The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:
[tex]F = kx[/tex]
where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).
Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:
[tex]W = (1/2) k x^2[/tex]
Solving for k, we get:
[tex]k = (2W) / x^2[/tex]
Plugging in the values for W and x, we get:
[tex]k = (2 * 18) / (4^2) = 2.25[/tex]
So the spring constant is 2.25 pounds per inch.
Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:
[tex]F = kx[/tex]
= [tex]2.25 * 3[/tex]
= 6.75 pounds
Finally, we can find the work required to stretch the spring an additional 3 inches:
[tex]W = (1/2) k x^2[/tex]
= [tex](1/2) * 2.25 * 3^2[/tex]
= 10.125 foot-pounds
Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
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12.5 × 1.989 pls help me
Rewrite in simplest radical form
The simplest radical form is x⁵.
What is radical form?Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.
The given radical form is [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex].
The radical and root of a number are the same thing.
Simplifying a radical eliminates the square roots, cube roots, fourth roots, etc.
In the given expression, 1/6 is the 6th root, in both numerator and denominator cancel out 6th root x.
That is, [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex] =x⁵ ([tex]x^{\frac{1}{6} }[/tex] in the denominator is gets cancelled with [tex]x^{\frac{1}{6} }[/tex] in the numerator)
Therefore, the simplest radical form is x⁵.
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Evaluate the expression when x= -7 and y=2 .
X - 2y
Answer:-3
Step-by-step explanation: -7 -4
Casey Na's average workweek during the first quarter of the year (13 weeks) was 43 hours. As part of his company's perfect attendance program, he earned a bonus of $975. Determine the extra overtime pay due Na for the first quarter
Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.
What is overtime pay?
Overtime pay is the additional compensation paid to an employee for any hours worked in excess of the standard working hours or beyond the standard workweek. The rate of overtime pay is usually higher than the regular rate of pay for an employee's normal working hours.
To determine the extra overtime pay due to Casey Na for the first quarter, we need to know his regular pay rate and the number of hours he worked each week.
Let's assume that Casey Na's regular pay rate is $20 per hour and that he worked 40 hours each week during the first quarter. This means that he worked 3 hours of overtime each week, for a total of 39 hours at his regular rate and 3 hours at his overtime rate.
To calculate his overtime pay for the first quarter, we can use the following formula:
Overtime pay = overtime hours x overtime rate
Since Casey Na worked 3 hours of overtime each week for 13 weeks, his total overtime hours for the first quarter were:
Total overtime hours = 3 hours/week x 13 weeks = 39 hours
His overtime rate is 1.5 times his regular rate, or $20 x 1.5 = $30 per hour.
Therefore, his overtime pay for the first quarter was:
Overtime pay = 39 hours x $30/hour = $1,170
Since he also earned a bonus of $975 for perfect attendance, his total extra pay for the first quarter was:
Extra pay = Overtime pay + Bonus = $1,170 + $975 = $2,145
Therefore, Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.
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which of the following statements is more accurate? question 42 options: observations are only as good as the hypotheses on which they are based. hypotheses are only as good as the observations on which they are based.
The more accurate statement is that hypotheses are only as good as the observations on which they are based.
A hypothesis is a tested assertion regarding the relationship between two or more variables or a suggested explanation for some observable occurrence in a scientific setting.
As a result, hypothesis are only as good as the observations upon which they are built.
For instance, if we stay up late, we will be fatigued the next day. Turning off your phone allows it to charge more quickly. All of them are hypotheses since they are based on observations and are only valid for as long as the observations stay true.
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Find the perimeter and area of the rectangle below
Perimeter and area of the rectangle would be 2(10x² + 7xy²) and 70x²y².
What is Perimeter and area?
The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.
