A = 1/4 0b^3c
need this rn algebra 1 will give a lot of points

Answers

Answer 1

Answer: c=\(\frac{4A}{b^3}\)

Step-by-step explanation:

A = 1/4b^3c

A*4=4*1/4b^3c

4A=4/4b^3c

4A=b^3c

c=4A/b^3

c=\(\frac{4A}{b^3}\)


Related Questions

Name the arc made by the given angle

Name the arc made by the given angle

Answers

The required arc made by the angle ∠UQT in the given circle is arc UT.

Given the diagram of circle, which is marked with different line segments.

Arc is the part of the circle. Diameter is the line passing through the centre of the circle, radius of the circle is the line segment between centre and other point on the circle, the chord is the line segment  points on the circle and diameter is the biggest chord, tangent is the line segment which intersect the circle at only one point and that point is known as point of tangency and secant is the line segment which cuts the circles.

That implies, the arc made by the angle  ∠UQT is arc UT.

Therefore, the required arc made by the angle ∠UQT in the given circle is arc UT.

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A teacher is calculating the marks for the students in her Data Management class. She assigns the following values to each category. Knowledge: 25% Application: 20% Thinking: 10% Culminating Project: 15% Final Exam: 15% Communication: 15% Kyle has not yet written his final exam, but his marks in the first five categories are 90, 79, 82, 70, and 85. a) Determine the weighted mean for Kyle before the final exam. b) How does this weighted mean differ from the unweighted mean?

Answers

Weighted Mean = (90 × 25% + 79 × 20% + 82 × 10% + 70 × 15% + 85 × 15%) / (25% + 20% + 10% + 15% + 15%)

Unweighted Mean = (90 + 79 + 82 + 70 + 85) / 5

One student, Kyle, hasn't taken his final exam yet, but his marks in the first five categories are 90, 79, 82, 70, and 85. This problem requires determining the weighted mean for Kyle before the final exam and comparing it to the unweighted mean.

To calculate the weighted mean for Kyle before the final exam, we need to multiply each category's mark by its corresponding weight, sum them up, and divide by the total weight. For Kyle, the weighted mean would be calculated as follows:

Weighted Mean = (Knowledge × 25% + Application × 20% + Thinking × 10% + Culminating Project × 15% + Final Exam × 15% + Communication × 15%) / (Total Weight)

However, since Kyle hasn't written his final exam yet, we can exclude the Final Exam mark and its weight from the calculation. The weighted mean would then be:

Weighted Mean = (90 × 25% + 79 × 20% + 82 × 10% + 70 × 15% + 85 × 15%) / (25% + 20% + 10% + 15% + 15%)

To find the difference between the weighted mean and the unweighted mean, we need to calculate the unweighted mean by simply taking the average of the marks in the first five categories:

Unweighted Mean = (90 + 79 + 82 + 70 + 85) / 5

By comparing the weighted mean and the unweighted mean, we can evaluate how much the inclusion of weights for different categories affects Kyle's overall mark.

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What is (0.3)^2 in expanded form?

Answers

Answer:(0.3)^2 in expanded form is:

(0.3) x (0.3) = 0.09

So (0.3)^2 is equal to 0.09.

Step-by-step explanation:

A baseball is thrown into the air from a height of 5 feet. the ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. which equation models the height of the baseball? assume that acceleration due to gravity is –16 ft/s2. h(t) = 16t2 49.64t 5 h(t) = -16t2 5t 49.64 h(t) = -16t2 49.64t 5 h(t) = 16t2 5t 49.64

Answers

The equation that models the height of the baseball is determined as H(t) = 5 + 49.64t -16(t)².

Maximum height reached by the base ball

The maximum height reached by the baseball is calculated as follows;

H = y₀ + v₀yt + ¹/₂gt²

Assuming negative direction for upward motion

H = y₀ + v₀yt - ¹/₂gt²

0 = y₀ + vt -16(t)²

0 = 5 + 3.2v - 16(3.2)²

0 = 5 + 3.2v - 163.84

3.2v = 158.84

v = 158.84/3.2

v = 49.64

Required equation model

H(t) = 5 + 49.64t -16(t)²

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Answer:C?

