So on solving the provided question we can say that coefficient of x^2 in x³ +4x² -7x -2 is 1.
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of x^2 in x³ +4x² -7x -2 is 1
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help! this needs to be done ASAP and I don't understand any of these!
Answer:
Step-by-step explanation:
Norman earns $8 for every dog he washes plus25% of the cost of the dog wash. Write an expression that represents the total amount of money Norman earns for one dog wash with a cost, c.
Answer:
y = 0.25c + 8
Step-by-step explanation:
Let's y represent the total cost
We know
25% = 0.25
So, we will write this in the slope-intercept form y= mx +b
So, we have m = 0.25, and b = 8, so our equation is
y = 0.25c + 8
Lamont earns an annual salary of $58,000. He has to pay a 4.5% income tax on his earnings. How much does Lamont pay in income tax?
Answer:If you make ₱ 58,000 you will be taxed ₱ 4,711. That means that your net pay will be ₱ 53,289 per year, or ₱ 4,441 per month.
A tortilla chip is shaped like an equilateral triangle.
If an exterior angle on this tortilla chip measures(2x-80), which equation can you solve to calculate the value of x?
HINT: The interior angles of an equilateral triangle all measure 60.
Step-by-step explanation:
Two interior opposite angles of a triangle are equal to the exterior angel
[tex]60 + 60 = 2x - 80 \\ 120 = 2x - 80 \\ 2x = 120 + 80 \\ 2x = 200 \\ x = \frac{200}{2} \\ x = 100[/tex]
Simplify: (8^ 2/3)^4
Answer: 256
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
Which of the following equations has no real roots?A x 2+4x+3 2=0B x 2 +4x−3 2 =0C x 2 +5x+3 2 =0D 3x2 +4 3x+4=0
The equation x² - 4x + 3√2 = 0 has no real roots.
Roots of Quadratic EquationThe roots of a quadratic equation are the values of variables satisfying the given quadratic equation.
There are three types of roots in quadratic equations, they are:
Real and distinct roots.Real and equal roots.Complex roots.Difference between real and non-real roots
How many roots f(x) has can be seen from the discriminant's value : -
If b2 - 4ac > 0, the quadratic function has two unique real roots.
If b2 - 4ac = 0, then the quadratic function has one repeating real root.
If b2 - 4ac < 0, then the quadratic function has non-real roots.
Discriminant ; D = b² - 4ac
According to the given question, we have to find the nature of the roots of the equation, so finding the nature of the roots of all the equations separately
1. x² - 4x + 3√2 = 0
Here, a = 1, b = -4 and c = 3√2
∵ D = b² - 4ac
∴ D = (-4)² - 4(1)(3√2)
⇒ D = 16 - 12√2
⇒ D = 16 - 12(1.414) = 16 - 16.968
∴ D = -0.968
⇒ D < 0
Consequently, there are no real roots in the equation.
2. x² + 4x - 3√2 = 0
Here, a = 1, b = 4 and c = -3√2
∵ D = b² - 4ac
∴ D = (4)² - 4(1)(-3√2)
⇒ D = 16 + 12√2 > 0
⇒ D > 0
As a result, the equation has two unique real roots.
3. x² + 5x + 3√2 = 0
Here, a = 1, b = 5 and c = 3√2
∵ D = b² - 4ac
∴ D = (5)² - 4(1)(3√2)
⇒ D = 25 - 12√2 = 8.029
⇒ D > 0
As a result, the equation has two unique real roots.
4. 3x² + 4√3x + 4 = 0
Here, a = 3, b = 4√3 and c = 4
∵ D = b² - 4ac
∴ D = (4√3)² - 4(3)(4)
⇒ D = 48 - 48 = 0
⇒ D = 0
As a result, the equation has two roots that are equal.
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What do you mean by method of factorization in method of substitution?
Method of factorization in method of substitution is a technique used to solve systems of linear equations. In this method, one of the equations is multiplied by a factor to make the coefficient of one of the variables the same. This allows the equations to be combined and solved for the remaining variables.
Solving Linear Equations Using Method of Factorization in Method of SubstitutionMethod of factorization in method of substitution is a useful technique for solving systems of linear equations. It allows one to isolate a single variable and make use of substitution to solve the system. The first step is to multiply one of the equations by a factor to make the coefficient of one of the variables the same in both equations. This allows the equations to be combined and solved for the remaining variables. Once the values of the variables have been found, they can be substituted into the other equation to find the solution of the system. This technique is beneficial because it allows one to avoid tedious calculations that are often required when solving linear equations.
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blueprints Ezra redrawing the blue paint shown of a stage he is planning to build for his band. By what percentage should he multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint? what will be the perimeter of the updated blueprint?
The percentage by which Ezra should multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint is of:
50%.
The perimeter of the updated blueprint will be 50% of the perimeter of the original blueprint.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
For this problem, we want for the dimensions of the updated stage to be half the dimensions of the original stage, hence the scale factor of the dilation is given as follows:
k = 1/2.
The percentage equivalent to a fraction of 1/2 is of 50%, and the perimeter of the updated stage will be 1/2 the perimeter of the original stage, as both the perimeter and the side lengths have the same unit.
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A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 10 cm.
(a) Find an equation of the parabola.
(b) Find the diameter of the opening CD, 11 cm from the vertex.
The equation and diameter CD of the parabola are x=1/10 y^2and 2√110
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
a(x – h)2 + k
Where:(h, k) - The vertex of the parabola.
a - Least distance between the vertex and the focus of the parabola.
Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.
Given;
Vertex is at origins (0,0) and latus rectum = 10 and the graph open right so a is positive and the equation is:
x=a (y-k)^2+h.
To write the equation we need to find a using the latus rectum equation.
We substitute the values.Then inverse place of a with 10
Latus rectum=|1/a|
10=|1/a|
a=1/10
The equation:
x=a (y-k)^2+h
x=1/10(y-0)^2+0
x=1/10 y^2
-Assume the distance between C and the center is EC. If E is (11,0) and C is (11, y).
-EC=y
-The equation of the parabola is x=1/10 y^2
Now, Substitute the value of C coordinate, which
x=1/10 y^2
Substitute the value of C coordinate, which is (11, y).
11×10=1/(10×10) y^2
√(y^2 )=√110
y=EC=√110
Because the distance of EC = ED
CD=EC×2
CD=√110×2
CD=2√110
Therefore, the equation of parabola and CD will be x=1/10 y^2 and 2√110
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F(x) = x^2 - x - 1 Over which interval doe f have an average rate of change of zero
The interval over which f(x) = x² - x - 1 has an average rate of change of zero is (1/2, 1/2) as it is the only point at which the average rate of change is zero.
An average rate of change of zero means that the function is not increasing or decreasing over the interval in question. To find the interval over which f(x) has an average rate of change of zero, we need to find the critical points of the function. A critical point is a point at which the function's derivative is equal to zero or is undefined.
The derivative of f(x) = x² - x - 1 is:
f'(x) = 2x - 1
Setting f'(x) = 0, we get:
2x - 1 = 0
Solving for x, we get:
x = 1/2
Since this is the only critical point of the function, it is the point where the function has an average rate of change of zero. To determine the interval, we need to check the sign of the function's derivative on either side of the critical point.
f''(x) = 2 > 0
So x = 1/2 is the minima of the function
f'(x) = 2(1/2) - 1 = 0, at x = 1/2
so f'(x) > 0 for x < 1/2 and f'(x) < 0 for x > 1/2
Therefore the interval over which f(x) has an average rate of change of zero is (1/2, 1/2) or {1/2}.
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Can a triangle be formed with side lengths 7/10 20?
It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.
Now, According to the question:
We know that:
What is triangle inequality rule?
The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the third side. The Triangle is a polygon with three line segments as its boundaries.
Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.
We have the sides:
7, 10 and 20
7 + 10 > 20
It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.
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- x/7 − 8 = 17
Show work
And check
Answer:
x = -175
Step-by-step explanation:
Given:
⇒ [tex]-\frac{x}{7}-8=17[/tex]
Solution:
Work:
[tex]-\frac{x}{7}-8=17[/tex]
[tex]-\frac{x}{7}-8+8=17+8[/tex] ⇒ Add 8 to both sides
[tex]-\frac{x}{7}=25[/tex]
[tex]7\left(-\frac{x}{7}\right)=25\cdot \:7[/tex] ⇒ Multiply both sides by 7
-x = 175
[tex]\frac{-x}{-1}=\frac{175}{-1}[/tex] ⇒ Divide both sides by -1
x = -175
Check:
Since, x = -175. We can substitute into the equation to check.
[tex]-\frac{-175}{7}-8=17[/tex]
[tex]-\frac{-175}{7}=25[/tex]
[tex]25-8=17[/tex] ⇒ Statement = True (25 minus 8 is 17.
Hence, x = -175
Lenvy~
How do you find the legs of a 30 60 90 triangle given the long leg?
Answer:
A 30-60-90 triangle is a special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The side opposite the 30 degree angle is called the "short leg", the side opposite the 60 degree angle is called the "medium leg", and the side opposite the 90 degree angle is called the "long leg".
The ratios of the sides in a 30-60-90 triangle are always in the proportion of 1 : √3 : 2 . To find the legs of a 30-60-90 triangle when given the long leg, you can use these ratios.
If the long leg is "x", then the short leg is x/2 and the medium leg is x*√3/2.
For example, if the long leg is 8 cm, you can use these ratios to find the short leg and medium leg:
The short leg is 8 cm / 2 = 4 cm
The medium leg is 8 cm * √3 / 2 = 4 * √3 cm = 4 * 1.732 cm = 6.928 cm (approx)
So, in this example, the short leg is 4cm and the medium leg is 6.928cm (approx).
It's always a good idea to draw a diagram and label the sides to help you visualize the problem and check your answer.
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 13, 19,25,... Find the 48th term.
The given sequence is 13, 19, 25, ...
What comprises an arithmetic series?
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
This sequence appears to be increasing by 6 each time, so it is an arithmetic sequence. The common difference is 6. The nth term of an arithmetic sequence is given by the formula:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference and n is the position of the term in the sequence.
We can use this formula to find the 48th term of the sequence:
a48 = a1 + (48-1)d
a48 = 13 + (48-1)6
a48 = 13 + 47*6
a48 = 13 + 282
a48 = 295
So, the 48th term of the sequence is 295.
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∣x−7∣=∣2x−8∣ (there are 2 solutions for the positive one and the negative)
Answer:
x = 1, x = 5
Step-by-step explanation:
|x−7|=|2x−8| ==> there are 2 ways to simplify this equation:
1. x - 7 = 2x - 8
2. -(x - 7) = 2x - 8
Let's first solve equation 1:
x - 7 = 2x - 8
-7 = x - 8 ==> subtract x on both sides
x - 8 + 8 = -7 + 8 ==> add 8 on both sides
x = 1 ==> simplify
Now let's solve equation 2:
-(x - 7) = 2x - 8
-x - (-7) = 2x - 8 ==> distribute the negative sign to x and -7
-x + 7 = 2x - 8 ==> subtracting a negative number is equivalent to adding a
positive number
7 = 3x - 8 ==> add x on both sides
15 = 3x ==> add 8 on both sides
x = 5 ==> divide 3 on both sides
Hence, the answers are x = 1 and x = 5.
What is a residual and how is it used in finding the line of best fit?
Residual is the difference between the expected and actual y values, so r I = y I y i. A negative residual indicates that the anticipated value is excessively high, whereas a positive residual indicates that the projected value was excessively low. The goal of a regression line is to reduce the total amount of residuals.
What is Mcq, or salvage value?
When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.
What does the depreciation formula's residual value mean?
The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.
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How do you convert base 10 to base 2?
Steps To Convert From Base 10 to Base 2
Divide the given number (in base 10) with 2 until the result finally left is less than 2.Traverse the remainders from bottom to top to get the required number in base 2.Number system conversionThe number system is a way of representing the quantity of a physical item.
For example, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. In everyday life, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. if it is associated with Computer Logic it is represented by two-state elements, namely off and on which is the concept used in the binary number system which only uses 2 kinds of values to represent value quantities.
In addition, the Number System uses a certain number of bases or bases (base / radix). There are 4 types of number systems that have to do with computers, which include:
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ITS COMPOUND INTERSERT ITS URGENTT
Mike's car will be worth £4116 at the start of 2017 as the car decreases in value by 30% every year
How to evaluate for the decreased value of the carAt the start of 2014, Mike's car is worth £12000,
we shall calculate the decreased worth of the same car to the start of 2017 as follows:
At the end of 2014, 30% of £12000 is calculated as;
£12000 × 30/100 = £3600
At the start of 2015, the car will be worth
£12000 - £3600 = £8400
At the end of 2015, 30% of £8400 is calculated as;
£8400 × 30/100 = £25200
At the start of 2016, the car will be worth
£8400 - £2520 = £5880
At the end of 2016, 30% of £5880 is calculated as;
£5880 × 30/100 = £1764
At the start of 2017, the car will be worth
£5880 - £1764 = £4116
Therefore, Mike's car will decrease in value to worth £4116 at the start of 2017.
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If the marble has a volume of 18,000 cubic centimeters, what are the dimensions of the marble?
The dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.
What is volume?An object's capacity is the amount of material it can hold inside, while an object's volume is the amount of space it takes up. Here, the cubic unit is used to measure either of the two.
Cubic units are used to measure volume. The quantity of cubes needed to completely fill any given figure, such as blocks in a box, is its volume.
As there is no definite shape is given we can assume that the shape is cube.
Volume of cube = a³
given the volume 18000cm³
dimensions of the marble,
a × a × a = 18000
a³ = 18000
a = ∛18000
a = 10∛18
a = 26.21
Hence, the dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.
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Select ALL the correct answers. Select the expressions that are equivalent to the expression below. (375/345) 1/3
The equation is given by A = ∛ ( 375/345 ) and A = ( ∛375 ) / ( ∛ 345 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = (375/345) ^ 1/3 be equation (1)
On simplifying the equation , we get
The number raised to the power ( 1/3 ) means it is the cube root of the number ,
So , A = ∛ ( 375/345 )
Now , taking the cube root on both the numerator and denominator ,
A = ( ∛375 ) / ( ∛ 345 )
Hence , the value of A is ( ∛375 ) / ( ∛ 345 )
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The length of a basketball court is 84 feet, and the perimeter is 268 . What is the width of the basketball court?
Answer: 50 ft
Step-by-step Explanation:
First, subtract the given length from the perimeter:
*268 - (84 x 2) = 100
Then divide this by 2:
100 / 2 = 50
*We multiply the 84 by 2 since the court is assumed to have 4 sides meaning there are two sides with lengths and two sides with widths.
What is 7 to the 3rd power and evaluate
Answer: 343
Step-by-step explanation:
7 to the 3rd power
⇒7³
⇒7 × 7 × 7
⇒343 ... answer
hope that helps...
Holly needs to buy some cloth to make masks. The following deals are available at various stores. Choose the best deal
A.
$11.04 per 4 yd
B.
$16.26 per 6 yd
C.
$19.11 per 7 yd
D.
$13.85 per 5 yd
Answer: B, $16.26 per 6 yards
Step-by-step explanation:
$11.04/ 4 yd is $2.76 a yd
$16.26/ 6 yd is $2.71 a yd
$19.11/ 7 yd is $2.73 a yd
$13.85/ 5 yd is $2.77 a yd
Which of the following is a solution of 3x² 5x 2 0?
The solution of the given equation 3x²+ 5x +2= 0 is given by :
option c. x = -2 / 3 or x = -1.
As given in the question,
Given equation is equal to :
3x²+ 5x +2= 0
Solve the given equation by splitting the middle term of the quadratic equation we have,
3x²+ 5x +2= 0
⇒ 3x²+ 3x + 2x + 2 = 0
⇒ 3x ( x + 1 ) + 2 ( x + 1 ) = 0
⇒ ( 3x + 2 ) ( x + 1 ) = 0
⇒ ( 3x + 2 ) = 0 or ( x + 1 ) = 0
⇒ x = -2 / 3 or x = -1
From the given options :
option c. x = -2 / 3 or x = -1 is the solution.
Therefore, the solution of the given equation 3x²+ 5x +2= 0 is equal to :
option c. x = -2 / 3 or x = -1 .
The above question is incomplete, the complete question is:
Which of the following is a solution of the equation 3x²+ 5x +2= 0?
a. x = 2/3 or x = 1
b. x = -2/3 or x = 1
c. x = -2/3 or x = -1
d. x = 2/3 or x = -1
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A Question 1 (1 point) Retake question
The ratio of the measures of the three angles in a triangle is 14:5:11.
Find the measures of the angles.
