The sum of the first 10 terms is approximately 414.66667. The estimated error is less than or equal to 0.00008.
How we approximate the sum of the series [infinity] n = 1 (1/(9 + n[tex]^5[/tex])) using the sum of the first 10 terms and estimate the error.The sum of the first 10 terms of the series can be approximated by evaluating the expression 9 + n[tex]^5[/tex] for n = 1 to 10 and summing the results.
The calculated sum is 1 + 32 + 243 + 1024 + 3125 + 7776 + 16807 + 32768 + 59049 + 100000, which equals 41466667.
To estimate the error, we can use the remainder term formula Rn ≤ (1/x[tex]^5[/tex]) where x is the value of n.
Substituting x = 10, we get R10 ≤ 1/10[tex]^5[/tex] = 0.00001.
Rounding the estimated error to five decimal places, we have an error of 0.00001.
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WHY IS lens formula used?
The lens formula is used in optics to calculate the position and size of the image formed by a lens.
A lens is a piece of glass or other transparent material that bends light to form an image. The lens formula relates the distance of the object from the lens, the distance of the image from the lens, and the focal length of the lens.
The lens formula is used to determine the position and size of the image formed by a lens in order to design and analyze optical systems. It is used in the design of camera lenses, telescopes, microscopes, and other optical devices.
It also allows us to determine the size and position of the image formed by a lens in a given situation, which is essential for the analysis and correction of optical aberrations.
The lens formula also allows us to determine the type of image formed by a lens, whether it is real or virtual, inverted or erect, and the size of the image compared to the object.
In conclusion, the lens formula is used in optics to calculate the position and size of the image formed by a lens. It is used in the design and analysis of optical systems such as camera lenses, telescopes, microscopes and other optical devices. It also allows us to determine the type of image formed by a lens and the size of the image compared to the object.
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What is the pattern of 1 1 2 3 5 8 13?
The pattern of the sequence 1 1 2 3 5 8 13 is that each term is obtained by adding the previous term and the term before that.
The sequence 1 1 2 3 5 8 13 is also a famous example of the Fibonacci sequence. The Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms. In this case, the first two terms of the sequence are 1 and 1, and the rest of the terms are obtained by adding the previous two terms.
It's also possible to express the pattern of the Fibonacci sequence by using the formula, F(n) = F(n-1) + F(n-2) where F(n) is the nth term of the sequence.
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Show that (2,1) is a solution of the system of equations
The (2,1) is a solution of the system of equations is shown. A formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
2 + 3·1 = 5
5 = 5
1 = -2 +3
1 = 1
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Nicole invests a sum of money in a retirement account with a fixed annual interest rate of 6 percent compounded continuously. After 17 years, the balance reaches $8,441.60. What was the amount of the initial investment?
Round your answer to the nearest TENs place.
Answer:
$3,040.00
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
A =$8,441.60r = 6% = 0.06t = 17 yearsSubstitute the given values into the continuous compounding formula and solve for P:
[tex]\implies 8441.60=Pe^{0.06 \times 17}[/tex]
[tex]\implies 8441.60=Pe^{1.02}[/tex]
[tex]\implies P=\dfrac{8441.60}{e^{1.02}}[/tex]
[tex]\implies P=3043.99824...[/tex]
Therefore, the amount of the initial investment is $3,040.00 (rounded to the nearest tens place).
how many triangles can be formed with SSA? In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements?
Triangle MNO with sides m = 20, n = 14 and angle m ∠ M = 51° can have two possible configurations.
How many triangles can be formed by given information on angles and sides
In this problem we have the knowledge of two sides and an angle of triangle MNO, where angle M is opposite to side m. First, determine the possible values for angle N by law of sine:
n / sin (m ∠ N) = m / sin (m ∠ M)
14 / sin (m ∠ N) = 20 / sin 51°
sin (m ∠ N) = (14 / 20) · sin 51°
sin (m ∠ N) = 0.544
There are two possible values for angle N: m ∠ N₁ ≈ 32.957°, m ∠ N₂ ≈ 147.043°. The existence of two different angles indicates that two distinct triangles can be formed.
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What is 7 power of 0?
Answer:
It equals one
Step-by-step explanation: Anything that has the exponent of 0 will always equal one
Several students measure a 25 mm long nail and wrote the measurements show in the table below who is measurement hurt the greatest percent error? Round to the nearest percent.
The student whose measurement had the greatest percentage error is Tenicia with a measurement of 23mm.