Step-by-step explanation:

edge

______ as a type of sales promotion is beneficial because they can encourage consumers to try out a product at reduced risk, but they can be detrimental because they reduce perception of value for the product or service.

Answers

Free samples or product trials as a type of sales promotion can be both beneficial and detrimental. They encourage consumers to try a product at reduced risk, but they can also reduce the perception of value for the product or service.

Offering free samples or product trials is a common sales promotion strategy to attract customers and encourage them to try a product or service. This approach has several benefits. Firstly, it lowers the perceived risk for consumers as they can experience the product without making a financial commitment upfront. This can be especially effective for new or unfamiliar products, as it allows potential customers to test the product's quality and functionality.

However, there can be drawbacks to this sales promotion technique. Providing free samples or trials can create the perception that the product or service has less value or is of lower quality. Consumers may develop a mindset of expecting free or discounted offerings, and it can undermine the willingness to pay the full price in the future. Additionally, if the free samples or trials are not managed effectively, it may attract individuals who are not genuinely interested in the product, leading to wastage of resources and potentially diluting the brand image.

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Which one of the following best defines the notion of the significance level of a hypothesis test?
a. The probability of rejecting H_o, whether it's true or not
b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
c. The probability of the type I error
d. The probability of the type II error

Answers

C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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Give the semantic type for each of the functions in (1).(1) a. λf(et) .tina(e)b. λg(e(et)).λx(e).g(x)(John(e))c. λf(et).λg(et). ∼(g(tina) ∧ f(tina))d. λg(et).λx(e). ∼(g(x))Simplify the expressions in (2) as far as possible using the beta-reduction rule and showing all intermediate steps.(2) a. (λx(e) .x)(mary(e))b. ((λx(e) .λf(et) .x)(tina(e) ))(tall(et) )c. ((λg(e(et)).λx(e).λy(e).g(y)(x))(shave(e(et))))(Mary(e))d. ((λg(e(et)).λx(e).g(x)(x))(shave(e(et))))(John(e))e. ((λf(et.)λg(tt).λx(e).g(f(x)))(tall(et)))(λy(t).1 − y)

Answers

Answer:

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PLS HELPS ME!!!!!!!!!!!!

PLS HELPS ME!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

1).

(a). Yes, the graph is linear.

(b). Rate of change is a slope m, m = (60 - 80) / (10 - 0) = - 2

2). Graph is not proportional, because y-intercept is (0, 80) and not (0, 0)

a grocery store is selling ground beef for $1.89 a pound. how much does it cost to buy 2.5 pounds of ground beef? please help my math teacher is gonna fail me

Answers

$1.89 X 2.5 pounds = $4.725

pls help (will give brainliest if possible!)

pls help (will give brainliest if possible!)

Answers

The real number √21 is an example of an irrational number. (Correct choice: C)

What number is real and irrational?

According to number theory, real numbers are formed by the following sets:

Natural numbers - Set of real numbers defined by N = {1, 2, 3, 4, 5, 6, ...}.Whole numbers - Set of real numbers defined by the union of the set of natural numbers and the number 0.Integers - Set of real numbers defined by the union of the set of whole numbers and Z = {- 1, - 2, - 3, - 4, - 5, - 6, ...}Rational numbers - Set of real numbers defined by numbers of the form m / n, where m and n are integers and n is not zero. All integers are also rational numbers, but not all rational numbers are integers.Irrational numbers - Set of real numbers that are not rational. All rational numbers can have an irrational representation, but not all irrational numbers are rational.

Then, by direct inspection we get the following conclusions:

The real number 5.85858585... is a rational number.The real number 63.4 is a rational number (317 / 50).The real number √21 is an irrational number. The real number √36 is a rational number (6).

