Answer:
To apply the first derivative test to the function f(x) = 2x^3 + 3x^2 - 12x + 5, we need to find its derivative:
f'(x) = 6x^2 + 6x - 12
Then, we need to find the critical points by solving for f'(x) = 0:
6x^2 + 6x - 12 = 0
Dividing both sides by 6, we get:
x^2 + x - 2 = 0
Factoring the left side, we get:
(x + 2)(x - 1) = 0
So the critical points are x = -2 and x = 1.
To determine the intervals where f(x) is increasing and decreasing, we need to evaluate f'(x) on each side of the critical points. We can use a sign chart to do this:
x | -2 | 1 |
------|-----|----|
f'(x) | -12 | 0 |
Since f'(x) is negative to the left of x = -2 and positive to the right of x = -2, the function is decreasing to the left of x = -2 and increasing to the right of x = -2. Since f'(x) changes sign at x = 1, there is a local minimum at x = 1.
Therefore, using the first derivative test, we can conclude that the function has a local minimum at x = 1.
Step-by-step explanation:
Eric worked in the neighborhood garden for 3 1-2 hours on Monday and for 4 1-4 hours on Wednesday. How many hours in all did eric work in the neighborhood garden
The total number of hours Eric worked is 7 3/4 hours.
What is addition in mathematics?
Addition is one of the four basic arithmetic operations in mathematics, along with subtraction, multiplication, and division. Addition is the process of combining two or more quantities or numbers to find their sum, or total. The symbol used to represent addition is the plus sign (+).
For example, if we want to find the sum of 3 and 4, we would write:
3 + 4 = 7
The number 3 and the number 4 are called addends, and the result of the addition operation is called the sum. Addition can involve whole numbers, fractions, decimals, and even negative numbers.
Addition has many applications in mathematics, science, and everyday life. It is used to calculate simple arithmetic problems, such as adding up the cost of items in a shopping cart, as well as more complex calculations, such as adding up the values in a data set or solving equations in algebra.
To find the total number of hours Eric worked in the neighborhood garden, we need to add the number of hours he worked on Monday and Wednesday.
Eric worked 3 1/2 hours on Monday, which can also be written as 7/2 hours.
Eric worked 4 1/4 hours on Wednesday, which can also be written as 17/4 hours.
To add these two amounts, we need to find a common denominator. The smallest number that both 2 and 4 divide into is 4. So we can convert 7/2 to 14/4 by multiplying the numerator and denominator by 2:
7/2 = 14/4
Now we can add the two fractions:
14/4 + 17/4 = 31/4
This is the total number of hours Eric worked in the neighborhood garden, in fraction form. To write it as a mixed number, we can divide the numerator by the denominator:
31 ÷ 4 = 7 with a remainder of 3
So the total number of hours Eric worked is 7 3/4 hours.
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Let A and B be events with P(A)=0.6, P(B)=0.4, and P(B|A)=0.4. Find P(A and B)
The probability of A and B, using conditional probability, is given as follows:
0.24 = 24%.
How to obtain the conditional probability?The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which the probabilities are listed and explained as follows:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.To obtain the probability of A and B, the needed parameters are already given in the problem, and are as follows:
P(B|A) = 0.4.P(A) = 0.6.Hence the probability of A and B is calculated as follows:
P(A and B) = P(A) x P(B|A)
P(A and B) = 0.6 x 0.4
P(A and B) = 0.24.
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A student solved the equation x²+ 5x -60 = 5x +4. The student's work is shown below.
Determine if the student made an error. If so, explain their error AND solve for the correct solutions.
Answer:
x = -8, 8
Step-by-step explanation:
The student did make an error. When factoring [tex]x^2-64[/tex], they used incorrect factors. Using FOIL method, the students factored equation would become [tex]x^2 +32x-32x-1024 = x^2-1024[/tex], which is not [tex]x^2-64[/tex].
Instead, the factors 8 and -8 should be used.
[tex]x^{2} +5x-60=5x+4\\x^2 +5x - 64=5x\\x^2-64=0\\(x+8)(x-8)=0\\x=-8, 8[/tex]
Answer: x = ±8
Step-by-step explanation:
The given equation is:
x² + 5x - 60 = 5x + 4
The student's work shows that they simplified the equation correctly to:
x² - 64 = 0
However, their factorization of the resulting equation is incorrect. Factoring x² - 64 using difference of squares we get:
(x + 8)(x - 8) = 0
So, the solutions for x are x = -8 and x = 8. The student's solutions of x = ±32 are incorrect.
Therefore, the student made an error in factoring the equation, and the correct solutions for x are x = -8 and x = 8.
I need help on number 14 please please
Answer:
A. 5 cm
Step-by-step explanation:
AB = BC
x + 3 = 3x - 1
x - 3x = -1 - 3
-2x = -4
x = -4/-2
x = 2
BC = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
3/4 of 3/5 i need some help quick
Answer:
Step-by-step explanation: First lets multiply the numerators, so 3*3 is 9, then we multiply the denominators, so 4*5 is 20. 9/20 or 0.45 will be your answer.
write an equivalent expression to 8k - (5 + 2k) without parentheses
Answer:
8k - (5 + 2k) can be simplified by distributing the negative sign to the terms inside the parentheses:
8k - 5 - 2k
Then, we can combine like terms by adding the constants -5 and 8k:
6k - 5
Therefore, an equivalent expression to 8k - (5 + 2k) without parentheses is 6k - 5.
Describe the graph of y = 1/2 x − 10 − 3 compared to the graph of y = 1 x .
The graph of y = [1/2(x -10)] - 3, compared to the graph of 1/x, represents these following transformations:
Horizontal compression by a scale factor of 2.Translation right 10 units.Translation down 3 units.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The translations for this problem are given as follows:
x -> x - 10: shift right 10 units.y -> y - 3: shift down 3 units.Additionally, there was a multiplication by 2 in the domain, meaning that the parent function was horizontally compressed by a factor of 2.
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Which of the numbers below is less than -3.5? Select all that apply A)-4.2 B)-3.8 C)-9/2 D) -5/3 E)-1.5
Answer: A) -4.2, B) -3.8 C) -9/2 (-4.5)
Step-by-step explanation: Think of a number line, you have 0-10, and -10-0, as you keep going down the number like, the numbers become less and less, just like how -4.2 is less than -3.5, because it is further to the left of the number line, meaning it is less than. Hope this helps!
A solid with the volume 100 cubic units is is dilated by a scale factor of k find the image for each given value of k
To find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).
What is volume?Volume is a measure of the amount of space occupied by an object or substance. It is expressed as a numerical value, usually in cubic units, such as milliliters (mL) or cubic centimeters (cc). It is also used to measure the capacity of a container, such as a bottle, or a tank.
Dilation is a transformation that changes the size of a shape. When a solid is dilated by a scale factor of k, the new solid will be k times larger than the original solid. For example, if a solid has a volume of 100 cubic units and is dilated by a scale factor of 2, the image solid will have a volume of 200 cubic units (2 x 100).
To find the image for each given value of k, we need to multiply the original volume of the solid (100 cubic units) by the scale factor (k). We can use the equation V = kV0, where V0 is the original volume and V is the new volume, to calculate the new volume of the solid.
For example, if k = 3, the new volume will be 3 x 100 = 300 cubic units. If k = 4, the new volume will be 4 x 100 = 400 cubic units. In general, for any given value of k, the new volume will be k times the original volume.
To summarize, when a solid with a volume of 100 cubic units is dilated by a scale factor of k, the image solid will have a volume of k times the original volume (V = kV0). Therefore, to find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).
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Find the missing side lengths. Leave your answers as radicals in simplest form.
The missing side lengths are computed below
How to determine the missing side lengthsTriangle 22
The side length x can be calculated using
sin(30) = 9/x
So, we have
x = 9/sin(30)
Evaluate
x = 18
For length y, we have
y = √(18² - 9²)
Evaluate
y = 9√3
Triangle 23
The side length y can be calculated using
sin(30) = y/√3
So, we have
y = √3 * sin(30)
Evaluate
y = 1/2√3
For length x, we have
x = √(√3² + (1/2√3)²)
Evaluate
x = √(15/4)
x = 1/2√15
Triangle 24
The side length y can be calculated using
cos(60) = y/2√3
So, we have
y = 2√3 * cos(60)
y = √3
For x, we have
x = √((2√3)² - (√3)²)
x = √9
x = 3
Triangle 25
The side length x can be calculated using
cos(60) = 5/x
So, we have
x = 5/cos(60)
x = 10
For y, we have
y = √(10² - 5²)
y = 5√3
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Jordan's football team gained 12 yards on their first play. On the second play, the team lost 8 yards. Which expression could be used to describe the total yards gained by Jordan's team?
The total yards gained by Jordan's team is 4.
What is Expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
On first day, Jordan's football team gained 12 yards.
On second day, Jordan's football team lost 8 yards.
So, The total yards(net) would be :
= total yards gained by team - total yards lost by team
= 12 - 8
= 4 yards.
Here, total yards gained by team is the first expression while total yards lost by team is the second expression.
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An online keyboarding course collects data comparing each students age to their typing speed. The equation of the line of best fit representing this data is y=-1.4x+117.8 , where x is the age (years) and y is the typing speed (words per minute). What is the expected typing speed of a student who is 17 years old?
Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.
What does speed feel like?It functions by dividing distance by speed. The time can also be calculated by dividing the distance traveled by the speed. You can determine the third input if you know the first two. For instance, we may get the speed as 120 x 2 = 60 miles per hour if a car travels 120 miles in two hours.
The equation of the line of best fit is:
y = -1.4x + 117.8
where x is the age in years and y is the typing speed in words per minute. To find the expected typing speed of a 17-year-old student, we can substitute x = 17 into the equation:
y = -1.4(17) + 117.8
y = -23.8 + 117.8
y = 94
Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.
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Question 7 Find the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) The quotient is
The quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.
To find the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1), we will use synthetic division.
Write down the coefficients of the dividend polynomial in descending order of the exponent of x. In this case, the coefficients are 1, -1, 9, -9, 9, -12.
Write down the constant term of the divisor polynomial. In this case, the constant term is -1.
Bring down the first coefficient of the dividend polynomial.
Multiply the constant term of the divisor polynomial by the first coefficient of the dividend polynomial and write the result under the second coefficient of the dividend polynomial.
Add the second coefficient of the dividend polynomial and the result from step 4.
Repeat steps 4 and 5 until all the coefficients of the dividend polynomial have been used.
The last result from step 5 is the remainder. The other results are the coefficients of the quotient polynomial.
The synthetic division is shown below:
-1 | 1 -1 9 -9 9 -12
| -1 2 -11 20 -29
---------------------
1 -2 11 -20 29 -41
The quotient is 1x^(4)-2x^(3)+11x^(2)-20x+29 and the remainder is -41.
Therefore, the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.
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4. Renee is going to buy a new car that has a list price of $19,675. She will be responsible for $1,420 in vehicle
registration fees, $85 in documentation fees, and 8.92% sales tax. She plans to trade in her current car, a 2002
Buick LeSabre in good condition, and finance the rest of the cost over four years at an interest rate of 11.34%,
compounded monthly. If the dealer gives Renee 85% of the listed trade-in value for her car, what will her monthly
payment be? Round all dollar values to the nearest cent.
Buick Cars in Good Condition
1909
2000
$1,000
$1,150
$2.282
$2.890
$1.794
$1,455
Model Year
Century
LeSabre
Regal
1998
3829
$2.075
$1,676
$1.291
$2.030
$1,520
2001
$1.488
$2.835
$2.214
$1.814
2002
$1,505
$3.374
$2.566
$1,950
a.
b.
$521.96
$508.80
O. $518.80
d. $504.46
Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.
How did we arrive at this value?To calculate Renee's monthly payment, we need to first determine the total cost of the new car after taxes and fees and subtract the trade-in value of her old car. Then, we can use the loan information to calculate the monthly payment.
