PLEASE HELPWhat is the point slope form of the line with slope that passes through the point (-4, - 7)?
Oy+4= f (x + 7)
Oy - 7 = } (x – 4)
O y+7=} (x+4)
Oy - 4= } (x – 7)

Answer:

The answer is 6>|-2|

Step-by-step explanation:

> is greater than

< is less than

= (you probably know)

Since |-2| is an absolute value and it is always positive(it equals 2), it isn't greater than 6, so 6>2.

Hope that helps!

Answer:

6>|-2|

Step-by-step explanation:

|-2| means absolute value, so regardless of the sign in the bracket its going to be positive. |-2| = 2.

So, 6 > 2

Answer:

Yes, but can be simplified to \(-\frac{1}{4}\)

Step-by-step explanation:

Since slope is the formula to determine the equation of a line, we use,

\(\frac{rise}{run}\)

In this sense, we can see that the rise is -2

The run, or how far along the x-axis the line goes until it reaches its desired point is 8.

Although you are correct in the \(-\frac{2}{8}\), don't forget to use your GCF to determine how low the fraction can go. (GCF or greatest common factor of 2 in this case) to get \(-\frac{1}{4}\)

I hope this answer finds you well, and I would be happy to help you again in the future! :D

Answer:

Nick's can travel 384 miles on a highway using a full tank of gas of his car

Step-by-step explanation:

Given

Fuel used by Nick's car = 12.5 gallon

In 12.5 gallon Nick can travel up to 240 miles

The gas tank of Nick's car can hold upto 20 gallons of fuel

With a full tank Nick can travel

\(\frac{240}{12.5} * 20 \\384\)miles

Answer:

b is 135 and c is 45.................thanks

Answer:

\(b=135\\c=45\)

Step-by-step explanation:

The angle that measures 135 degrees and angle b are opposite angles. Opposite angles are congruent. Therefore, angle b=135.

\(b=135\)

A straight line has an angle measure of 180 degrees. This means that 135+c would equal 180 degrees.

\(135+c=180\)

Subtract both sides by 135

\(135+c-135=180-135\\c=45\)

I hope this helps!

Answer:

C) \(628\:\text{cm}^2\)

Step-by-step explanation:

\(SA=2\pi rh+2\pi r^2\\\\SA=2\pi(\frac{10}{2})(15)+2\pi(\frac{10}{2})^2\\ \\SA=150\pi+50\pi\\\\SA=200\pi\:\text{cm}^2\approx628\:\text{cm}^2\)

The equation for the trigonometric graph given above is:

y = 4sin(2x + (π/2))

y = 4 cos 2x

It is to be noted that the domain value of θ  is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.

Note that

y = A Sin (Bx - C) + D

The vertical shift → D

Horizontal [Phase] shift → C/B

Wavelength [Period] →  (2/B) π

Amplitude → | A |

Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)

Wavelength | Period | → (2/B)π → π → (2/2)π

Amplitude → 4

Hence, working the above further we get:

y = 4sin(2x + (π/2))

y = 4 cos 2x

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Answer(s):

\(\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x\)

Step-by-step explanation:

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4sin\:2x,\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{4}\:unit\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle \frac{\pi}{4}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \(\displaystyle [-1\frac{1}{4}\pi, 0],\)from there to \(\displaystyle [-\frac{\pi}{4}, 0],\)they are obviously \(\displaystyle \pi\:units\)apart, telling you that the period of the graph is \(\displaystyle \pi.\)Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

None of the provided answer choices (6.95, 9.78, 8.69, 5.46) can be determined based on the given data.

To calculate the time required for the 250th unit, we need to use the learning curve formula. The learning curve formula is often expressed as:

\[ T_n = T_1 \times (n^b) \]

Where:

- \( T_n \) is the time required for the nth unit.

- \( T_1 \) is the time required for the first unit.

- \( n \) is the cumulative number of units produced.

- \( b \) is the learning curve index.

In this case, the learning rate is 30%, which means the learning curve index (\( b \)) is given by the formula:

\[ b = \log(0.7) / \log(2) \]

Let's calculate the learning curve index:

\[ b = \log(0.7) / \log(2) \approx -0.152 \]

Now we can calculate the time required for the 250th unit using the formula:

\[ T_{250} = T_1 \times (250^b) \]

However, we are not given the value of \( T_1 \) in the question, so it is impossible to calculate the exact time required for the 250th unit with the given information.

Therefore, none of the provided answer choices (6.95, 9.78, 8.69, 5.46) can be determined based on the given data.''

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(a) The maturity value of the loan is $15,246.33.

(b) The amount of interest paid on the loan is $7,246.33.

To calculate the maturity value of the loan, we can use the formula for compound interest: A = \(P(1 + r/n)^(nt)\), where A is the maturity value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $8000, the interest rate (r) is 9%, the loan duration is 9 years, and interest is compounded quarterly, so n = 4. Plugging these values into the formula, we get A = \(8000(1 + 0.09/4)^(4*9)\) = $15,246.33.

