The given cubic equation has no roots.
What are cubic equations?Traditionally, a cubic problem can be solved by converting it into a quadratic equation, which can then be solved by factoring or the quadratic formula. A cubic equation has three roots, just like a quadratic equation has two. Three real roots or one real root and two imaginary roots are both possible for a cubic equation. Cubic equations must also always be arranged in their standard form first.
The following strategies can be used to resolve a cubic equation:
Using Graphical Method to Find Integer Solutions with Factor Lists
Given that the cubic equation is: 8x²-5x³+7-12x
Regrouping the equation in standard form:
- 5x³ + 8x² - 12x + 7
Here, the constant is 7. Take the factors of the constant.
7 = 1, 7
Substitute the value of the factors as follows:
G(1) = - 5(1)³ + 8(1)² - 12(1) + 7 = -5 + 8 - 12 + 7 ≠ 0
G(7) = -5(7)³ + 8(7)² -12(7) + 7 = -1715 + 392 - 84 + 7 ≠ 0
Hence, the given cubic equation has no roots.
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hola, porfavor, ayuda.
Función Objetivo
Maximizar: Z = 30X1 + 50X2
Sujeto a:
Restricción 1: X1 + 3X2 ≤ 200
Restricción 2: X1 + X2 ≤ 100
X1, X2 ≥ 0
The values of X1 and X2 that maximize the function Z = 30X1 + 50X2 are given as follows:
X1 = 50.X2 = 50.The maximum value is given as follows:
4000.
How to maximize the function?The function for this problem is defined as follows:
Z = 30X1 + 50X2.
The constraints are given as follows:
X1 + 3X2 ≤ 200X1 + X2 ≤ 100.X2 has the higher multiplier, hence we should:
Minimize X1.Maximize X2.The maximum value of X2 is obtained when:
X2 = 100 - X1.
Replacing into the first equation, the value of X1 is given as follows:
X1 + 3(100 - X1) = 200
-2X1 = -100
2X1 = 100
X1 = 50.
Hence the value of X2 is of:
X2 = 100 - X1
X2 = 50.
The maximum value of the function is obtained as follows:
Z = 30 x 50 + 50 x 50
Z = 4000.
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3 c ≈ how many mL? Round to the nearest hundredth if necessary.
Answer: It is not possible to convert 3 c to mL without a conversion factor. There are several different units of measurement for volume, including cubic centimeters (cc), milliliters (mL), and cubic meters (m^3). To convert from one unit to another, you need to know the conversion factor.
The conversion factor between cubic centimeters (cc) and milliliters (mL) is 1:1, meaning they are equivalent units of measurement. So, 3 cc is equal to 3 mL.
Step-by-step explanation:
What is the area of the circle? (Approximate using π = 3.14)
circle with a segment drawn from one point on the circle to another point on the circle through the center of the circle labeled 10 feet
A. 15.7 ft2
B. 31.4 ft2
C. 314 ft2
D. 78.5 ft2
The area of the circle with a radius of 5 feet will be 78.5 square feet. Then the correct option is D.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The diameter of the circle is 10 feet. Then the radius is given as,
r = d / 2
r = 10 / 2
r = 5 feet
Then the area of the circle is given as,
A = πr²
A = 3.14 x 5²
A = 3.14 x 25
A = 78.5 square feet
The area of the circle with a radius of 5 feet will be 78.5 square feet. Then the correct option is D.
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31. Let A be a set. Show that ∅ × A = A ×∅=∅.
Answer:
Rational number
Step-by-step explanation:
because all rational number multiple by0 is 0
what operation does the power 1/2 represent
Answer:
Square root
Step-by-step explanation:
Something to the 1/2 power means the square root of that number.
Let f(x) = x ¹/2 and g(x) = 2x² . Find (fg) (x) then evaluate the
product when x=9.
Answer:
see explanation
Step-by-step explanation:
using the rules of exponents/ radicals
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a} )^m[/tex]
then
(fg)(x)
= f(x) × g(x)
= [tex]x^{\frac{1}{2} }[/tex] × 2x²
= 2 × [tex]x^{(\frac{1}{2}+2) }[/tex]
= 2[tex]x^{\frac{5}{2} }[/tex]
when x = 9 , then
= 2 × [tex]9^{\frac{5}{2} }[/tex]
= 2 × [tex](\sqrt{9})^5[/tex]
= 2 × [tex]3^{5}[/tex]
= 2 × 243
= 486
A farmer builds a fence with two gates, each 4 meters wide, around a square field X meters on a side. The cost of the fence is $20 per meter plus $350 per gate. Give an expression for the project cost in terms of X.