Total cost of the new car:
List price: $19,675
Vehicle registration fees: $1,420
Documentation fees: $85
Sales tax: 8.92% of ($19,675 + $1,420 + $85) = $1,894.51
Total cost = $19,675 + $1,420 + $85 + $1,894.51 = $22,074.51
Trade-in value of the old car:
2002 Buick LeSabre in good condition: $3,374 (from the table)
85% of trade-in value: 0.85 x $3,374 = $2,867.90
Net cost of the new car:
$22,074.51 - $2,867.90 = $19,206.61
To calculate the monthly payment, we can use the formula for the present value of an annuity:
PV = PMT x (1 - (1 + r)^(-n)) / r
where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate (11.34%/12), and n is the number of payments (4 years x 12 months/year = 48).
Solving for PMT:
PMT = PV x r / (1 - (1 + r)^(-n))
PMT = $19,206.61 x 0.1134/12 / (1 - (1 + 0.1134/12)^(-48))
PMT = $504.46
Therefore, Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.
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Which operation can you apply to the ratio 1 to 2 to get the ratio 3 to 6?
Answer:
x3
Step-by-step explanation:
I need help on number 14 please please
Given - two tangent lines are drawn from the point B
To find - the value of BC
Explanation - when tangent lines are drawn for outside of the circle then the length of line formed is equal
We get
AB=BC
[tex]x+3 =3x-1\\x-3x=-1-3\\-2x=-4\\x=2[/tex]
BC= [tex]3x-1 =3(2)-1=6-1=5[/tex]
The length of BC = 5
Final answer - The option A is correct, the length is 5
A golf course charges a cart fee of $5 for members and $10 for nonmembers. Last Sunday, the number of members with carts was at least twice the number of nonmembers. The golf course had collected at most $300 in cart fees.
If x is the number of members and y is number of nonmembers. Using the inequalities below, tell which graph represents the possible solution for the number of each kind of golfer?
Plot the coordinates on the graph to obtain the graph of the system of inequalities.
What is graphing method to solve the equation?As Math World correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines.
The visual technique actually just requires three easy actions to complete: Slope-Intercept Form should be applied to both equations.
Each linear equation's graph should be shown in the same coordinate plane. Identify the system's solution.
If the lines cross, the system's solution may be found by using the coordinates of the crossing point. The problem cannot be solved if the lines are parallel.
Let us suppose number of members =x.
Let us suppose the number of non members = y.
The system of equation for the following situation is:
5x + 10y ≤ 300
x ≥ 2y
Substitute different values of x to obtain different values of y.
Plot the coordinates on the graph to obtain the graph of the system of equations.
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What is the volume for the prism? 4 m 1.5 m 2 m
Answer: 12 [tex]m^{3}[/tex]
Step-by-step explanation:
Volume = length x width x height
Volume = 4 m x 1.5 m x 2 m
Volume = 12 cubic meters
which segments or segment are perpendicular?
thanks for helping
Answer: A. Segment CD only
Step-by-step explanation:
Perpendicular lines form 90 degree angles. The only segment that creates a 90 degree angle is CD. And we know this due to the little box that represents 90 degrees.
RATIONAL EXPRESSIONS Writing equivalent rational expressions with monomial... Fill in the blank to make equivalent rational expressions. (3)/(x^(6))=(prod )/(5x^(9))
To make equivalent rational expressions, we need to multiply the numerator and denominator of the left-hand side of the equation by the same value.
In this case, we can multiply both the numerator and denominator by (5x^(3))/(5x^(3)) to get the equivalent expression on the right-hand side. (3)/(x^(6)) * (5x^(3))/(5x^(3)) = (15x^(3))/(5x^(9))
Therefore, the value that we need to fill in the blank is (15x^(3)). So the equivalent rational expression is:
(3)/(x^(6))=(15x^(3))/(5x^(9))
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Help with this question
A window for a new house is shown. How many square feet of glass does the window require, if it is double-paned? Enter your answer in the box.
A kite with a height composed of 3.2 and 4 feet, and a width composed of 2 feet and 2 feet.
