Find g(x) if the indefinite integral of f(x) need little help

Find G(x) If The Indefinite Integral Of F(x) Need Little Help

Answers

Answer 1

Answer:

g(x) = 4x² - x

General Formulas and Concepts:

Algebra II

Functions

Function NotationPiecewise Functions

Calculus

Integration

IntegralsIntegral NotationIntegration Constant C

Integration Rule [Reverse Power Rule]:                                                               \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

*Note:

Integrating a piecewise function requires you to integrate both parts.

Step 1: Define

Identify.

\(\displaystyle f(x) = \left \{ {{8x - 1 ,\ x \leq 4} \atop {31 ,\ x \geq 4}} \right.\)

\(\displaystyle \int {f(x)} \, dx = \left \{ {{g(x) + C ,\ x \leq 4} \atop {31x + C ,\ x \geq 4}} \right.\)

Step 2: Find function g(x)

We can see that the 2nd part of the piecewise function already has been integrated:

[Integral] Set up:                                                                                             \(\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = \int {31} \, dx ,\ x \geq 4\)[Integral] Rewrite [Integration Property - Multiplied Constant]:                 \(\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31 \int {} \, dx ,\ x \geq 4\)[Integral] Integrate [Integration Rule - Reverse Power Rule]:                     \(\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31x + C ,\ x \geq 4\)

To find function g(x), we simply have the same setup:

[Integral] Set up:                                                                                             \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x - 1} \, dx ,\ x \leq 4\)[Integral] Rewrite [Integration Rule - Addition/Subtraction]:                       \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x} \, dx - \int {1} \, dx ,\ x \leq 4\)[Integrals] Rewrite [Integration Property - Multiplied Constant]:               \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \int {x} \, dx - \int {} \, dx ,\ x \leq 4\)[Integrals] Integrate [Integration Rule - Reverse Power Rule]:                   \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \bigg( \frac{x^2}{2} \bigg) - x + C ,\ x \leq 4\)Simplify:                                                                                                         \(\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 4x^2 - x + C ,\ x \leq 4\)Redefine:                                                                                                       \(\displaystyle g(x) = 4x^2 - x + C ,\ x \leq 4\)

The integration constant C is already included in the answer, so our answer is g(x) = 4x² - x.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration (Applications)


Related Questions

Find the missing digit for the following bank identification numbers:
71100139█




321000█56

Answers

Answer:

711001392

321000759

Step-by-step explanation:

hope it helps ^o^

Type such digits that's are correlated to both numbers but they are not present in both rather than present in one.

They can be 2 and 7 or 5 and 9

711001392321000756

You can write other one also

Question 16 of 50
The point (1, -4) is a solution of the system:

x + 2y = -7
-4y = -x


True

False

Answers

Answer:

False

Step-by-step explanation:

1 + 2 (-4) = -7

1 - 8 = -7

-7 = -7


-4 (-4) = -1

16 = -1

What is the volume of this shape in terms of π (PI)?

What is the volume of this shape in terms of (PI)?

Answers

Answer:

Step-by-step explanation:

1/3 bh=96 pi/3=32 pi

Answer:

\(\displaystyle V = 32\pi \ in^3\)

General Formulas and Concepts:

Symbols

π (pi) ≈ 3.14

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Geometry

Volume of a Cone Formula: \(\displaystyle V = \frac{1}{3} \pi r^2h\)

r is radiush is height

Step-by-step explanation:

Step 1: Define

Identify

r = 4 in

h = 6 in

Step 2: Find Volume

Substitute in variables [Volume of a Cone Formula]:                                    \(\displaystyle V = \frac{1}{3} \pi (4 \ in)^2(6 \ in)\)Evaluate exponents:                                                                                         \(\displaystyle V = \frac{1}{3} \pi (16 \ in^2)(6 \ in)\)Multiply:                                                                                                             \(\displaystyle V = \frac{1}{3} \pi (96 \ in^3)\)Multiply:                                                                                                             \(\displaystyle V = 32\pi \ in^3\)

Solve the equation n + 75 = 155

Answers

Answer:

n = 80

Step-by-step explanation:

Just subtract 75 on both sides.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°. What is the angle between the ground and steepest slope on the real rollercoaster?​

Answers

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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BRAINLY I NEED HELP ASAPPPP!!
After game 6, her mean number of points scored per game is 9.
How many points did Maya score in game 6?

A. 4
B. 8
C. 9
D. 10

Answers

Answer:

b

Step-by-step explanation:

8

1.8 L
1,500 mL
Is this greater than,less than,or equal to?

Answers

Answer: use math)way

Step-by-step explanation:

Find the slope of the line that passes through (5, 3) and (8, 2).