Answer:
The project cost in terms of X can be expressed as 20X + 700. This can be determined by using the information from mathportal.org, which states that the cost of the fence is $20 per meter plus $350 per gate. Since the field is X meters on a side and there are two gates, each 4 meters wide, the total cost of the project can be expressed as 20X + 700.
Step-by-step explanation:
BIG IDEAS MATH
K
Tell whether the information in the figure allows you to conclude that point P lies on the perpendicular bisector of
LM.
L
P
M
Yes
O No
N
Explain your reasoning.
Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.
What is a perpendicular bisector?A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.
A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.
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Full Question:
Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.
A) No. You would need to know that LK ⊥ MK
B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
The length of a rectangle is eight meters more than the width. Write an Algebraic Expression to find the area.
I kinda think that this Question is incomplete but this is what my teacher gave me. Thank you for Solving.
Answer: 8xw=a
Step-by-step explanation:
w=width
a=area
Avery was modeling the number of people standing in line to enter a park. She saw that at 8:04am. there was 35 people standing in line and at 8:09 a.m. there were 65 people standing in line. If represents the number of people standing in line and m represents the minutes since 8:00 a.m., answer the follow questions.
a). Represent the information given in the problem as two coordinate points, where the input is the minutes since 8:00 a.m. and the output is the number of people in line.
b). If the relationship between the minutes since 8:00 a.m. and the number of people in line is linear, then what is the slope of the linear function? Include units in your answer.
c). Assuming the relationship is linear, how many people were standing in line at 8:00 a.m.? Show how you found your answer.
d). Write a linear function for the number of people standing in line, n, as a function and number of minutes, m, since 8:00 a.m.
(e) If the linear function in (d) is valid until the park opens at 9:00 a.m., how many people are standing in line when the park opens?
The value of b set to 2 is the third option, which is the correct one.
Find the linear equation ?The provided equation is h(x) = -x + 5.
We obtain b=5 when comparing with the slope-intercept form y = mx+b.
Consequently, the y-intercept is at 5.
To lower the graph by three units, we must make changes.
As per the transformational laws, f(x)+c shifts c units upward, whereas f(x)-c shifts c units downward.
Therefore, we need to subtract the supplied function by 3 in order to move the graph down 3 units, and we get
y = -x+5 -3
y = -x +2.
Here, the y-intercept is 2.
The provided equation is h(x) = -x + 5.
The value of b set to 2 is the third option, which is the correct one.
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Mitchell plans to use ASA to prove that two triangles made from a rectangular piece of wood are the same. Which diagram would support his plan to use ASA?
The solution is given below.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
According to this, the correct answer is: given below.
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Find the average rate of change of the function f(x)= -1x^2+5x-7, on the interval x€[-4,3].
The average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is 0.857.
What is rate of change?Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.
The average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is calculated by taking the difference of the function's values at the endpoints of the interval, divided by the difference in the corresponding x-values. By plugging in the endpoints of the interval into the equation, we find that f(-4)=-25 and f(3)=6. Thus, the average rate of change of the function f(x)=-1x^2+5x-7 on the interval x€[-4,3] is calculated by taking the difference of -25 and 6, divided by the difference of -4 and 3, which is equal to 6/7 or 0.857. Therefore, the average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is 0.857.
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La sexta parte de la diferencia de dos números. En oración algebraica
The phrase "La sexta parte de la diferencia de dos números" in algebraic sentence can be written as [tex] \frac{x}{6} [/tex] where "x" represents the difference between two numbers.
The quantity [tex] \frac{x}{6} [/tex] is a fraction that represents one-sixth of the difference between two numbers. In other words, if you have two numbers "a" and "b", and you subtract them to find their difference "a-b", then [tex] \frac{x}{6} [/tex] would equal [tex] \frac{(a - b)}{6} [/tex].
The fraction [tex] \frac{x}{6} [/tex] gives us a portion or a ratio of the difference between the two numbers, and in this case, it's one-sixth of that difference. So, if you want to find what one-sixth of the difference between two numbers is, you can simply divide that difference by 6.