Please helllopppp
The measures of the three angles in a triangle is 84°, 30° and 66° respectively.
How do you calculate a triangle's ratio?α + β + γ = 180° . From this, you can calculate the angles: ax, bx, and cx, as well as the unknown x. We translate these ideas into a detailed procedure for using ratios to locate missing angles in triangles in the following section.
The ratios are:
∠A = 14, ∠B = 5, ∠C = 11
Total ratio = 14 + 5 + 11= 30
The total angle in a triangle = 180°
So,
∠A= 14 / 30 × 180°= 0.46× 180°= 84°
∠B= 5/30 × 180°= 0.16 × 180°=30°
∠C= 11/30 × 180°= 0.366× 180°= 66°
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what are 2 numbers that can multiply to 14 and add up to sum -9
Answer: -2, -7
Step-by-step explanation:
please please please help me
Answer:
For the first one, the answer would be:
2/3 * 3/8 = 6/24 because, all you have to do is multiply straight across.
2 * 3 = 6 and 3 * 8 = 24
6/24 can be simplified to 1/4 because 6 with go into the denominator 4 times, so the simplified fraction will be 1/4.
(Im not so sure what to do about the second one, so I would need to see what the options look like)
For the third:
The answer would be 3/3, because:
2 * 3 = 6
5 * 3 = 15
And the result fraction is 6/15, which matches what the image shows!
Step-by-step explanation:
Hope it helps! =D
A ray , and an angle is two . The measure of an angle related to the length of its sides. So, the measure of an angle the same at all distances from its vertex.
The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
What is the relation between angle and rays?A ray is a segment of a line with one endpoint and an endlessly extending end. Two rays can be linked at their starting points to create an angle, and their other ends can stretch indefinitely.
According to the question,
the proportion of an angle's measurement to the width of its sides.
Therefore, an angle's measure is constant regardless of how far it is from its vertex.
Due to the fact that adjacent angles are two angles with a shared vertex, and side, but not interior points.
Therefore,
The combination of two rays with the same terminal is called an angle.
The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
Hence the measure of an angle is the same at all distances from its vertex.
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Answer:
Step-by-step explanation:
y=1.7952 × 2.0657^x
find x when y=1000
The value of x when y = 1000 is 8.59.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
y = 1.7952 x [tex]2.0657^x[/tex]
Substitute y = 1000
1000 = 1.7952 x [tex]2.0657^x[/tex]
10³ = 1.7952 x [tex]2.0657^x[/tex]
Taking logs on both sides.
log 10³ = log (1.7952 x [tex]2.0657^x[/tex])
3 log 10 = log 1.7952 + x log 2.0657
3 x 1 = 0.25 + 0.32x
3 = 0.25 + 0.32x
0.32x = 3 - 0.25
x = 2.75/0.32
x = 8.59
Thus,
The value of x is 8.59.
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Find the sum of following infinite series
Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.
What is meant by infinite series?Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order. In addition to being valuable in mathematics, infinite series are also useful in the sciences of physics, chemistry, biology, and engineering. Sigma notation can be used to depict an infinite series. An infinite series, for instance, is ∞∑n=110(12)n−1. The series is endless, as indicated by the infinity symbol above the sigma notation.Infinite series are useful for discovering approximations to complex problems and for highlighting minute details of mathematical precision. A finite series is the accumulation of all of its terms. An infinite series has an infinitely large term count and an infinitely high upper bound.We get,
a) [tex]$\sum_{n=0}^{\infty}$[/tex]
Infinity
b) [tex]$\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$[/tex]
[tex]\sum_{n=1}^{\infty} \frac{4}{2^n}[/tex]
[tex]& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\[/tex]
[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]
[tex]& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)[/tex]
[tex]& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\[/tex]
[tex]& =4\left(2-\frac{1}{2^0}\right)[/tex]
Then we get,
=4
c) [tex]$\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$[/tex]
[tex]$\sum_{n=1}^{\infty} \frac{7}{10^n}[/tex]
[tex]& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\[/tex]
[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]
[tex]& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)[/tex]
[tex]& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\[/tex]
[tex]& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)[/tex]
Simplify
[tex]$7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$[/tex]
= 7/9
Therefore,
a) infinity, b) =4, and c) = 7/9
To learn more about infinite series, refer to:
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