Answers

The slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

To find the slope of the line passing through the points (5, 3) and (8, 2), we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

Let's substitute the coordinates of the given points into the formula:

x1 = 5, y1 = 3

x2 = 8, y2 = 2

slope = (2 - 3) / (8 - 5)

Calculating the numerator and denominator:

slope = -1 / 3

Therefore, the slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

Note: The slope represents the rate of change between the y-coordinates and x-coordinates of two points on a line. In this case, for every 3 units increase in the x-coordinate, the y-coordinate decreases by 1 unit.

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for each of the following systems, find the probability that the system is functional. assume that component kis functional with probability pkindependent of other components.

Answers

The probability that the system is functional is determined by the probability of each component being functional.

Probability is a measure of the likelihood of an event occurring. In this context, we are interested in the probability that a system is functional. A system is functional if all its components are functional.

Let's consider the following systems:

A system with two components, A and B.

The probability that the system is functional is equal to the probability that both components are functional. This is calculated as the product of the individual probabilities of each component being functional.

=> P(A and B are functional) = P(A is functional) * P(B is functional)

A system with three components, A, B and C.

The probability that the system is functional is equal to the probability that all three components are functional. This is calculated as the product of the individual probabilities of each component being functional.

=> P(A, B, and C are functional) = P(A is functional) * P(B is functional) * P(C is functional)

A system with n components, A1, A2, A3, ... An.

The probability that the system is functional is equal to the probability that all n components are functional. This is calculated as the product of the individual probabilities of each component being functional.

=> P(A1, A2, A3, ... An are functional) = P(A1 is functional) * P(A2 is functional) * ... * P(An is functional)

Complete Question:

For each of the following systems, assume that component k is functional with probability p independent of other components. Find the probability that the system is functional.

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Choose the best selection for the
quadrilateral with vertices at the
following points:
(-3,0), (-3,-3), (0,-3), (0,0)
Hint: Start by graphing the points.
Distance Formula: d = √(x2-x₁)² + (Y2 − ₁)²
A. Trapezoid
C. Rectangle
B. Rhombus
D. Square

Answers

Answer:

  D. Square

Step-by-step explanation:

You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).

Graph

A graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.

The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.

The figure is all of a rectangle, rhombus, and square.

The most specific name for the figure is Square.

__

Additional comment

A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.

<95141404393>

Choose the best selection for thequadrilateral with vertices at thefollowing points:(-3,0), (-3,-3),

An angle measures 12 less than the measure of its supplementary angle what is the measure of each angle

Answers

Answer:84

Step-by-step explanation:

2x-12+180

2x=168

x=84

light travels about 186,000 mi / s. The function d(t) = 186,000t gives the distance d(t), in miles, that light travels in t seconds. How far does light travel in 36 s?

Answers

The distance that the light travels on 36 seconds is 6696000 miles.

How to calculate the distance?

From the information, it was illustrated that light travels about 186,000 mi/s and the function d(t) = 186,000t gives the distance.

Therefore, the distance in 36 seconds will be:

d(t) = 186,000t

= 186000 × 36

= 6696000 miles.

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Which graph represents -9x + 4y < 8?



Which graph represents -9x + 4y &lt; 8?

Answers

Answer:

Step-by-step explanation:

Which graph represents -9x + 4y &lt; 8?

Answer: just find the graph like this

Step-by-step explanation:

Which graph represents -9x + 4y &lt; 8?

Value: 2
Looking at the list of equalities below, which property does equality 2 demonstrate?
Equality 1: 8x5 = 5x8
Equality 2: (8x5) x 6.75 = 8 x (5x6.75)
Equality 3: 8 x (5+6.75) = 8 x 5 +8 x 6.75
Equality 4: 8x1 = 8
a. Commutative property of multiplication
O b. Distributive property
O c. Identity property of addition
O d. Associative property of multiplication
Check Answer

Answers

The property which equality 2 demonstrate is: d. Associative property of multiplication.

What is the associative property of multiplication?

The associative property of multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged (grouped).

This ultimately implies that, the associative property of multiplication suggest that the way in which factors are arranged (grouped) when multiplying three (3) numbers does not change the product.

Mathematically, the associative property of multiplication can be represented by this expression:

(a × b) × c = a × (b × c)  ≡ (8 × 5) × 6.75 = 8 × (5 × 6.75)

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Find the equation of the plane that passes through the line of intersection of the planes 2x−3y−z+1=0
and 3x+5y−4z+2=0, and that also passes through the point (3,−1,2)

Answers

The equation of the plane that passes through the line of intersection of the two planes and passes through the point (3,-1,2) is x - 2y + 7z - 17 = 0  .

The Plane we want to find passes through the line of intersection of the planes, so it is perpendicular to the normal vectors of both planes.

The Normal Vector of the plane 2x - 3y - z + 1 = 0 is (2, -3, -1), and

the normal vector of the plane 3x + 5y - 4z + 2 = 0 is (3, 5, -4).

The cross product of these two vectors gives a vector which is perpendicular to both of them, and

hence , it lies along the line of intersection of the two planes:

the cross product of (2, -3, -1) x (3, 5, -4) is  = (-7, -2, 1)  ;

The vector (-7, -2, 1) is the direction vector of the line of intersection.

Now to find the equation of the plane that passes through the point (3, -1, 2) and is perpendicular to this direction vector.

we let , equation of the plane be ax + by + cz + d = 0. We know that the point (3, -1, 2) lies on the plane, so we have:

⇒ a(3) + b(-1) + c(2) + d = 0  ;

⇒ 3a - b + 2c + d = 0  ;

We also know that the plane is perpendicular to the direction vector (-7, -2, 1), so we have:

⇒ a(-7) + b(-2) + c(1) = 0  ;

⇒ -7a - 2b + c = 0  ;

Let  say a = 1. Then we have :

⇒ a = 1

⇒ -7a - 2b + c = 0

⇒ 3a - b + 2c + d = 0

Substituting a = 1 into the first equation gives:

⇒ -7 - 2b + c = 0  ;

Solving for c in terms of b gives:

⇒ c = 2b + 7

Simplifying ,

we get ;

⇒ 3 - b + 2(2b + 7) + d = 0  ;

Solving for d in terms of b gives:   ⇒ d = -2b - 17  ;

Therefore, the equation of the plane is x - 2y + 7z - 17 = 0 .

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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03

Answers

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question:

\(p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015\)

What is the probability that the sample proportion will differ from the population proportion by less than 0.03?

This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So

X = 0.08

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.08 - 0.05}{0.015}\)

\(Z = 2\)

\(Z = 2\) has a pvalue of 0.9772

X = 0.02

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.02 - 0.05}{0.015}\)

\(Z = -2\)

\(Z = -2\) has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

What is the y-intercept of f(x) =
100-(3) * ?
5
A. (1,0)
B. (0,0)
(¹3)
D. (0, 1)
C.

Answers

Answer:

X intercepts: (100/3,0)

Y intercepts: (0,100)

help and i ill give brainliest

help and i ill give brainliest

Answers

Answer:

11

Step-by-step explanation:

f(16) = 7 + 16/4

= 7 + 4

= 11

HELP!!!!
The train journey from Station A to Station B takes 3 hours. The train journey from Station B to Station C takes two and one-half hours. How many minutes are both train rides combined?

120 minutes
180 minutes
300 minutes
330 minutes

Answers

Answer:

330 Minutes

Step-by-step explanation:

A->B is 3 hours

1 hour=60 minutes

3 hours=180 minutes

B->C is 2 1/2 hours

2 hours=120 minutes

1/2 hour=30 minutes

180+120+30=330 minutes

(9,-3) and (9,-4) the slope is what

Answers

Answer:

Undefined

Step-by-step explanation:

84 POINTS NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

84 POINTS NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

11.7

Step-by-step explanation:

If you were to plot the points in the graph, you could do the Pythagorean theorem. The distance of x is 6 and the distance of y is 10. \(6x^{2} + 10^{2} =c^{2}\). After you square the numbers and add them you end up with 136. \(136=c^{2}\). Taking the square root of 136 is close to 11.7

Answer:

Distance (d) = √((2 - -4)^2 + (-7 - 3)^2)

= √(6)^2 + (-10)^2

= √(136)

= 2√(34)

= 11.661903789691

11.661903789691 rounds to 11.7

You are a math tutor at your school.
On the last day of school, you bring in a bag of 48 pieces of candy for your students.
You want to share the candy equally with your 6 students.

How many pieces of candy will each student get?


CLEAR CHECK

54 pieces per student


42 pieces per student


8 pieces per student


0.13 piece per student

Answers

Reduce the current rate of 48 pieces per 6 students to 8 pieces per one student. Divide 48 pieces by 6 students to get 8 pieces per student.

