, we have:} \\ G^{\prime}(a)=15\times9(2)^8 \\ G^{\prime}(a)=34560 \end{gathered}\)* Find b if log, 81=4. A) 5 B) 4 C) 3 D) 2 E) !
Answer:
B
Step-by-step explanation: