The length of segment is 24/√2
Given that,
Having radii of 2 and 4, respectively, and being externally tangent, are circles with centers O and P. The circle with the center at O has points A and B, while the circle with the center at P has points C and D, so that
AD and BC are frequent tangents to the outside of the circles.
To find : What is the hexagon's area?
ADPO and OPBC are congruent right trapezoids with legs 2 and 4 and with OP equal to 6. Draw an altitude from O to either DP or CP,
Creating a rectangle with width 2 and base x, and a right triangle with one leg 2, the hypotenuse 6, and the other aa Using the Pythagorean theorem, is equal to , and x is also equal to the height of the trapezoid. The area of the trapezoid is thus
length = 1/2 * (4+2).4√2 = 12√2
and the total length is two trapezoids, or 24/√2
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How do you prove theorem 8.9 Class 9?
In the triangle the line segment joining the midpoints 'S' and 'T' of the sides PQ and PR implies that ST || QR.
As given in the question,
Diagram is attached.
As per the attached diagram we have,
Given : In triangle PQR with midpoints S and T of sides PQ and PR respectively.
To prove : ST is parallel to QR.
Proof : First construct a line through R parallel to PQ such that it meet the extended line of ST at point 'U'
In triangle PST and triangle RTU,
PQ|| RU and SU is the transversal
∠PST ≅ ∠RUT ( alternate angles )
∠PTS ≅ ∠RTU ( vertically opposite angles)
PT ≅TR ( 'T' is the midpoint of PR )
By AAS we have
ΔPST ≅ΔRTU
By congruent part of congruent triangle we have,
PS ≅ RU
⇒ SQ ≅ RU
In quadrilateral QSUR,
SQ ≅ RU
SQ || RU ( as PQ || RU by construction )
Quadrilateral with one pair of opposite side congruent and parallel implies it is a parallelogram.
Quadrilateral QSUR is a parallelogram.
⇒ SU || QR
S - T - U
⇒ ST is parallel to QR
Therefore, in the given triangle line segment formed by joining the midpoints of the other two sides is parallel to third side.
The above question is incomplete , the complete question is :
Prove theorem 8.9 : The line segment joining the midpoints of the two sides of the given triangle is parallel to the third side .
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In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through $W$, $X$, $Y$, and $Z$. What is the maximum possible distance from $A$ to $P$
In this problem, you have a square with side length 6 and four smaller squares with side length 2 placed in the corners. The points W, X, Y, and Z are the vertices of the smaller squares. The goal is to find the maximum possible distance between points A and P.
[asy] size(200); pair A,B,C,D,P,W,X,Y,Z; A=(0,4); B=(4,4); C=(4,0); D=(0,0); P=(2,2); W=(0,6); X=(6,6); Y=(6,0); Z=(0,0); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); draw(A--P--C); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); label("P",P,S); label("W",W,N); label("X",X,NE); label("Y",Y,S); label("Z",Z,SW); [/asy]
The point A is located on the bottom-left corner of the square with side length 6, and the point P is the center of the square $ABCD$. To find the maximum distance from A to P, we need to find the longest diagonal of the square $ABCD$.
The longest diagonal of a square is the one that goes from one corner of the square to the opposite corner. In this case, the longest diagonal goes from point A to point C, which is a distance of 6 units. Therefore, the maximum possible distance from A to P is 6 units.
As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for Osts 10, where time t is measured in minutes and temperature H(t) is measured in degrees Celsius. Values of H(t) at selected values of time t are shown in the table. Use a trapezoidal sum with the four subintervals indicated by the table to estimate 1 10 Soº H
By using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.
What is Trapezoidal sum?
The trapezoidal rule is a method for roughly approximating the definite integral in calculus. The area of the region that roughly fits the shape of a trapezoid under the graph of the function f(x) is how the trapezoidal rule operates.
A Riemann sum is a technique for calculating the area under a curve by adding the areas of rectangles or trapezoids drawn along the curve. Triangular Riemann Sum: A trapezoidal Riemann sum determines the area under a curve by adding the areas of trapezoids.
Let, [tex]\frac{1}{10}\int\limits^1_00 {H(t)} \, dt[/tex] is the average temperature of the tea, in degree Celsius, over the 10 minutes.