Given the length l = 10x² and width w = 7xy² of a rectangle, the perimeter P and area A can be calculated as follows:
1) Perimeter P:
P = 2(l + w)
= 2(10x² + 7xy²)
2)Area A:
A = l * w
= 10x² * 7xy²
= 70x²y²
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Transcribed image text: (1 point) Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in Rº that does not contain the origin. A= b
Matrix A is: A = [1 2 3] and Matrix B is: B = [1]
[2 4 6] [2]
[1 1 1] [3]
An example of a 3x3 matrix A and a 3x1 matrix B such that the solution set of Ax = b is a line in R³ that does not contain the origin:
A = [1 2 3]
[2 4 6]
[1 1 1]
B = [1]
[2]
[3]
To check that the solution set of Ax = b is a line in R³, we can solve for x in terms of a parameter t:
Ax = b
[1 2 3] [x1] = [1]
[2 4 6] [x2] [2]
[1 1 1] [x3] [3]
Ax = b
x1 + 2x2 + 3x3 = 1
2x1 + 4x2 + 6x3 = 2
x1 + x2 + x3 = 3
Dividing the second equation by 2 and subtracting it from the first equation, we get:
-x1 - x2 = -1
Solving for x2 in terms of x1 and x3, we get:
x2 = -x1 + 1 - (3/2)x3
Solving for x3 in terms of a parameter t, we get:
x3 = t
Then, x1 can be expressed in terms of t as:
x1 = -t + 1
Therefore, the solution set of Ax = b is:
x = [-t + 1]
[-t + 1 - (3/2)t]
[t]
which is a line passing through the point (1, 1/2, 0) with a direction vector [-1, -3/2, 1].
A × [0; 0; 0] = [0; 0; 0]
Therefore, the origin is not on the line of solutions.
So, Matrix A is:
A = [1 2 3]
[2 4 6]
[1 1 1]
and Matrix B is:
B = [1]
[2]
[3]
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Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had. (5 points)
Answer:
# of appointments is 3
Step-by-step explanation:
He makes $75 per appointment, which means this immediate value is directly dependent on the number of appointments (x). So it can be given by 75x.
Tips are simply added, tips are not directly dependent on the number of visits as customers will tip differently so we can add $40 to the equation.
Now we must negate the expenses, each appointment there is a fee of $10. So it can be given as 10x.
We know that this all must equal $235.
So the equation is as follows:
235 = (75x)+40-(10x)
Simplifying we get
235 = 65x + 40
195 = 65x
195/65 = x
x = 3
Therefore, Logan had 3 appointments.
© 31. Think About a Plan The Millenium Wheel, also known as the London Eye, contains 32 observation cars. Determine the angle of rotation that will bring Car 3 to the position of Car 18. • How do you find the angle of rotation that a car travels when it moves one position counterclockwise?
• How many positions does Car 3?
The angle of rotation that will bring Car 3 to the position of Car 18 is 11.25 degrees. The angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees. Car 3 needs to move 15 positions counterclockwise to reach Car 18.
a. We have to determine the angle of rotation that will bring Car 3 to the position of Car 18 on the London Eye, so we will first calculate the number of positions that Car 3 needs to move counterclockwise to reach Car 18.
We know that there are 32 observation cars on the London Eye, so the distance between two adjacent cars will be 360/32 = 11.25 degrees.
b. To find the angle of rotation that a car travels when it moves one position counterclockwise, we will divide the full rotation of the London Eye by the number of observation cars (i.e. 32).
360/32 = 11.25 degrees
Next, to determine the angle of rotation that would bring Car 3 to the position of Car 18, we will multiply the number of positions that Car 3 needs to move counterclockwise and the angle of rotation for each position as follows -
15 x 11.25 = 168.75 degrees
Therefore, the angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees.
c. To find the number of positions that Car 3 needs to move counterclockwise to reach Car 18, we will subtract the position number of Car 18 from that of Car 3 and then take the absolute value, as it is a cyclical rotation.
|18 - 3| = 15
Hence, Car 3 needs to move 15 positions counterclockwise to reach Car 18.
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which pair of events are overlapping when rolling a single six-sided die? a.) getting an even number getting a number less than 5 b.) getting a prime number getting a number greater than 5 c.) getting a 2 getting an odd number d.) getting an even number
The overlapping events when rolling a single six-sided die are (a) "getting an even number" and "getting a number less than 5."
The overlapping event occurs in option (a), where getting an even number and getting a number less than 5 have some numbers in common. The numbers 2 and 4 are both even and less than 5. Hence, these two events overlap. The other options do not overlap because getting a prime number, getting a number greater than 5, and getting a 2 do not have any numbers in common. The overlapping events when rolling a single six-sided die are (a) "getting an even number" and "getting a number less than 5."