Let's say that the two numbers you want to find the difference between are 15 and 6. To find their difference, we would subtract the smaller number from the larger one:
15 - 6 = 9
So, the difference between these two numbers is 9. To find one-sixth of this difference, we would divide the difference by 6:
[tex] \frac{9}{6} = 1.5[/tex]
So, one-sixth of the difference between 15 and 6 is 1.5.
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y 10- 9 8 -NW AGO J 7 6 5 4 3 2 A В. 0 1 2 3 4 5 6 7 8 9 10 a) What are the coordinates of A? b) What are the coordinates of B? X
The coordinates of point A' and B' are A'(-12,8) and B'(20, 0)
How to determine the coordinates of point A' and B'?A dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
In this case, the point A (-3, 2) and B (5, 0) are transformed under a dilation of 4 with respect to the origin.
So the images are
A' = (kx, ky) = (-3*4, 2*4) = (-12, 8)
B' = (kx, ky) = (5*4, 0*4) = (20, 0)
So the image point of A(-3,2) under a dilation of 4 with respect to the origin is A'(-12,8)
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Complete question
The triangle ABC is dilated by a scale factor of 4 with the center of dilation at the origin.
a) What are the coordinates of A?
b) What are the coordinates of B?
if A (-3, 2) and B (5, 0)
In Exercises 17–20, u is an acute angle and sin u and cos u are
given. Use identities to find tan u, csc u, sec u, and cot u. Where
necessary, rationalize denominators
20.
Answer:
Tan u = sin u/cos u, csc u = 1/sin u, sec u = 1/cos u, and cot u = cos u/sin u. The denominators of the fractions can be rationalized by multiplying the numerator and denominator by the conjugate of the denominator.
Step-by-step explanation:
27 Answer:
Given the simple interest formula, I = Prt, solve for t
28 Answer:
Rewrite the equation so that y is a function of x:
7x + y = 13
29 Answer:
Rewrite the equation so that y is a function of x:
3x + 5y = 15
30 Answer:
Use the result in question #28 to find y when x = -1.
31 Answer:
Use the result in question #29 to find y when x = -1.
32 Answer:
Find the unit rate: 3 tablespoons for 1.5 servings.
33 Answer:
Find the unit rate: $10.99 for 12 slices of pizza.
34 Answer:
Convert the measure. Round your answer to the nearest tenth.
15 teaspoons to tablespoons (1 tablespoon = 3 teaspoons).
35 Answer:
Find the percent. Round to the nearest whole percent.
159 people in favor out of 350 people surveyed.
28. t = I / (Pr)
29. y = -(3x / 5) + (15 / 5)
30. y = -3/5 x + 3
31. y = -3/5 * -1 + 3 = 3 + 3/5 = 3.6
32. 2 tablespoons per serving
33. $0.92 per slice
34. 5 tablespoons
35. 45% (159 / 350 = 0.45 and 0.45 * 100 = 45)
What is a simple interest?Simple interest is a method of calculating the interest charge on a loan or deposit based on a constant interest rate and the original principal amount. The formula for simple interest is I = Prt, where P is the principal amount, r is the interest rate as a decimal, t is the time period in years, and I is the interest amount. In simple interest, the interest amount is calculated only on the original principal, not on any accumulated interest from prior periods.
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What is 55/99 rounded to the nearest half?
Answer:
1/2 i think this is it
Step-by-step explanation:
Un gerente de oficina pide una calculadora o un calendario para cada uno de los 60 empleados de la oficina. Cada calculadora cuesta $15 y cada calendario cuesta $10. El pedido total ascendió a $800. Parte A: Escribe el sistema de ecuaciones que modela este escenario. (5 puntos) Parte B: Utilice el método de sustitución o el método de eliminación para determinar el número de calculadoras y calendarios pedidos. Mostrar todos los pasos necesarios. (5 puntos)
The system of equations is
15x + 10y = 800
x + y = 60
and the solution to these equations is
x = 40
y = 20
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that an office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800.
We can write the system of equations as -
15x + 10y = 800
x + y = 60
We can write -
y = 60 - x
So, we can write -
15x + 10(60 - x) = 800
15x - 10x + 600 = 800
5x = 200
x = 40
Then -
y = 20
Therefore, the system of equations is
15x + 10y = 800
x + y = 60
and the solution to these equations is
x = 40
y = 20
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{Question in english is -
An office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800. Part A: Write the system of equations that models this scenario. (5 points) Part B: Use the substitution method or the elimination method to determine the number of calculators and calendars ordered. Show all the necessary steps. (5 points)
}
What is the best description of the relation in item 2
Answer:
Step-by-step explanation:
One input(x-value) can only have one output(y-value) in order to be a function
can you answer this for me please
The length of LN for the triangle is 18.