[tex]\frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = \frac{1}{10}(2*\frac{66+60}{2}+ 3*\frac{60 + 52}{2}+4*\frac{52+44}{2}+1*\frac{44+43}{2} \\ \frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = 52.95[/tex]
Hence, by using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.
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A cube with side length 5h^2 is sTacked on another cube with side length 3k . What is the total volume of the cubes in factored form?
(5h^2)^3 + (3k)^3
(5h^2 + 3k) + (25h^4 - 15 h^2k + 9k^2)
(5h^2 + 3k) + (25h^4 + 15 h^2k + 9k^2)
(5h^2 + 3k)^3
The correct option is Option A: (5h^2)^3 + (3k)^3
The total number of cubic units that the cube totally occupies is the definition of a cube's volume. A cube is a solid three-dimensional object with six square faces. Volume is simply the total amount of space an object takes up. A thing with a bigger volume would take up more room.
Total Volume = V₁ + V₂
V₁ = Volume of Cube 1
V₂ = Volume of Cube 2
Volume of Cube = (Side Length)³
V₁ = (5h²)³
V₂ = (3k)³
∴ Total Volume = (5h²)³ + (3k)³
And this cannot be simplified further.
Therefore, the correct option is Option A: (5h^2)^3 + (3k)^3
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Find an equation for a line passing through (10,10) that is perpendicular to the line with equation 5x+8y=-9. Write your equation in
The equation of a line passing through (10,10) that is perpendicular to the line with equation 5x + 8y = -9 is y - 10 = (8/5)(x - 10) or y = (8/5)x - 6.
Get the slope of the line 5x + 8y = -9 by rewriting it in slope-intercept form. Subtract 5x from both sides and divide by 8.
y = (-5/8)x - (9/8)
The slope of this line is -5/8. The negative reciprocal of -5/8 is 8/5. Therefore, the slope of the line that is perpendicular to 5x + 8y = -9 is 8/5.
Using point-slope form, determine the equation of the line.
y - y₁ = m(x - x₁)
y - 10 = (8/5)(x - 10)
or using the slope-intercept form,
y = mx + b
y = (8/5)x + b
10 = (8/5)10 + b
b = -6
y = (8/5)x - 6
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A set of data with a normal distribution has a mean of 16.4 and a standard deviation of 3.2. 68% of the data falls between what two numbers?
68% of the data falls between one standard deviation from the mean which is 13.2 and 19.6
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The empirical rule states that 68% of the data falls within one standard deviation, 95% within two standard deviation from the mean and 99.7% falls within three standard deviation from the mean.
Given a mean of 16.4 and a standard deviation of 3.2.
68% of the data falls one standard deviation from the mean = 16.4 ± 3.2 = (13.2, 19.6)
68% of the data falls between 13.2 and 19.6
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use a linear approximation (or differentials) to estimate the given number. (1.999)5
The approximate value of [tex](1.999)^5[/tex] is 31.92.
Describe linear approximation :A linear approximations in maths is the use of a linear function to estimate a generic function. They are frequently used to create first order methods for solving or approximating equation solution in the method of finite difference.
To estimate [tex](1.999)^5[/tex]
we’ll find the linearization of f(x) = [tex]x^5[/tex]
at a = 2. Since
f′(x) = 5[tex]x^4[/tex]
, f(2) = 32, and
f′(2) = 80,
we have L(x) = 32+80(x−2). Thus,
[tex]x^5[/tex] ≈ 32 + 80(x − 2) when x is near 2,
so (1.999)5 ≈ 32 + 80(1.999 − 2) =
32 − 0.080 = 31.92.
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function f(x) = 4(1.5)x?
Answer:
The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5
Step-by-step explanation:
what is the value of t? 7+8t-9=62
Answer:
t = 8
Step-by-step explanation:
8t - 2=62
8t =62+2
8t = 64
t = 64÷8
t = 8
Answer: t = 8
Step-by-step explanation:
For each of the following wages, determine the Social Security tax that would be withheld. Use $106,800 for maximum taxable earnings. i. $23,660 ii. $89,000 iii. $166,090 a. i. $146.69 ii. $551.80 iii. $1,029.76 b. i. $1,466.92 ii. $5,518.00 iii. $10,297.58 c. i. $146.69 ii. $551.80 iii. $662.16 d. i. $1,466.92 ii. $5,518.00 iii. $6,621.60 Please select the best answer from the choices provided A B C D
The correct answer is C) i. $146.69 ii. $551.80 iii. $662.16.