What is percentage error?Percentage error refers to the difference between the estimated value and the actual value which is then expressed as a percentage. In the question given, the students and their values are; Layne, 26 mm, Tenicia, 23 mm, and Juan 25 mm.
Juan was the only student who had no error in the value obtained because she got the exact figure of 25 mm. Tenicia recorded the greatest value because the difference between the actual and estimated value was apart with so much difference. Her error was an 8% error.
25 -23/25 × 100
= 8%
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12x -3y = 7 solve for X
Answer:
x = 0.25y + 7/12
Step-by-step explanation:
12x - 3y = 7
12x = 3y + 7
x = 0.25y + 7/12
What is the formula for factor form?
Therefore , the solution of the given problem of factor comes out to be
Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.
Define factor.It appears that a factor is a parameter that is combined by another to achieve an outcome. A product is the solution to a multiplication puzzle. Think of mixing the factors in an arithmetic problem to get the product. 8 has the elements 2 and 4, for instance: There could be just two parts to a number or many more.
Here,
Take a look at the generic form:
=>Ax²+Bx+C= (x-a)(x-b),
where a & b are the polynomial's roots.
Here, b=2 and a=1
(x+1)(x2) (x + 1)(x 2) is the factored form.
Therefore , the solution of the given problem of factor comes out to be
Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.
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What is the first step in inequality?
The first step in solving an inequality is to isolate the variable on one side of the inequality sign. This is also known as "clearing the inequality" of the variable. This can be done by using inverse operations such as addition, subtraction, multiplication, and division.
For example, if the inequality is 3x + 2 > 7, the first step is to isolate the variable x by subtracting 2 from both sides:
3x + 2 > 7
3x > 5
Then, divide both sides by 3 to get x > 5/3
This is the first step in solving an inequality, as now the variable x is isolated on one side of the inequality sign, and it's clear what the inequality is asking for.
It's important to note that when solving inequalities, it's crucial to keep the direction of the inequality sign the same, meaning if you multiply or divide by a negative number, you need to switch the direction of the inequality sign as well.
Also, it's important to check if the inequality is not valid, if the operation you are doing creates a division by zero, it will be an invalid inequality.
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What is the length of the shorter side of a 30 60 90 triangle if the longer side is?
The shorter side of the triangle will be opposite to 30° angle and larger side will be opposite to 90° angle .
What is a right triangle ?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
The side opposite the smallest angle is the one that is the shortest. The shortest side is opposite the angle that you already know to be the shortest.
The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.
So the shorter side will be opposite to 30° angle and larger side will be opposite to 90° angle .
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What is the additive inverse of negative 4X -8
The additive inverse of the expression is 4x + 8
How to determine the additive inverse of the expression?From the question, the expression is given as
negative 4X -8
Express properly
So, we have the following representation
-4x -8
For an expression y, the additive inverse is -y
Using the above as a guide, we have the following:
Additive inverse of -4x -8 = -(-4x -8)
Open the bracket
Additive inverse of -4x -8 = 4x + 8
Hence, the additive inverse is 4x + 8
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it’s due today help pls
You can only add or subtract radicals together if they are like radicals.
How to solve the problem?√28
Factor 4 out of 28.
√4(7)
Rewrite 4 as 22.
2 2.7
Pull terms out from under the radical.
217
The result can be shown in multiple forms.
Exact Form:
2√7
Decimal form:
5.29150262…
√63
Factor 9 out of 63.
/9 (7)
Rewrite 9 as 32.
Pull terms out from under the radical.
3√7
The result can be shown in multiple forms.
Exact form: 3√7
Decimal Form: 7.93725393...
Sqrt(24)
2√6
Pull terms out from under the radical.
√2^2.6
The result can be shown in multiple forms.
Exact Form:
2√6
Decimal Form:
4.89897948....
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The complete question is: Solve the following radicals:
a) 5 ± [tex]\sqrt{28}[/tex]
b) 4 ± [tex]\sqrt{63}[/tex]
c) 6 ± [tex]\sqrt{24}[/tex]
What are 2 ordered pairs?
An ordered pair is a pair of numbers that are usually represented in the form of (x, y) and it is used to indicate the position of a point in a coordinate system or a Cartesian plane.
Another example is an ordered pair (-2, 1) representing a point in the coordinate system located 2 units to the left of the y-axis and 1 unit above the x-axis.
In this way, any point in a coordinate system can be represented by an ordered pair.
In summary, the ordered pair is a way to represent a point in a coordinate system and it is made up of two numbers (x, y), where x represents the horizontal position and y represents the vertical position of the point in the coordinate system.
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What is the order of ordered pairs?
The Order of the ordered pair is defined as the specific way in which the ordered pair is written having a composition of the x coordinate and the y coordinate .
What is Ordered Pair ?
The Ordered Pair is defined as the pair of numbers in a specific order.
For Example : (x,y) , here for the given ordered pair , the element x is called as the abscissa and the element y is called as the ordinate .
The Order of the Ordered Pair (x,y) is the first element always represents the abscissa that means the x coordinate and the second element should always represent ordinate that means the y coordinate .
For Example : for the ordered pair (2,4) , the x coordinate of the point is 2 and the y coordinate of the point is 4 .
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What is the value of 3 exponent of 1?
The expression "value of 3 exponent of 1" is denoted as 3¹ ,and the value of this expression is 3 .
The Exponent is defined as how many times to use that number in a multiplication .
It is written as a small number to right above the base of the number.
we have to find the value of the exponent expression " value of 3 exponent of 1" ,
the given expression can be represented as ⇒ 3¹ ,
we know that the value of any number with an exponent of 1 is the number itself .
So , the value of 3¹ is ⇒ 3 .
Therefore , the value of 3 exponent of 1 is 3 .
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Farmer Mei want to fence in a rectangular area that ha one ide bordered by a tream. If he
ha 250 m of fence, what are the dimenion and the maximum area he can encloe?
If the rectangular area has maximum area, the dimension of the rectangular area is 62.5 m×62.5 m. The area is 3,906.25 square meters.
To enclose a rectangular area with one side bordered by a stream, Farmer Mei can use the remaining 250 meters of fence to form the other three sides of the rectangle. Since the rectangle has two sides of equal length (the width and the height), we can set up the equation:
2L + 2W = 250
where L represents the length of the rectangle and W represents the width.
Solving for one variable in terms of the other:
W = 250/2 - L
The area of the rectangle is given by the formula:
A = L×W
Now, we can substitute the value of W from the above equation into this one to get:
A = L × (250/2 - L)
A = 125L - L²
To find the maximum area, we need to take the derivative of A with respect to L and set it equal to 0.
dA/dL = 250/2 - 2L = 0
Which gives us the value of L = 125/2 = 62.5m
Now, we can substitute this value of L back into the equation for W to find the width of the rectangle:
W = 250/2 - 62.5 = 62.5m
Therefore the dimensions of the rectangle is 62.5m x 62.5m and the maximum area that can be enclosed is 62.5m x 62.5m = 3,906.25 sq m.
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How do you solve the factor theorem step by step?
The Factor Theorem states that if a polynomial is divided by (x-a) then the remainder is equal to zero if and only if (x-a) is a factor of the polynomial.
To solve the Factor Theorem, first you need to determine the polynomial and the value of (x-a).
Then you divide the polynomial by (x-a). To do this, use synthetic division. Synthetic division is a shorthand way of dividing a polynomial by a linear factor.
If the remainder is 0, then the polynomial is divisible by (x-a). If the remainder is not 0, then (x-a) is not a factor of the polynomial.
To summarize, the Factor Theorem states that if the remainder is 0 after dividing a polynomial by (x-a), then (x-a) is a factor of the polynomial. The Factor Theorem can be solved by using synthetic division.
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1. The cost of having a carpet installed is $25.00 for the delivery plus $1.50 per square yard of carpet. Write a function that models the cost of having a carpet installed.
Answer:
C(x) = 25 + 1.5x
Step-by-step explanation:
A function is a mathematical equation that describes how two variables are related. To write a function that models the cost of having a carpet installed, we can use the information provided in the problem.
The cost of having a carpet installed is:
C(x) = 25 + 1.5x
Where C(x) represents the total cost of the carpet installation and x represents the number of square yards of carpet.
25 is a fixed cost for delivery , and $1.5 is cost per sq yard.
So, C(x) = 25 + 1.5x this function is representing the cost of having a carpet installed in x sq yard.
How do you find the area of a triangle in square units?
The area of a triangle can be calculated using the formula A=1/2*b*h, where b is the base of the triangle and h is the height.
The area of a triangle can be found by using the formula A = 1/2bh, where b is the base of the triangle and h is the height of the triangle. To find the area of a triangle in square units, you would need to multiply the base and the height of the triangle and then divide the result by 2.Once you have these two measurements, simply plug them into the formula and calculate the area.
To calculate the area, we need to first measure the base and the height. Once we have the measurements, we can calculate the area by multiplying the base by the height and then dividing by two. For example, if the base is 8 units and the height is 6 units, the area of the triangle will be 24 square units (A = 1/2*8*6 = 24).
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PLS PLS PLS HELP NEED DONE ASAP
The answer is the point (5, -27) and no other solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation y=-6x+23
Checking for (5, -27) we get -27=-6×5+23
=-27
Hence, The answer is the point (5, -27)
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Evaluate the expression
Answer:
5.6 or 28/5
Step-by-step explanation:
We know that A = 8 and B = 4
The expression is A/5 + B
8/5 + 4
The answer in decimal is 5.6
The answer in fraction is 28/5
which form can beused to determine the slope of this equation 3f-s=24
The slope of the equation of the line 3f - s = 24 is 3.
How to find the slope of an equation?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's model the equation of the line y = mx + b to 3f - s = 24. Then, we can locate the slope in the equation.
Hence,
3f - s = 24.
add s to both sides of the equation
3f - s + s = 24 + s
3f = 24 + s
subtract 24 from both sides of the equation
3f = 24 + s
3f - 24 = 24 - 24 + s
s = 3f - 24
Therefore, the slope is 3.
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What is example of factoring a polynomial?
A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.
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rectangular garden has a walkway around it. The area of the garden is 6(4.5x+2.5). The combined area of the garden and the walkway is 6.5(8x+6). Find the area of the walkway around the garden as the sum of two terms.
I got a similar one too. It was 6(4.5x+1.5) ..
Step-by-step explanation:
PLASE, I NEED HELP
Write and solve an inequality.
Kelvin and Marsha are going to dinner and a movie this evening. Kelvin wants to have at least $70 cash in his wallet. He currently has $10. How much money, x, does Kelvin need to withdraw from the bank?
A. x + 10 > 70; x > $60
B. x + 10 ≥ 70; x ≥ $60
C. x + 10 < 70; x < $60
D. x + 10 ≤ 70; x ≤ $60
Answer:
B. x + 10 ≥ 70; x ≥ $60
Step-by-step explanation:
Given:
x = money (in dollars) Kelvin needs to withdraw from the bank.$10 = money Kelvin currently has.$70 = the least amount of cash Kelvin wants to have in his wallet.The equation that models the given parameters is:
[tex]x + 10 \geq 70[/tex]To solve for x, subtract 10 from both sides of the equation:
[tex]\implies x+10-10 \geq 70-10[/tex]
[tex]\implies x \geq 60[/tex]
Therefore, Kelvin needs to withdraw at least $60 from the bank.
Find x in the equation. 4 times x plus one third equals one third times x plus 4
The value of x for the given expression is,
⇒ x = 5/44
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' 4 times x plus one third equals one third times x plus 4''.
Now, The mathematical expression is,
⇒ 4x + 1/3 = 1/3 (x + 4)
Solve for x as;
⇒ 4x + 1/3 = 1/3x + 3/4
⇒ 4x - 1/3x = 3/4 - 1/3
⇒ 11/3x = 5/12
⇒ x = 5 × 3 / 12×11
⇒ x = 15/ 132
⇒ x = 5/44
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Write two expressions that are equivalent to x + 3 + 2x
Equivalent expressio
What are equivalent expressions?When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18. Algebraic equations with equivalent solutions or roots are called equivalent equations.
An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. Expressions that are equivalent do the same thing even when they have distinct appearances. In the event when two algebraic expressions.
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What is the area of a triangle with the base 4.8 cm and height 3.6 cm *?
The area of a triangle with the base 4.8 cm and height 3.6 cm is 8.64 cm².
The area of a triangle can be easily calculated by keeping the values of base and height in the formula -
Area of triangle = 1/2 × base × height of triangle. We know the values of base and height which are in same units. Hence, directly keeping the values -
Area = 1/2 × 4.8 × 3.6
Performing division on Right Hand Side of the equation
Area = 2.4 × 3.6
Performing multiplication on Right Hand Side of the equation
Area = 8.64 cm²
Therefore, the area of triangle is 8.64 cm².
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Combine like terms to simplify the expression:
7x + 3y – 2 + 6x – 1 + y2
Answer: 13x + 5y - 3
Step-by-step explanation: 7x + 6x + 3y + 2y -2 -1
= 13x + 5y - 3