What are triangles?A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees
Given triangle JKL,
and MN is parallel to JK,
taking ΔJKL and ΔLMN
∠L = ∠L (common angle)
because MN is parallel to JK, so corresponding angles are equal,
so ∠K = ∠N
and ∠J = ∠M
ΔJKL ≈ ΔLMN(triangles are similar)
since both triangles are similar the ratio of their corresponding sides is equal,
JL/LM = JK/MN = LK/LN
and JK = 55 and LK = 33
and MN = 12 + LN
JK/MN = LK/LN
substitute the values
55/(12 + LN) = 33/LN
55LN = 33(12 + LN)
55LN - 33LN = 396
22LN = 396
LN = 396/22
LN = 18
Hence the length of LN is 18.
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The small square has the length of Ycm
The large square has the length of 12cm
The area of the small square is 1/9 the area of the large square
Answer:
Y=4cm
Step-by-step explanation:
We can use the relationship between the side length and area of a square to solve for Y. Let's call the area of the small square "A" and the area of the large square "B". From the problem statement, we know:
A = 1/9 * B
Since the area of a square is equal to the side length squared, we can substitute this relationship into the equation above:
Y^2 = 1/9 * 12^2
Solving for Y:
Y^2 = 1/9 * 144
Y^2 = 16
Y = sqrt(16)
Y = 4
So, the side length of the small square is 4 cm.
The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.
Question 4 (Essay Worth 10 points)
(05.06 HC)
Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of equations models the scenario:
4x+2y = 16
x+y=4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set.
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context.
The graph is the graph of straight lines
The point (2, 3) is not included in the solution area
How to describe the graphFrom the question, we have the following parameters that can be used in our computation:
4x+2y = 16
x+y=4
The equations are linear equations
This means that they are straight linesA different solution is 4 cupcakes and 0 fudgeIs the point (2, 3) included in the solution areaWe have
(x, y) = (2, 3)
This gives
4(2) + 2(3) = 16 -- false
2 + 3 = 4 -- false
Hence, it is not in the solution
Interpret a different solution setWe have
4x+2y = 16
x+y=4
This gives
4x+2y = 16
4x + 4y=16
So, we have
2y = 0
And:
y = 0
This means that
4x + 2(0) = 16
x = 4
So, the solution set is (4, 0)
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Law of Exponents: Power to a Power & Power of a product rules, I’m not understanding how is this the correct answer. Explanation Please & Show all Work!
The expression (3a⁸)⁹ * (3b⁵)² is solved to get 3¹¹a⁷²b¹⁰
How to solve the expressionpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base number multiplies itself.
The problem is solved as follows
= (3a⁸)⁹ * (3b⁵)²
raising the terms by power of 9 and 2 accordingly
= (3^9 * a^(8 * 9)) * (3^2 * b^(5 * 2) )
= (3^9 * a^(72)) * (3^2 * b^(10) )
collecting base 3
= (3^9 * 3^2 * a^(72) * b^(10))
= (3^(9 + 2) * a^(72) * b^(10))
= (3^(11) * a^(72) * b^(10))
rewriting the expressions
= 3¹¹a⁷²b¹⁰
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Find the value of x.
D
168°
y
x = [? ]°
Enter
Answer: It is 84 degrees
Jeff purchased 7 gumballs for $0.25 each and 3 pieces of gum. He spent a total of $2.05. How much did each piece of gum cost?
Write the equation for this
problem.
Answer:
Each piece of gum is 10cents
Step-by-step explanation:
7 x 0.25 then subtract that from 2.05 then divide by the 3pieces of gum
Answer: (0.25 x 7) + 3x = 2.05 and $0.10 per piece of gum
Step-by-step explanation:
Jeff purchased 7 gumballs for $0.25 each, which is [tex](0.25*7)[/tex]
Jeff then purchased 3 pieces of gum, but we don't know for how much so the cost becomes [tex]x[/tex] and then [tex]3x[/tex]
The final cost then comes down to $2.05, therefore [tex](0.25*7)+3x=2.05[/tex] and solve for [tex]x[/tex] to find the cost of each piece of gum
[tex]1.75+3x=2.05[/tex]
[tex]3x=0.3[/tex]
[tex]x=0.1[/tex]
Brad took 5 kicks and made 4 goals:4
5 . Sydney will take 10 shots and she
wants to make an equivalent fraction of the goals. How many goals must she
make
Answer: : Sydney must take 8 goals.