What is social security tax ?
Social Security tax is a payroll tax that is imposed on both employees and employers to fund the Social Security program in the United States. The tax is used to provide benefits to retired and disabled workers, as well as to the families of deceased workers. The tax is imposed on wages and salaries earned by employees.
A. i. $146.69 ii. $551.80 iii. $1,029.76
B. i. $1,466.92 ii. $5,518.00 iii. $10,297.58
C. i. $146.69 ii. $551.80 iii. $662.16
D. i. $1,466.92 ii. $5,518.00 iii. $6,621.60
The Social Security tax rate is 6.2% for the employee and 6.2% for the employer, for a total of 12.4%. However, the employee portion of the tax is only applied to the first $142,800 of earnings in 2021. Any earnings above this amount are not subject to the employee portion of the Social Security tax.
The correct answer is C) i. $146.69 ii. $551.80 iii. $662.16.
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Answer:
its D
Step-by-step explanation:
because of PEMDAS
angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each. How many books and magazines did angelina buy
In all, she purchased 1 book and 6 periodicals, taking into account the inequality.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, Angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each.
Let "b" be the number of total book and "m" be the number of magazine she bought.
Inequality from the given data
m + b = 7
since, Angelina spent $23.65 on books and magazines
thus,
5.95 * b + 2.95 * m = 23.65
from equation 1
5.95b + 2.95(7 - b) = 23.65
5.95b + 20.65 - 2.95b = 23.65
3 b = 3
b = 1
from any equation
m = 6
Therefore, she total bought 1 book and 6 magazines according the given inequality.
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you are driving on a highway and are about 140 miles from a state border. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side. find the minimum and maximum numbers of hours you will have cruise control on.you will travel at least hour(s) and at most hour(s) with cruise control on.
The minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).
To find the minimum and maximum numbers of hours you will have cruise control on, you need to calculate the distance you will travel with cruise control on and divide it by your speed.
The minimum distance you will travel with cruise control on is
140 miles - 30 miles = 110 miles.
The maximum distance you will travel with cruise control on is
140 miles + 30 miles = 170 miles.
To convert these distances into hours, you will divide them by your speed of 60 miles per hour.
Minimum hours: 110 miles / 60 mph = 1.83 hours
Maximum hours: 170 miles / 60 mph = 2.83 hours
Therefore, the minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).
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this is a late assignment and I am really close to failing please help
Answer: 14.825
Step-by-step explanation:
First , do 2 * 5.3 because it's 2a, you'll have to do 2 * a. This equals 10.6.
Second, you'll need to do 5.3 * 1.25. Why? Because in the problem you need to do a * b, which is that. It equals 6.62500.
Lastly, put it all together! 10.6 + 6.62500 - 2.4 equals 14.825.
please help me on this math question
Answer:
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the amount Alex has at the end of 7 years)
P = the initial investment (£4000)
r = the annual interest rate (x/100)
n = the number of times interest is compounded per year (let's assume it is compounded annually)
t = the number of years invested (7)
Plugging in the given values and solving for x:
5263.73 = 4000(1 + x/100)^7
So x = ((5263.73/4000)^(1/7))-1*100
x = 6.33% (approximately)
So, the interest rate is 6.33%.
The area and perimeter of arectangular field are 60m² and 32 m respectively. Find the length and breadth of the fueld
Jerome has $3,000 to invest in an account that yields 2.1% annual interest which is compounded quarterly. If he leaves the money untouched in the account for 4 years, how much money will he have?
Jerome will have $3261.93 after 4 years
How to calculate how much money Jerome will have?
The formula for compound interest is A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for.
In this case, P = $3,000, n = 3, r = 2.1% = 0.021, t = 4 years. Thus:
A = P(1 + r/n)^(nt)
A = 3000(1 + 0.021/3)^(3×4)
A = 3000(1 + 0.021/3)^(12)
A = $3261.93
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X, Y and Z form the vertices of a triangle, where
∠
YXZ = 57°,
∠
YZX = 47°, and XZ = 7.2cm.
Calculate the length of YZ rounded to 1 DP
Answer:
Step-by-step explanation:
1kg of apples costs £1.12 more than 1 kg of pears.