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HELP PLEAES clarence made a scale drawing of a classroom. the scale in the drawing is 2 inches represenst 9 feet the actual length of the classroom is 36 feet what is the length of the classroom on the scale drawing
The length of the rectangular classroom will be 8 inches on the scale drawing.
What is a rectangle defined as?
Rectangles are four-sided polygons having internal angles of 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from the square in that its opposite sides are of equal length.
If one side of a rectangle is 20 cm long, the other side must be 20 cm long as well.
Two diagonals cross form a rectangle. Both diagonals are the same length.
P = 2 (Length + Width) defines the perimeter.
Rectangle Area=Length*Breadth
Now,
As total length of room =36 feet
and 9 feet = 2 inch on drawing scale
then length of classroom on drawing scale is = 36/9*2
=8 inch
Hence,
The length of the rectangular classroom will be 8 inches on the scale drawing.
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CAN SOMEONE HELP FAST!!
In a certain city, E street, W street, C street, and D street are parallel streets that intersect K street and M street. How long is K street between C street and D street?
Answer:
The required measure of Street K between Street C and D is 337.5 ft.
Step-by-step explanation:
have a nice day.
Which of the following is the surface area of the right cylinder below?
radius 7
height 2
Answer:
395.8406(answer depends on what place you round to)
Step-by-step explanation:
The equation is A=2πrh+2πr^2. Plug it what you know, and it'd look like this: A=2π(7)(2)+2π(7)^2. Use your calculator and you get the answer.
if y x 3 equals to 3/5 y
Answer:
since y = 0 when x = 0
Step-by-step explanation:
We can start by solving for y in the equation:
y * x = 3/5 y
Dividing both sides by y:
x = 3/5
So the equation y * x = 3/5 y can be simplified to:
y = 5/3 x
This equation shows that there is a proportional relationship between y and x, where y is always equal to 5/3 times x. This relationship can be represented on a graph by plotting points (x, y) and drawing a line through them. The slope of the line will be 5/3, and the y-intercept will be 0, since y = 0 when x = 0.
Answer:
y = ±1/√5
Step-by-step explanation:
3y = 3/5y
⇒3y×5y = 3
⇒15y² = 3
⇒y² = 3/15
⇒y² = 1/5
⇒y = ±1/√5
PLEASE LOOK AT IMAGINE BELOW
Answer: D
Step-by-step explanation:
2. In rectangle HOME, HM and OE are diagonals that intersect at P.
Write at least 6 unique statements about HOME and justify your statements with definitions, postulates or theorems
1. It should be noted that HD = EM and HE = OM. In this case, the opposite sides are equal in the rectangle.
2. It should be noted that EHO = HOM = OME = MEH = 90°. In this case, all angles are equal to 90°.
What are postulate?Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates have two functions: they define undefined terms and act as a foundation for the proof of subsequent propositions.
A line segment is determined by two points. A line segment may be extended along a line indefinitely. The other information is attached.
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Is Rainbow Six Siege Good
Answer:
yes beacuse he have nice grapics and u can play with your friends.
Step-by-step explanation:
Answer: Yes it is very good i recommend getting it, but it takes a ton of time to get use to it.
Step-by-step explanation:
106-5(22-2+5 so does anyone know the anwer+
Rick is 11 3 4 years old. Lane is 1 3 8 years older than Rick and Jane is 1 1 5 years older than Lane. How old is Jane
The age of the jane is 565/48 years old.
Age problemProblems on ages is a common topic from which questions are asked in almost all Government exams in the quantitative aptitude section.
in this the ages has been found by solving the relationship between the ages given in the question.
the age of rick is = 11 3/4 years old
= 47/4 years old
the age of the lane is 1 3/8 years older than rick
so we add 1 3/8 in the age of rick to find out the age of lane,
so, the age of Lane is = 47/4 + 1 3/8
= 47/4 + 11/8
= (94 + 11)/8
= 105/8 years old .
the age of the jane is 1 1/5 years older than Lane
so we add 1 1/5 in the age of lane to find out the age of jane,
so, the age of jane is = 105/8 + 1 1/5
= 105/8 + 6/5
= (525 + 40)/48
= 565/48 years old .