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Find the square root of the following decimal numbers.
(b) 0.0016

Answers

The square root of the decimal number is √0.0016 = 0.04

How to find the square root of the decimal number?

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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x + 5y = -2 2x + y = 5 The point of intersection of the lines has a y-coordinate of _____. 1 3 -1

Answers

Answer:

Y =-1

Step-by-step explanation:

There is an easy way to find the answer. Basically you want x + 5y = -2 and then you subtract that from 2x + y = 5. What can you do to one of these equations so that when you add them together they will get rid of the x so you just have the y period so the way I did it was double the 2x plus 5y period so now we have 2X plus 10y equals -4. Subtract that from 2x plus y equals 5. The answer is -9y = 9 so y = -1

Answer:

Y = -1

hope this helps

The equation w(w + 6) = 40 represents the area of a rectangle where w represents the width. What are the dimensions of the rectangle?

Answers

Answer:

The dimensions are thus 4 by 10 units

Step-by-step explanation:

Rewrite w(w + 6) = 40 in standard quadratic form ax^2 + bx + c = 0:

w^2 + 6w - 40 = 0

This factors as follows:

w^2 + 6w - 40 = 0  =>  (w + 10)(w - 4) = 0.

Solving for w, we get w = 4 (and also the unhelpful w = -10).

The width of the rectangle is 4 and the length is 4 + 6, or 10.

The dimensions are thus 4 by 10 units, with area = 40 units^2

y = 1/2 x + 1
-2x + 4y = 4
need an answer please
y = -x - 3
y + x = 2

Answers

There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.

What is an Equation?

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The first system of equations are,

y = 1/2 x + 1

-2x + 4y = 4

Multiplying throughout the first equation by 4, we get

4y = 2x + 4

and the second equation is 4y = 2x + 4

Both the equations are same and so the lines coincide.

They have infinitely many solutions.

The second system of equations are,

y = -x - 3

y + x = 2 ⇒ y = -x + 2

Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.

Here m is the slope.

Given lines have the coefficient of x same, and so slopes are same.

So the lines are parallel.

Two parallel lines does not have a solution.

Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.

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Evaluate the expression for b= 12

Evaluate the expression for b= 12

Answers

Answer:

-5

Step-by-step explanation:

substitute -b for -12 and add 7

A full waterbed mattress is 6 ft by 2 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 lb /ft3. Find the weight of the water in the mattress to the nearest pound.

Answers

Answer:

749 lbs

Step-by-step explanation:

weight of the water in the mattress = volume of the mattress x weight of water

volume of the mattress = volume of a cuboid = length x width x height

6 x 2 x 1 = 12 ft³

weight of the water in the mattress = 12 x 62.4 = 748.8 lbs

749 lbs to the nearest pound

Which criteria can be used to prove triangles are congruent select all that apply?

Answers

The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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Plot three points for the line and graph the line. Points (-4, 2)slope -1/3

Answers

We must plot three points for the line and graph it, for the line we know, a point and its slope, which are:

\(\begin{gathered} (-4,2) \\ m=-\frac{1}{3} \end{gathered}\)

To do this we first determine the function that describes this line, with the form y=mx+b where "y", we know it at a point being 2, "x" is -4 and m is the slope, now we clear b

\(\begin{gathered} 2=-\frac{1}{3}\cdot(-4)+b \\ 2=\frac{4}{3}+b \\ b=2-\frac{4}{3} \\ b=\frac{2}{3} \end{gathered}\)

So our function is as follows:

\(y=-\frac{1}{3}x+\frac{2}{3}\)

Having the function, we can now collect values for "x" and find the points to solve for and find the "y" value, in this case, we use x=-1, x=0, and x=2.

These values are random, they can be any desired value.