To calculate the amount of interest paid on the loan, we subtract the principal amount from the maturity value: Interest = Maturity value - Principal amount = $15,246.33 - $8000 = $7,246.33.

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get x = 128 is not a step

Explanation

Question 23

To get the value of x, let us get y as shown below

Next, we will make use of the fact tha y and (x+85 ) are vertical angles so that

For question 23, x = -5

For question 24

The total angle in a circle is 360 degrees so that

solving for x

For question 24, x =-3

It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

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Answer:

c) 16 cm²

Step-by-step explanation:

Given information,

→ Base = 4 cm

→ Height = 8 cm

Area of triangle formula,

→ Area = ½ × b × h

Now the area of triangle is,

→ ½ × b × h

→ ½ × 4 × 8

→ 2 × 8

→ 16 cm²

Hence, the area is 16 cm².

The best measure to determine the variability is mean which is equal to 69.48

We are given the data:

48, 55, 60, 61, 62, 63, 64, 65, 66, 66, 68, 70, 70, 71, 71, 72, 74, 74, 75, 76, 77, 77, 78, 79, 81 and 86​

The best measure to determine the variability is mean.

Total number of observations = 26

Sum of observations (S) will be:

S = 48 + 55 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 66 + 68 + 70 + 70 + 71 + 71 + 72 + 74 + 74 + 75 + 76 + 77 + 77 + 78 + 79 + 81 + 86​

S = 1809

Mean = Sum / total

Mean = 1809 / 26

Mean = 69.58

Therefore, the best measure to determine the variability is mean which is equal to 69.48

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The set of sides √3, √13 and 4 could be used to form a right angled triangle.

We know that,

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Pythagoras theorem can be used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

For a right triangle with sides √3, √13 and 4:

Using Pythagoras:

4² = (√3)² + (√13)²

16 = 3 + 13

16 = 16

The sides √3, √13 and 4 form a right angled triangle.

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The given statement "A successful proof can indeed turn a conditional statement into a theorem.'' is true because a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

In mathematics, a conditional statement is a proposition that asserts a relationship between two or more mathematical objects or concepts. It consists of a hypothesis and a conclusion.

A conditional statement is typically expressed in the form "If A, then B," where A represents the hypothesis and B represents the conclusion.

To establish a conditional statement as a theorem, one needs to provide a valid proof that demonstrates the truth of the statement. A proof is a logical argument that follows a series of logical deductions from axioms, definitions, and previously established theorems.

When a proof is successfully constructed for a conditional statement, it provides rigorous justification for the truth of the conclusion based on the given hypothesis.

By demonstrating the logical validity and coherence of the argument, the proof confirms the truth of the conditional statement and establishes it as a theorem.

The process of proving a conditional statement involves carefully reasoning through logical steps, utilizing mathematical principles and logical inference rules.

It requires precise and accurate reasoning, ensuring that each step in the proof is valid and consistent with the underlying mathematical framework.

Once a conditional statement has been proven, it is elevated to the status of a theorem. Theorems are fundamental results in mathematics that have been rigorously proven and hold true within a given mathematical system.

They serve as building blocks for further mathematical investigations and form the foundation of mathematical knowledge.

In summary, a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

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The Non-real solutions for the equation \(x^{4} -x^{3}+10x^{2} -16x-96=0\) are (-4i, 4i).

Non-real solution:

An answer to a mathematical equation with the root of a negative number that cannot be determined using solely real numbers—i.e., numbers that can be described along a single axis—is referred to as a non-real solution.

If a quadratic has a negative discriminant, then the quadratic equation has a Non-real solution.

Given,

         \(x^{4} -x^{3}+10x^{2} -16x-96=0\)

On factorizing the above equation, we get

             \((x-3)(x-2)(x^{2} +16)=0\)

Applying Zero Product Property,

\(x^{2} +16 = 0\)      or     \(x-3=0\)     0r     \(x+2=0\)

Taking \(x^{2} +16 = 0\), we get

                \(x^{2} =-16\)

                x = ± \(\sqrt{-16}\)

                x = ± 4i              [∵ i = √-1]

Hence,

      The Non-real solutions for the equation \(x^{4} -x^{3}+10x^{2} -16x-96=0\) are (-4i, 4i).

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Answer:

C

Step-by-step explanation:

edge 2026

Answer:

87/13 and 6.69230769231

Step-by-step explanation:

The quotient from the given division is 7 and the remainder is 20.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, dividend =384 and the divisor =52.

Here, 384 divided by 52

So, 384/52

52|384|7

    364

_______

     20

So, the remainder =20 and the quotient =7.

Therefore, the quotient from the given division is 7.

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To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

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Answer:

The slope m of the line is;

Explanation:

Given the graph in the attached image.