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I need help solving this assignment. 1
6
g+3=4–
1
3
g
The solution of the equation 16g + 3 = 4 - 13g is g = 1/29
An equation is a statement that two expressions are equal. In other words, it's a mathematical sentence that says that the value on the left side of the equation is equal to the value on the right side.
In your problem, you have the equation:
16g + 3 = 4 - 13g
To solve this equation, the goal is to isolate the variable "g" on one side of the equation, so we can find its value. To do that, we need to use some algebraic techniques.
First, we can simplify the equation by combining like terms. We can add 13g to both sides of the equation to get:
16g + 13g + 3 = 4
Now we can combine the like terms on the left side of the equation:
29g + 3 = 4
Next, we want to isolate the variable "g" on one side of the equation. To do that, we can subtract 3 from both sides of the equation:
29g = 1
Finally, we can solve for "g" by dividing both sides of the equation by 29:
g = 1/29
So the solution to the equation is g = 1/29.
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Complete Question:
I need help solving this assignment.
Solve the equations 16g+3=4–13g
I need help with number 8
[tex](3x^2+5x+4)+(6x+1)~~ = ~~3x^2+11x+5 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ (3x^5+15x^3+4)+(-3x^5+2x^2-8)\stackrel{ \textit{not on all cases} }{~~ = ~~15x^3+2x^2-4} ~~ \bigotimes[/tex]
Elisa packs her suitcase before the trip the suitcase weighs 49 pounds the airline only allowed suitcases that way up to 23 km can Elisa take the suitcase on the plane show your work for every 10 kg there are about 22 pounds
The suitcase weighs 2.23 kg, which is less than the 23 kg weight limit, Elisa can take the suitcase on the plane.
To determine if Elisa's suitcase is within the weight limit of 23 kg, we need to convert the weight of the suitcase from pounds to kilograms.
the suitcase weighs 49 pounds the airline only allowed suitcases that way up to 23 km is it correct weight or not
First, we need to convert 10 kg to pounds: 10 kg * (22 pounds / 1 kg) = 220 pounds
Next, we need to convert 49 pounds to kilograms: 49 pounds / (22 pounds / 1 kg) = 2.23 kg.
Since the suitcase weighs 2.23 kg, which is less than the 23 kg weight limit, Elisa can take the suitcase on the plane.
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Please answer ASAP What is the value of x? Enter your answer, as a decimal, in the box. Enter the numerical value only.
In the similar triangle, x = 67.5 ft
What are similar triangles?Similar triangles are triangles in which the ratio of their sides are equal.
How to find the value of x?Given the similar triangles, ΔMNP and ΔMAB
By the ratio of similar triangles, we have that
MP/MN = MB/MA
We observe that MN = MA + AN
So, MA = MN - AN
So, MP/MN = MB/MA
MP/MN = MB/(MN - AN)
Given that
MP = 97.5 FT, MN = 71.5 FT, AN = 22 FT and MB = xWe have that
MP/MN = x/(MN - AN)
Making x subject of the formula, we have that
x = (MN - AN)MP/MN
So, substituting the values of the variables into the equation, we have that
x = (MN - AN)MP/MN
x = (71.5 ft - 22 ft)97.5 ft/71.5 ft
x = 49.5 ft × 97.5 ft/71.5 ft
x = 4826.25 ft²/71.5 ft
x = 67.5 ft
So, the value of x = 67.5 ft
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Consider the function f(x) = (x - 3)².
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
The inverse of f(x) has no restriction on the domain.
The graph of the inverse function is given below.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x - 3)²
The inverse of f(x).
Step 1:
Make f(x) = y
y = (x - 3)²
Step 2:
Interchange x and y
x = (y - 3)²
Step 3:
Solve for y.
square root on both sides.
x² = y - 3
y = x² + 3
So,
[tex]f^{-1}[/tex](x) = x² + 3.
a)
[tex]f^{-1}[/tex](x) = x² + 3
we see that for any values of x, [tex]f^{-1}[/tex](x) is a function.