\(\begin{gathered} x=-1 \\ y=-\frac{1}{3}\cdot(-1)+\frac{2}{3} \\ y=\frac{1}{3}+\frac{2}{3} \\ y=1 \end{gathered}\)

The first point is (-1,1)

\(\begin{gathered} x=0 \\ y=-\frac{1}{3}\cdot0+\frac{2}{3} \\ y=\frac{2}{3} \end{gathered}\)

The second point is (0,2/3)

\(\begin{gathered} x=2 \\ y=-\frac{1}{3}\cdot(2)+\frac{2}{3} \\ y=-\frac{2}{3}+\frac{2}{3} \\ y=0 \end{gathered}\)

The third point is (2,0)

In conclusion the points are:

\(\begin{gathered} (-1,1) \\ (0,\frac{2}{3}) \\ (2,0) \end{gathered}\)

Now, to plot this line, what we have to do is plot the points found and draw a line through all the points.

The graph with the given point, the three points found and your graph should look like the following graph.

Plot three points for the line and graph the line. Points (-4, 2)slope -1/3

how many 5-card hands can be formed from an ordinary deck of 52 cards if exactly two suits are present in the hand?

Answers

In an ordinary deck of 52 cards, there are a total of 2,598,960 different 5-card hands that can be formed if exactly two suits are present in the hand. There are 7,722 different 5-card hands that can be formed from an ordinary deck of 52 cards if exactly two suits are present in the hand.

To determine the number of 5-card hands with exactly two suits, we need to consider the combinations of suits that can be chosen. There are four suits in a deck of cards: hearts, diamonds, clubs, and spades. To have exactly two suits, we can choose any two suits out of these four.

The number of ways to choose 2 suits out of 4 can be calculated using combinations. In general, the number of combinations of choosing k items out of n is given by the formula C(n, k) = n! / (k!(n-k)!), where n! represents the factorial of n.

In this case, we need to choose 2 suits out of 4, so the number of combinations is C(4, 2) = 4! / (2!(4-2)!) = 6.

Once we have chosen the suits, we need to determine the number of ways to select 5 cards from these two suits. Each suit has 13 cards, so there are 13 cards to choose from in each suit. We can use the formula for combinations again to calculate the number of ways to choose 5 cards from 13: C(13, 5) = 13! / (5!(13-5)!) = 1,287.

Finally, we multiply the number of combinations of suits (6) by the number of ways to select cards from each suit (1,287) to get the total number of 5-card hands: 6 * 1,287 = 7,722.

Therefore, there are 7,722 different 5-card hands that can be formed from an ordinary deck of 52 cards if exactly two suits are present in the hand.

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Help ASAP! 100 Points!! Look AT PHOTO!

Help ASAP! 100 Points!! Look AT PHOTO!

Answers

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

If the diameter of a circle is 8. 4 in. , find the area and the circumference of the circle. Use 3. 14 for pi. Round your answers to the nearest hundredth

Answers

The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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Solve:
- 17 < 2x - 35
Give your answer as an interval.

Answers

Photo has the answer
Solve:- 17 &lt; 2x - 35Give your answer as an interval.

A mouse ran a 360 centimeters course in 9 seconds , how fast did it run ?

Answers

Answer:

r=d/t

r=360 cm / 9 sec= 40 cm per second

Hope that helps :)

Answer:

40 centimeters per second.

Step-by-step explanation:

360 divided by 9= 40

ChIcKeN nUgGeTs :>

The Grove City Triathlon is a race that consists of a 1-mile swim, a 20-mile bicycle ride, and a 6-mile run. Payton is competing in the triathlon. She has finished the swimming and biking parts of the race and is about to start the running part. The graph shows Payton's total time in the triathlon, in minutes, as a function of her average running speed, in miles per minute. According to the graph, how many minutes did it take Payton to finish the swimming and biking parts of the triathlon? A 80 B 82 C 85 D 86

The Grove City Triathlon is a race that consists of a 1-mile swim, a 20-mile bicycle ride, and a 6-mile

Answers

Answer:

85 minutes to complete the whole triathlon.