We want to find the slope of the graph.

The slope can be calculated using the formula;

Taking two points from the graph;

Substituting the coordinates, we have;

Therefore, the slope m of the line is;

The y-intercept of the line is at;

Writing the slope intercept form of the equation;

where;

m = slope

b = y-intercept

substituting the slope and the y intercept we have;

Therefore, the equation of the line is;

The function f(x) = 10x - x² is a quadratic function.

A quadratic function is a polynomial function of degree 2, which means the highest power of the variable is 2. In the given function, the variable x is raised to the power of 1 in the term 10x, and it is raised to the power of 2 in the term -x². This indicates that the function is a quadratic function.

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants. In the given function, a = -1, b = 10, and c = 0 (since there is no constant term). So, the function f(x) = 10x - x² fits the form of a quadratic function.

Quadratic functions are known for having a graph in the shape of a parabola. In this case, the parabola opens downward because the coefficient of the x² term is negative (-1). The graph of the function will have a vertex at the maximum point, which in this case is (5, 25).

Therefore, the function f(x) = 10x - x² is indeed a quadratic function.

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Answer:

27,44,95

Step-by-step explanation:

These numbers are in order from least to greatest, hope this helped!

Answer:

27, 44, 95

Step-by-step explanation:

Since 27 is smaller than 44 and 95 it goes first and since 95 is bigger than 27 and 44 it goes at the end and 44 is in the middle

In this problem, we need to create an expression that after applying one of the properties of exponents to simplify it, we obtain the given answer.

The first answer we have is:

The second one is:

The third one is:

a. The first property is the product of powers:

In the first answer, we have the exponent 2/9, and we can express it as:

Then, the expression can be:

For the second answer we can rewrite the expression as:

For the third answer, we have:

b. Power of a power property:

First answer:

Second answer:

Third answer:

c. Power of a product:

First answer:

Second answer:

Third answer:

d. Negative exponent:

First answer:

We can express the exponent as:

Second answer:

Third answer:

e. Zero exponent:

First answer:

Second answer:

Third answer:

f. Quotient of powers:

First answer:

Second answer:

Third answer:

g. Power of a quotient:

First answer:

Second answer:

Third answer:

1. The official lines of authority. 2. The formal lines of communication. 3. The base level of the organization.

Organizational structure box-and-lines diagrams show at least three things:

1. The official lines of authority: These diagrams illustrate the formal hierarchy within an organization, indicating the chain of command and reporting relationships. The lines represent the flow of authority and communication, highlighting who reports to whom. For example, a manager may have multiple employees reporting to them, and those employees may further have their own subordinates.

2. The formal lines of communication: These diagrams also depict the formal channels through which information flows within the organization. They show how information is passed between different levels and departments. For instance, a diagram may show that information flows vertically from top management to lower-level employees or horizontally between departments.

3. The base level of the organization: These diagrams display the entry-level positions within the organizational structure. This helps to understand the foundational roles that exist and how they fit into the larger structure. For instance, the diagram may indicate positions such as interns, junior associates, or entry-level staff.

In summary, organizational structure box-and-lines diagrams provide a visual representation of the official lines of authority, the formal lines of communication, and the base level of the organization. These diagrams help individuals understand the hierarchy, communication flow, and entry-level positions within an organization.

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The required inequality is \(p\geq2\)

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by \(> , < , \geq, \leq\)

A one degree inequation is known as linear inequation.

On the day of the test, the teacher instructed the students to take out no less than 2 pencils from their backpacks.

Let the number of pencils be p

So the required inequality is \(p\geq2\)

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Answer:

0.85 kg is 850 grams

Step-by-step explanation:

Since the prefix kilo means  \(10^3\), we can write,

0.85 kg as,

(using 10^3 for kilo,)

\((0.85)*(10^3) g\\=850g\)

So, 0.85 kg is 850 grams

Answer:850 grams

Step-by-step explanation:To calculate a kilogram value to the corresponding value in gram, just multiply the quantity in kg by 1000.

Here is the formula,

Value in grams = value in kg× 1000

Here we need to convert 0.85kg into grams. Using the conversion formula above,

value in gram=0.85×1000=850 grams.

Answer:

Solution

here,

X=?

now,

X+90+42=180 (Sum of angles of Triangle)

or, X=180-132

or, X=48

Hence the value of X is 48 degrees

a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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Answer:

  7360 ft·lb

Step-by-step explanation:

You want the work done by a 320-lb gorilla climbing to a height of 23 feet.

Work is the product of force and distance:

  W = (weight)·(height) = (320 lb)(23 ft) = 7360 ft·lb

The gorilla does 7360 ft·lb of work.

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Additional comment

Time comes into play when you want the power involved. If the climbing is done in 10 seconds, the power required is about 1.34 horsepower. (1 hp = 550 ft·lb/s)

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