1kg of apples costs £2.35 less than 1 kg of bananas.
Jackson buys 3 kg of apples, 3 kg of pears and 2 kg of bananas. The total cost is £25.02
How much does 1 kg of apples cost?
Answer:
1 kg of apples cost £2.96-----------------------------------------------
Let the cost of a 1 kg of apples be x.
Then pear costs x - 1.12 and banana costs x + 2.35.
The total cost is 25.02:
3x + 3(x - 1.12) + 2(x + 2.35) = 25.023x + 3x - 3.36 + 2x + 4.7 = 25.028x + 1.34 = 25.028x = 25.02 - 1.348x = 23.68x = 23.68/8x = 2.96hat is the probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck?
The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck is 1/221.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck can be calculated as:
There is a total of 52 cards in a deck and 4 aces and 4 queen cards.
So, the probability is
4/52 * 4/51 = 1/221
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This square-based oblique pyramid has a volume of 125\text{ m}^3125 m 3 125, start text, space, m, end text, cubed. 5\text{ m}5 m5\text{ m}5 m What is the height of the pyramid
If the volume of the square based Pyramid is 125 m³ and the base is of 5m then the height of the pyramid is 15 m .
The Volume of the Square based pyramid is = 125 m³ ;
the measure of the side of base of pyramid is = 5m ;
So , the Area of the base of pyramid is = [tex]5 \times 5[/tex] = 25 m² ;
We know that the formula for the Volume of the pyramid is = [tex]\frac{1}{3} \times Area\; Of \;Square \times Height[/tex] ;
Substituting the values ;
we get ;
⇒ [tex]125= \frac{1}{3} \times 25 \times Height[/tex] ;
On solving further ,
we get ;
⇒ [tex]\frac{125\times 3}{25}[/tex]
⇒ 15 m .
Therefore , The Height of the Pyramid is 15 m.
The given question is incomplete , the complete question is
This square-based oblique pyramid has a volume of 125 m³ and the length of the side of the base is 5m . What is the height of the pyramid ?
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I need help bru im from Chicago need help
Answer:
3.20
Step-by-step explanation:
one person drives 70,000 miles in a car that averages 30 miles per gallon (mpg). how much gasoline are they using?
The person is using approximately 2,333.333 gallons of gasoline.
The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
To calculate the amount of gasoline used, you can use the formula:
gasoline used = total miles driven / mpg
Where total miles driven is 70,000 miles and mpg is 30.
Plugging these values into the formula, we get:
Gasoline used = 70,000 miles / 30 mpg = 2,333.333 gallons
So the person is using approximately 2,333.333 gallons of gasoline.
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Chris is buying a yard of material for a art project. two stores have the material she needs. compare prices to find which material is the better. explain how you know
artistic supplies- $1.25ft
craft center- $3 yards
3. Pencils are sold at a unit rate of 36 pencils per box.
Use the variables and number in the box to write an equation to
represent the proportional relationship. The letter b represents the
number of boxes, and p represents the total number of pencils.
Use the unit rate as the constant of proportionality.
Numbers and letters cannot be used more than once. Write
each number or letter in the appropriate box.
36
b
Р
HINT, H
The unit rates
constant of p
the equation
where m is th
proportional
The constant of proportionality for the proportional equation is 36.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
Box = b
Number of pencils in one box.
p = 36
Now,
The proportional equation for b and p.
p ∝ b
p = mb
where m is the constant of proportionality.
Now,
b = 1
p = 36
p = mb
36 = m x 1
m = 36
Thus,
The constant of proportionality is 36.
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What is the equation of the line in slope-intercept form that passes through point (4, 5) and is parallel to the line y = −2x − 2?
Answer:
y = -2x + 13
Step-by-step explanation:
In order to write an equation of the line in slope-intercept form, we first have to look at the equation:
y = mx + b
We know that m represents slope, and b represents the y-intecept, in other words, what y is equal to when x is equal to zero.
We already have y and x, (4,5), and the slope of the line, since the two lines are parellel, they share the same slope. So now, we have to pulg those values into the equation and solve for b:
(4,5)
y = 5
x = 4
m = -2
y = mx + b
(5) = (-2)(4) + b
5 = -8 + b
13 = b
So, equation of the line in slope-intercept form that passes through point (4, 5), is y = -2x + 13
Remeber that you can always graph to check your work!