What is called in probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty. Probability and possibility are synonymous. It is a branch of mathematics that deals with the occurrence of a random event. The value ranges from 0 to 1. In mathematics, probability has been introduced to predict the likelihood of events occurring.The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

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solve for x

(look at photo)

solve for x(look at photo)

Answers

By definition of proportion, the value of x is,

⇒ x = 80

We have to given that;

In a triangle,

Perpendicular = 60

Now, By Pythagoras theorem we get;

60² = 36² + y²

3600 = 1296 + y²

y² = 3600 - 1296

y² = 2304

y = 48

Hence, By definition of proportion;

⇒ x / 48 = 60 / 36

⇒ x = 80

Thus, By definition of proportion, the value of x is,

⇒ x = 80

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the general solution of the equation cos3x +cos2x =sin3x/2 + Sinx/2 is​

Answers

Answer:

I am doiiiiiiinnnnggg just wait

4xy+16x≈+40 what is the answer...please hurry

Answers

Answer:

X = 10/(y-4)

Step-by-step explanation:

4X(y-4) = 40

X(y-4) = 10

X = 10/(y-4)

Based upon past experience, Barry expects no overdrafts. He expects no 2nd copies of statements. Barry estimates that he will use network ATMs about 5 times a month with either bank. Barry decides in the end to choose EECU. Assuming that both banks provide the necessary services equally well, and based upon the tables of fees given above, how much can Barry reasonably expect to save annually by choosing EECU in this case over E-town bank?
a.
$72
b.
$78
c.
$144
d.
$24

Answers

Answer:

Based upon past experience, Barry expects no overdrafts. He expects no 2nd copies of statements. Barry estimates that he will use network ATMs about 5 times a month with either bank. Barry decides in the end to choose EECU. Assuming that both banks provide the necessary services equally well, and based upon the tables of fees given above, how much can Barry reasonably expect to save annually by choosing EECU in this case over E-town bank?

a.  $72

b.   $78 <<<CORRECT

c.   $144

d.   $24

 

Step-by-step explanation:

October 2021 EDGE

Barry can expect to save a total of $144 per year by choosing EECU over E-town bank.

Option C is the correct answer.

What is a bank account?

A bank account is a financial account that is opened with a bank or financial institution, which enables individuals or businesses to deposit, withdraw, or transfer money. It is a safe and convenient way to manage money and conduct financial transactions.

We have,

To calculate how much Barry can save annually by choosing EECU over E-town bank, we need to compare the fees charged by both banks for the services Barry expects to use.

According to the tables of fees given above:

- E-town bank charges $2.50 per out-of-network ATM transaction, while EECU charges $1.00.

- E-town bank charges $1.50 per month for paper statements, while EECU charges $0.00.

Based on Barry's expectations, here's how much he can expect to pay annually for these services with each bank:

Out-of-network ATM transactions:

Barry expects to use network ATMs about 5 times a month.

With E-town bank, that would cost him 5 x $2.50 x 12 = $150 per year.

With EECU, that would cost him 5 x $1.00 x 12 = $60 per year.

So Barry can save $150 - $60 = $90 per year by choosing EECU over E-town bank for ATM transactions.

Paper statements:

Barry expects no 2nd copies of statements, so this cost is irrelevant. However, if Barry received paper statements, E-town bank would charge him $1.50 per month, or $18 per year. EECU, on the other hand, does not charge any fee for paper statements, so Barry would save $18 per year by choosing EECU over E-town bank for this service.

So,

By choosing EECU over E-town bank, Barry can expect to save a total of $90 + $18 = $108 per year.

Thus,

Barry can expect to save a total of $144 per year by choosing EECU over E-town bank.

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i enter the bedroom. there are 34 people. i kill 30 people. how many people are there in bedroom​

Answers

Answer:

35

Step-by-step explanation:

Even if you killed 30 people, 34 people remained in the room (30 dead and 4 alive).

You must add a person which is YOU.

Answer:

there are 35 people in the bedroom.

Step-by-step explanation:

please help me with trigonometry

please help me with trigonometry

Answers

The length of the guy wire to the nearest foot would be = 10 ft.

How to calculate the length of the guy wire?

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

Solve 2-3 cos x=5+3 cosx for 0° ≤ 180°

Answers

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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My question:

As an analogy of a circuit with resistance, think of an obstacle race . Which parts of a circuit do the obstacles represent? which part of the circuit do the people respresent?

Answers

The electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

In the analogy of a circuit with resistance, we can compare it to an obstacle race. Here's how we can relate the different elements:

Circuit: The entire obstacle race course represents the circuit itself. It includes all the components and paths that the participants will go through.

Obstacles: The obstacles in the race represent the resistors in the circuit. Just like resistors impede the flow of electrical current in a circuit, obstacles in the race impede the progress of the participants.

People/Participants: The people participating in the race represent the flow of electric current in the circuit. They are the "charge" moving through the circuit, encountering and overcoming obstacles (resistors) to reach the finish line.

The goal of the participants (people) is to navigate through the obstacles (resistors) and complete the race (circuit) by reaching the finish line.

Similarly, in an electrical circuit, the goal is for the electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

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