Step-by-step explanation:
Brad took 5 kicks and made 4 goals: 4/5.This means denominator is total kicks and numerator is number of goals.Now for Sydney total shots are 10.so we have to find equivalent fraction of 4/5 with denominator as 10.If we multiply denominator 5 by 2 we get denominator as 10.So that means we have to multiply the fraction 4/5 with 2/2This gives us 8/10 as equivalent fraction of 4/5.Numerator represents goals.
49) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has10more of the twenties. The total value of the money is $725. Find the number of five-dollar bills that the teller has?
The bank teller has 21 five-dollar bills.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's represent the number of five-dollar bills "x". Then, the number of twenty-dollar bills would be "x + 10".
The total value of the money is $725, so we can write the equation:
5x + 20(x + 10) = 725
Expanding the second term and simplifying, we get:
5x + 20x + 200 = 725
Combining like terms, we get:
25x = 525
Dividing both sides by 25, we get:
x = 21
So, the teller has 21 five-dollar bills.
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The function y = -4(x - 3)^2 + 8 shows the daily profit (in hundreds of dollars) of a taco food truck, where x is the price of a taco ( in dollars). Find and interpret the zeros of this function. Select two answers: one for the zeros and one for the interpretation.
The zeros of the function y = -4(x-3)² + 8 are -1 and 7 and the intercept is 13
What are zeros of a function?The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
when y = 0
-4(x-3)² +8 = 0
expanding the equation
-4( x²-6x +9)+8 = 0
-4x² +24x -36 +8 = 0
-4x²+24x -28 = 0
divide through by 4
-x²+6x-7 = 0
-x²+7x -x -7 = 0
(-x²+7x)(-x-7) = 0
-x( x-7) 1(x-7)
1-x = 0 or (x-7 )= 0
x = -1 or 7
therefore the zeros are -1 and 7
to find the intercept:
x= 0
y = -4(0-3)²+8
y =-4+9+8
y = 13
therefore the intercept is 13
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Write an equation (In the form of g(m) = P(1+r)^m) for the exponential function from the table below.
Answer:
Equation is
[tex]\mbox {\large \boxed{g(m) = 4.411 (0.94988)^m}}[/tex]
Step-by-step explanation:
We have to translate the information in the table as an equation of the form
[tex]g(m) = P(1 + r)^m\cdots \cdots(1)[/tex]
Let's take the date from the table
For m = 1, g(m) = 4.19
Substituting these values in equation (1) we get:
[tex]g(1) = P(1 + r)^1[/tex]
[tex]4.19 = P(1 + r)^1[/tex]
[tex]P(1 + r)^1 = 4.19 \; \textrm{ (by switching sides)}[/tex]
[tex]P(1+r) = 4.19\; \cdots \cdots (2)\\\textrm{ (an expression raised to the power 1 is the expression itself)}[/tex]
For the next entry in the table, m = 2, g(m) = 3.98
Plugging into (1)
[tex]3.98 = P(1 + r)^2 \cdots\cdots(3)[/tex]
or
[tex]P(1 + r)^2 = 3.98[/tex]
Divide equation (3) by equation (2)
[tex]\dfrac{P(1+r)^2}{P(1+r} = \dfrac{3.98}{4.19}[/tex]
[tex]\textrm{The P terms cancel and } \dfrac{(1 + r)^2}{(1+r)} = 1 + r[/tex]
==> [tex]1 + r = \dfrac{3.98}{4.19}\\\\1 + r = 0.94988\\\\[/tex]
Plugging this value of 1 + r into equation (2):
[tex]P( 0.94988) = 4.19\\\\P = \dfrac{4.19}{0.94988}\\\\P = 4.411\\\\[/tex]
So the equation is
[tex]g(m) = 4.411 (0.94988)^m[/tex]
We can verify this is correct for m = 2, 3 and 4
[tex]m\quad\quad g(m) = 4.411(0.94988)^m\\\------------------\\2\quad\quad 4.411(0.94988)^2 = 3.97992 \approx 3.98\\\\3\quad\quad 4.411(0.94988)^3 = 3.78044 \approx 3.78\\\\3\quad\quad 4.411(0.94988)^4 = 3.59097 \approx 3.59\\\\[/tex]