Hence, the amount of glass needed in square feet is 2 × 14.4 = 28.8 sq feet.
What purposes serves Square?A square in geometry is a two-dimensional plane figure with four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are somewhat comparable, but only the opposite sides of a rectangle are equal. So, only if all four of a rectangle's sides are the same length can it be said to be a square.
Only the window of a new house was advertised.
a kite with a height of 3.2 and 4 feet, a width of 2 feet, and a width of 2 feet.
Two panes make up the window.
To determine: How so many sq ft of glass is needed for the window,
Triangle area equals (1/2) base x height.
= (1/2) × 2 × 3.2 + (1/2) ×2 × 3.2 + (1/2) × 2 × 4 + (1/2) × 2 × 4
=2 × 3.2 + 2 × 4
= 2 × (3.2 + 4)
= 2 × 7.2
= 14.4 sq feet
Double-paned glass is a given.
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What you guys are doing is not fair. Give. Me answer
Answer: stop being a brat
Step-by-step explanation:
I NEED TO FINISH THIS TEST I HAVE ONLY 3 MINUTES LEFT!!
What is this number in standard form?
(8×10) + (2×1/100) +( 9×1/1,000)
heres the answer:
8x10=80
2x1=2/100= 0.02
9x1=9/1000= 0.002
0.002+0.02+80=
80.002!!
A consumer price analyst claims that prices for liquid crystal display (LCD) computer monitors have a mean of $ 170 and a standard deviation of $ 53.
1. What is the probability that a randomly selected LCD computer monitor costs less than $ 180? Assume here that the prices are normally distributed.
2. You randomly selected 9 LCD compute monitors. What is the probability that their mean cost is less than $ 180? Assume here that the prices are normally distributed
3. You randomly selected 36 LCD compute monitors. What is the probability that their mean cost is less than $ 180?
1. The probability of getting a z-score of 0.189 or less is 0.5753.
2. The probability of getting a z-score of 1.13 or less is 0.8708.
3. The probability of getting a z-score of 3.02 or less is 0.9982.
What is Normally distributed data:Normally distributed data refers to data that follows a normal distribution, also known as a Gaussian distribution or bell curve.
In a normal distribution, the data is symmetric around the mean and the majority of the data is clustered around the mean with decreasing density as the data moves further away from the mean.
Here we have
The mean price for liquid crystal display (LCD) computer monitors is $ 170 and the standard deviation is $ 53.
Find the z-score associated with $ 180 using the formula:
z = (x - μ) / σ
where x is the value we need to find the probability, μ is the mean, and σ is the standard deviation.
z = (180 - 170) / 53
z = 0.189
Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.189 or less is 0.5753.
To find the probability that the mean cost of 9 randomly selected LCD computer monitors is less than $ 180, find the standard deviation σ/√n.
The standard deviation of the sample means is σ/√n = $53/√9 = $17.67.
Now we need to find the z-score associated with $ 180 using the formula:
z = (x - μ) / σ/√n
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
z = (180 - 170) / (53 / √9)
z = 1.13
Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.13 or less is 0.8708.
To find the probability that the mean cost of 36 randomly selected LCD computer monitors is less than $ 180, we can use the same formula as in part 2, with n = 36:
z = (x - μ) / σ/√n
z = (180 - 170) / (53 / √36)
z = 3.02
Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.02 or less is 0.9982.
Therefore,
1. The probability of getting a z-score of 0.189 or less is 0.5753.
2. The probability of getting a z-score of 1.13 or less is 0.8708.
3. The probability of getting a z-score of 3.02 or less is 0.9982.
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5. Jabu's investment of R2 200 earned R528 in two years. a. Calculate the simple interest rate for this investment. b. If she decides to invest the total amount (original principal amount plus interest) for another two years at the same rate, what interest will she earn over the second two years. c. What is the difference in interest earned over the first two years, compared with interest earned over the second two years?
The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is R9,338.80.
What is the future value determined?The future payment to be made at the end of the seventh year is determined by computing the future values in two stages. The first stage computes the future value before the payment at the end of the first year. The second stage computes the future value for six years.
here, we know,
The future value is computed by compounding the present value at an interest rate.