So,
There is no restriction on the domain.
b)
The graph is given below.
c)
The inverse equation is
[tex]f^{-1}[/tex](x) = x² + 3.
Thus,
The inverse of f(x) has no restriction on the domain.
The inverse equation is [tex]f^{-1}[/tex](x) = x² + 3.
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Solve the right triangle
Answer:
AC = 1.5 cmA = 61°B = 29°Step-by-step explanation:
You want the missing side and the angles for the right triangle with leg BC = 2.7 cm and hypotenuse AB = 3.1 cm.
CosineThe cosine of angle B is given by ...
Cos = Adjacent/Hypotenuse
cos(B) = CB/AB = 2.7/3.1
Then the angle is ...
B = arccos(2.7/3.1) ≈ 29.429°
B ≈ 29°
Angle A is the complement of angle B:
A = 90° -29°
A = 61°
SineThe sine ratio is ...
Sin = Opposite/Hypotenuse
Then side AC can be found from ...
sin(B) = AC/AB
AC = AB·sin(B) = 3.1·sin(29.429°) ≈ 1.523
AC ≈ 1.5 . . . . cm
The triangle solution is ...
A = 61°B = 29°AC = 1.5 cm__
Additional comment
The mnemonic SOH CAH TOA is intended to help you remember the trig ratios above, in addition to ...
Tan = Opposite/Adjacent
Determine two unique values of 0 in the interval [0, 2pi)such that sin 0 = 1/2. ( picture included)
The two unique values of sin theta in radians are
π/67π/6When is Sin of angle = 1/2The sine function has a range of [-1, 1], so there are multiple angles that correspond to a sine of 1/2.
The most commonly used values are π/6 (30 degrees) and 7π/6 (150 degrees), which are in the first quadrant and second quadrant and have a positive sine value of 1/2.
It's worth noting that there are an infinite number of angles that correspond to a given sine value, since the sine function has period 2π. These angles are related to the angles by adding or subtracting multiples of 2π.
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help me get this right i really have to pass
Answer:
yes
Step-by-step explanation:
13.
14.
15.
Classify <1
Classify <2
Classify
Answer:
< 1 is acute (less than 90⁰)
<2 is acute
<BOA is obtuse (greater than 90⁰)
i need help with rhombi
The unknown sides of the figure are
< KNL = 89.85 degrees
< KJL = 50 degrees
< JKM = 40 degrees
< JML = 80 degrees
How to find the unknown sidesA rhombus has it's interior angles equal to 360 degrees and the opposites and angels are equal
hence angle MLK = MJK = 100 degrees
< JML = < JKL = say x
2x + 2(100) = 360
2x = 360 - 200
2x = 160
x = 80
< MJL + < KJL = MJK adjacent angles
50 + < KJL = 100
< KJL = 50 degrees
The sides of a rhombus are equal
JM = KL = 15.6
ML = JK = 15.6
Given that NK = 12 and NL = 10, using cosine rule we solve for < KNL
cos < KNL = (15.6² - 12² - 10²) / -2 * 12 * 10
cos < KNL = 1/375
< KNL = arc cos (1/375)
< KNL = 89.85
< JKM + < JKL + <JNK = 180 sum of angles on a triangle
<JNK = 180 - 89.85 = 90.15
< JKM + 50 + 90.15 = 180
< JKM = 180 - 50 - 90.15
< JKM = 39.85 approximately 40
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Betty is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $2 per pound for the lobster she picks. At the second restaurant, Betty would pay $3 per pound for the lobster, in addition to $15 for the meal. Betty realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Betty pay for her dinner? What is the weight?
Dinner would cost $ __ at either restaurant if Betty's lobster weighed __ pounds.
Dinner would cost $123 at either restaurant if Betty's lobster weighed 36 pounds.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.In the context of this problem, the slope and the intercept are defined as follows:
Slope: cost of each pound of lobster.Intercept: cost of the meal.Hence the functions for each restaurant are given as follows:
y1(x) = 51 + 2x.y2(x) = 15 + 3x.The costs are the same when:
y1(x) = y2(x)
51 + 2x = 15 + 3x
x = 36.
The cost is of:
y = 15 + 3 x 36
y = $123.
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