Step-by-step explanation:

The lowest point of the graph shows 85 minutes.

Hope this helps!

Answer:

According to the graph we can determine that it took Payton C) 85 minutes to finish the swimming and biking parts of the triathlon.

Step-by-step explanation:

We can see where the graph ends, this is where Payton finishes the swimming and biking parts of the triathlon. The lowest point of the graph on the y axis (Her Total Time in Minutes) is 85 minutes, therefore we can determine it took her 85 minutes. Hope this helped :) Good luck!

Complete the steps of a one-mean hypothesis test with Population SD unknown ritical Value Approach Complete the steps of a one-mean hypothesis test with Population SD unknown - Critical Value approach Question An investment blog states the average small business loan is 20 thousand dollars. A business loan broker would like to test the claim that the average small business loan is different than the amount stated in the investment blog. To test this claim at the 5% significance level, the business loan broker collects the following data on a sample of 25 small business loans and records the amount of the loan. The following is the data from this study: Sample size=25 small business loans Sample mean= 18.5 thousand dollars Sample standard deviation = 5 thousand dollars Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=..<, or > to represent the correct hypothesis.) Provide your answer below: null hypothesis: 20 alternative hypothesis: 20

Answers

There is the not sufficient evidence that the average small business loan is different that the amount stated in the  investment blog.

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Here we have given that,

Claim: To check whether the average small business loan is different that the amount stated in the  investment blog.

The hypothesis is,

H0: μ= 20 thousand dollars  Versus  H0: μ ≠ 20 thousand dollars

We have given that,

n= Number of observation = 25

x bar  = sample mean =18.5

S= sample standard deviation =5

Here, population standard deviation is unknown, we use the one sample t test.

t - statistics = (x bar - μ) / (s / √n)

                   = (18.5 - 20) / (5 / √25)

                   = -1.342

we get,

the Test statistic is -1.342

Now we find the P-value

α = level of significance = 0.05

Degrees of freedom = n - 1 = 25 - 1 = 24

This is two tailed test as our interest is to show the population mean is equal or not equal to zero.

Now, we can find the P-value

P-value = 0.1922     Using EXCEL = TDIST( | t-statistics | = 1.342 , D.F=24, tail=2)

Hence, There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.

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the side lenghts of a triangle are in the ratio 3:4:5. the longest side has a lenght of 30cm.what is the perimeter?
give answer in cm

Answers

Answer:

72 cm

Step-by-step explanation:

If g(x)=3(x+3)^2-2, which statement is true?

If g(x)=3(x+3)^2-2, which statement is true?

Answers

Answer: B

Step-by-step explanation:

I suppose that f(x) is the curves drawn in red

Minimum f(x)=-8 (for x=-3)

Minimum g(x) =-2 (for x=-3)

Minimum g(x) > minimum f(x)

Answer B

How do the areas of the triangles compare?

Original
3 in.
5 in.
4 in.
Area = 6 in.²

Scaled
15 in.
25 in.
20 in.
Area = 150 in.²

Answers

Answer:

The area increased by a factor of 25, from 6 in^2 to 150 in^2, when the scale factor for the sides was 5.  

Step-by-step explanation:

The area increased from 6 in^2 to 150 in^2 when the Original triangle was scaled by a factor of 5 (in inches):

 Original  Scaled     Factor

     3               15           5

     5               25          5

     4               20          5

             Area (in^2)                    

      6             150         25

The larger increase in the sale factor for area is due to the area equation for a triangle:  Area = (1/2)b*h.  Since both the base and height both increase by a factor of 5, the are increses by a factor of 25:

     Original:         A = (1/2)b*h

     Scaled by 5:   A = (1/2)((5b)*(5h)) or (1/2)(25)(b*h)  [(1/2)b*h is the original area)

                         Area(scaled) = 25*A(original)