I hope this helps! :)
How do I do this help me please
Answer: A. Yes
B. Yes
C. No
Step-by-step explanation:
A. 2z = 40 and z = 20, 20 is a solution of the equation because when you substitute z = 20 into the equation 2z = 40, the equation becomes true.
B. n + 5 = 20 and n = 15, 15 is a solution of the equation because when you substitute n = 15 into the equation n + 5 = 20, the equation becomes true.
C. v = 12 and v = 16, 12 is not a solution of the equation because v is assigned to 12 and 16 both, but the equation only has one solution, a variable can't be assigned to two different values.
In general, when solving equations, we check if the value of the variable makes the equation true. if it does it's a solution, if not it's not a solution.
A student used the sieve of eratosthenes to find all prime numbers less than 100. create a step-by-step set of directions to show how to complete it. use the word bank to help guide your thinking as you write the directions. some words may be used just once more than once or not at all.please help i am lost
Utilizing the Sieve of Eratosthenes method is simple. In order to encircle the remaining numbers, we must cancel all multiples of each prime number starting with 2 (including the number 1, which is neither a prime nor a composite).
What the sieve of Eratosthenes to find all prime numbers?The Sieve of Eratosthenes can be used to locate all prime numbers that are less than 100, as seen in the example below. In ten rows, start by writing the numbers 1 through 100.
Therefore, based on the preceding table, we can conclude that the prime numbers 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are. There are ten prime numbers between 50 and 100 in all. The required prime numbers are those that are surrounded.
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evaluate the double integral_d (x^2 + 2y) dA, D is bounded by y = x, y = x^3, x ≥ 0
After evaluating the double integral, the result, 0.27, is determined by the stated statement.
What is the definition of an integral?In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or maybe a new function, the inverse of which comprises the original result (indefinite integral). The value produced after integrates or adding the words of a function that is split into an unending number of terms is referred to as an integral value in general.
The double integral is an example.
[tex]\iint_D\left(x^2+2 y\right) d A[/tex] where d is enclosed by the lines y = x & y = x³.
In the region D, x varies from 0 to 1, and y varies from y = x³ to y = x
[tex]\therefore \iint_D\left(x^2+2 y\right) d A=\int_{x=0}^1 \int_{y=x^3}^x\left(x^2+2 y\right) d y d x[/tex]
[tex]=\int_{x=0}^1\left[x^2 y+y^2\right]_{x^3}^x d x[/tex]
[tex]=\int_{x=0}^1\left[x^2\left(x-x^3\right)+\left[x^2-\left(x^3\right)^2\right]\right] d x=\int_{x=0}^1\left[x^3-x^5+x^2-x^6\right] d x[/tex]
[tex]\left.=\frac{x^4}{4}-\frac{x^6}{6}+\frac{x^3}{3}-\frac{x^7}{7}\right]_0^1[/tex]
= [tex]\frac{1}{4}-\frac{1}{6}+\frac{1}{3}-\frac{1}{7}[/tex]
= 23/84
= 0.27
[tex]\therefore \iint_D\left(x^2+2 y\right) d A=0.27[/tex]
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in the hardy boys adventure while the clock ticked, the pendelum of the grandfather clock at the purdy place is 44 inches long and swings through an arc of 6. find the length of the arc taht the pendelum traces
On solving the provided question we can say that equation of pendulum traces an arc, s, that is roughly 4.61 inches long.
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.
6° = 6° X [tex]\pi /180 = \pi /30[/tex]
s = r∅
s = 44 X [tex]\pi /30[/tex]
s = 4.61
Hence, The pendulum traces an arc, s, that is roughly 4.61 inches long.
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How do you know if there are no solutions?
If you attempt to solve an equation and the result is false, the problem has no solutions.
If both sides of a linear equation have unique constant values but the same variable term, then the problem has no solutions.
For instance, in the equation [tex]3x+8=1+3x[/tex],
the variable term is the same, [tex]3x[/tex], but the constant terms, 8 and 1, are on opposite sides of the equation. It, therefore, lacks solutions. Try the equation to determine why.
[tex]3x+8=1+3x\\8=1[/tex]
following mathematics, the term is not possible. so, here equation has no solutions. so how we can know that equation has no solution if mathematical inequality is wrong.
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