Current debt = R6,421,00
Compound interest rate = 11% per year
Compounding period = Quarterly
Future Value in 1 Year:
N (# of periods) = 4 quarters (1 year x 4)
I/Y (Interest per year) = 11%
PV (Present Value) = R6,421.00
PMT (Periodic Payment) = R0
Results:
Future Value (FV) = R7,156.98
Total Interest = R735.98
Future Value (FV) = R7,156.98
Payment in one year's time = R2,287.00
Balance = R4,869.98
Future Value at the end of the 7th Year:
N (# of periods) = 24 quarters (6 years x 4)
I/Y (Interest per year) = 11%
PV (Present Value) = R4,869.98
PMT (Periodic Payment) = R0
Results:
Future Value (FV) = R9,338.80
Total Interest = R4,468.82
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Prove the following statement. Your work should be legible, and all of your logic should be clear and justified. Sin^4 (A) – cos^4 (A) = 1 - 2 cos^2 (A)
we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.
To prove the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A), we can use the following steps:
Step 1: Use the identity sin^2(A) + cos^2(A) = 1 to express sin^4(A) in terms of cos^4(A).
sin^4(A) = (1 - cos^2(A))^2
Step 2: Expand the expression on the right hand side.
sin^4(A) = 1 - 2cos^2(A) + cos^4(A)
Step 3: Rearrange the terms to get the expression on the left hand side.
sin^4(A) - cos^4(A) = 1 - 2cos^2(A)
Step 4: Verify that the expression on the left hand side is equal to the expression on the right hand side.
1 - 2cos^2(A) = 1 - 2cos^2(A)
Therefore, the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) is proven to be true.
In conclusion, we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.
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A 6 th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function y=(x-3)^(a)(x-b)^(c) where:
The answer of function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].
A 6th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function[tex]y=(x-3)^4(x+1)^2[/tex].
This is because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times, and the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.
Therefore, the values of a, b, and c in the function y=(x-3)^(a)(x-b)^(c) are:
a = 4, because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times.
b = -1, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.
c = 2, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.
So, the function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].
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A small plane lands at a point 331 miles east and 86 miles north of the point at which it took off. Find the distance the plane flew and the direction. Distance
=∣
miles Direction
=
degrees North of East Question Help:
□
Message instructor
The direction the plane flew is 14.6 degrees North of East.
So, the final answer is:
Distance = 342 miles
Direction = 14.6 degrees North of East
The distance the plane flew can be found using the Pythagorean Theorem, which states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c^2 = a^2 + b^2. In this case, the distance east (331 miles) is one side of the triangle and the distance north (86 miles) is the other side.
So, we can plug in the values and solve for c:
c^2 = 331^2 + 86^2
c^2 = 109561 + 7396
c^2 = 116957
c = √116957
c = 342 miles
Therefore, the distance the plane flew is 342 miles.
To find the direction, we can use trigonometry. The direction is the angle between the east-west line and the line connecting the starting point and the landing point. We can use the tangent function to find this angle:
tan θ = opposite/adjacent
tan θ = 86/331
θ = tan^-1(86/331)
θ = 14.6 degrees
Therefore, the direction the plane flew is 14.6 degrees North of East.
So, the final answer is:
Distance = 342 miles
Direction = 14.6 degrees North of East
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HELP LpEASE 25 POINTS
Area of circle A is 113.04 in²
Area of circle B is 200.96 in²
Area of circle C is 452.16 in²
Area of circle B is 254.34 in²
The number of times that the area of Circle D greater than Circle A is 2.25
What are the areas of the circles?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 3.14
R = radius
here, we have,
Area of circle A = 3.14 x 6² = 113.04 in²
Area of circle B = 3.14 x (6 + 2)² = 200.96 in²
Area of circle C = 3.14 x (8 + 4)² = 452.16 in²
Area of circle B = 3.14 x (12 - 3)² = 254.34 in²
Number of time that is the area of Circle D greater than Circle A = 254.34 in² / 113.04 in² = 2.25
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Complete question:
The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?