A box of granola weighs 24 ounces and a box of bran flacks weighs 6/8 as much as the ronal A box of Corn Pops weighs 1 1/8 as much as the ronal what is the least number of ounces found in either box or ronal bran flakes or Corn Pops

Answers

Answer:

54 ounces

Step-by-step explanation:

A box of granola weighs 24 ounces and a box of bran flacks weighs 6/8 as much as the ronal

The number of ounces of the bran flakes = 6/8 of the box of the granola

= 6/8 × 24 ounces

= 18 ounces

A box of Corn Pops weighs 1 1/8 as much as the granola

Hence, the number of ounces of the box of corn pops =

1 1/8 of the granola box

= 9/8 × 24 ounces

= 27 ounces

The least number of ounces found in either box or ronal bran flakes or Corn Pops is calculated as:

We solve using LCM Method

Multiples of 18:

18, 36, 54, 72, 90

Multiples of 27:

27, 54, 81, 108

Therefore,

LCM(18, 27) = 54

The least number of ounces found in either box or ronal bran flakes or Corn Pops is 54 ounces

For the expression (1 + b) "", determine the appropriate f(x) and a, and evaluate L(x) = f(a) + f'(a)(x - a). Calculate the numerical error in the linear approximation. 72. [3 marks] For y = 3x - x + 6, find the differential and evaluate for x = 2 and dx = 0.1. + Drag and drop an image or PDF file or click to browse... Time la Q3 (9 points) Section 4.3: 130, 140. 130. [6 marks] Find the local and absolute minima and maxima for the function y = x - 12x over the interval (-00,00). 140. [3 marks] A company that produces cell phones has a cost function of C(x) = x? - 1200x + 36, 400, where is the cost in dollars and x is the number of cell phones produced (in thousands).

Answers

For the expression (1 + b), f(x) = 1 + x and a = 0. Therefore, L(x) = f(0) + f'(0)(x-0) = 1 + x. We have a local maxima at x = -2 and a local minima at x = 2. Since the function y = x^3 - 12x is a cubic function and has no bounds, there are no absolute minima or maxima over the interval (-∞,∞).

The numerical error in the linear approximation is 0 because the linear function is an exact match for the original function.
For y = 3x - x + 6, the differential is dy/dx = 2x + 3. When x = 2 and dx = 0.1, dy/dx = 2(2) + 3 = 7, and the differential is 7(0.1) = 0.7.
To find the local and absolute minima and maxima for y = x - 12x over the interval (-00,00), we take the derivative of y with respect to x: y' = 1 - 12 = -11. The only critical point is at x = 1/12. We evaluate y'' = -11 at x = 1/12 to find that it is a local maximum. There is no absolute maximum or minimum over the given interval.
For the cost function C(x) = x^2 - 1200x + 36,400, we take the derivative with respect to x to find the critical point: C'(x) = 2x - 1200 = 0, which gives x = 600. This is the only critical point. To determine whether it is a minimum or maximum, we evaluate C''(x) = 2 at x = 600. Since C''(600) > 0, we know that x = 600 is a local minimum.
The local and absolute minima and maxima for the function y = x^3 - 12x over the interval (-∞,∞).
1. To find the local minima and maxima, we need to find the critical points of the function. To do this, we first find the first derivative of the function:
y'(x) = d(x^3 - 12x)/dx = 3x^2 - 12
2. Next, set the first derivative equal to zero and solve for x:
3x^2 - 12 = 0
x^2 = 4

x = ±2
3. Now, find the second derivative of the function:
y''(x) = d(3x^2 - 12)/dx = 6x
4. Use the second derivative test to classify the critical points:
y''(-2) = -12 (negative, so it is a local maxima)
y''(2) = 12 (positive, so it is a local minima)
5. Thus, we have a local maxima at x = -2 and a local minima at x = 2. Since the function y = x^3 - 12x is a cubic function and has no bounds, there are no absolute minima or maxima over the interval (-∞,∞).

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