On converting the length , 151 centimeter is equivalent to 4.954 feet .
The Units of measuring the length are used to measure the distance between two points of an object. There are several units of measuring length , which are : meter , centimeter , kilometer , feet .
We have to convert 151 cm to feet,
So , we use the conversion factor of 0.03281 feet per centimeter , which means that there are approximately 0.03281 feet in 1 centimeter.
So , to convert 151 cm to feet, we multiply the number of centimeters by this conversion factor ;
Using this method, we get ;
⇒ 151 cm × 0.03281 feet/cm = 4.954 feet ;
Therefore, 151 cm is equal to approximately 4.954 feet.
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PLEASE HELP ASAP. WILL GIVE BRAINLIEST AND 100 POINTS I NEED HELP.
6= 130
is the first 1 I'm sorry i don't the rest
PLEASE ANSWER QUICKLY I NEED HELP AND ITS DUE IN 2 HRS
A graph that represents the number of books made in 4 hours include the following: B. graph B.
How to write the required linear inequality?In order to write a linear inequality to describe this situation, we would assign variables to the number of books and the number of hours respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of hours.Let the variable x represent the number of books.Since this printer makes more than three (3) copies of book every hour, a linear inequality which models or represents this situation is given by:
y > 3x
When the number of hours, x = 4 hours, the number of books made can be calculated as follows;
y > 3x
y > 3(4)
y > 12.
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A plastic rod has been bent into a circle of radius R=8.20 cm. It has a charge Q1
=+4.20 pC uniformly distributed along one-quarter of its circumference and a charge Q2
=−6Q 1
uniformly distributed along the rest of the circumference (in the above figure). With V=0 at infinity, what is the electric potential at
(a) the center C of the circle and (b) point P, on the central axis of the circle at distance D=6.71 cm from the center?
a) The electrical potential V (center) at the center C of the circle due to the charges Q1 and Q2 is -2.30 V.
b) The total electrical potential at the point P due to charge Q1 and Q2 , located at a distance of 6.71 cm is -1.78V.
Given that:
Radius of the circle, r = 8.20cm
Charge distributed along one-quarter of the circumference of the circle,
Q1 = +4.20pC
Charge distributed along 3/4th of the circumference of the circle,
Q2 = 25.20pC
Distance of the point from the center, d = 6.71cm
The electric potential at infinity is. V = 0
Using the concept of potential at a point on a thin rod, we can obtain the individual potential due to each charge. The sum of these values can now be used to obtain the desired potential value at the center and at the point, taking into account the distance to the point.
Formula:
The potential due to a point charge at a distance r from the point charge is determined by the equation V = [tex]\frac{1}{4\pi E_0} * \frac{q}{r}[/tex] ---------------- (1)
The potential due to the collection of point charges is determined by formula:
V = ∑[tex]\frac{1}{4\pi E_0} * \frac{q}{r}[/tex] -------------------- (2)
(a) The potential VQ1 at the center C of the circle due to the charge Q1 is determined using equation (i) as:
[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_1}{R}[/tex] --------------------- (3)
Here, R is the radius of circle
The potential VQ1 at the center C of the circle due to the charge Q1 is determined using equation (i) as:
[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_2}{R}[/tex] ----------------------- (4)
Now the potential V(center) at the center C of the circle due to charges Q1 and Q2 is the sum of the potential due to charge Q1 and the potential due to charge Q2. This is given using equations (a) and (b) in equation (ii) as:
[tex]V_Center = \frac{1}{4\pi E_0} * \frac{Q_1}{R} + \frac{1}{4\pi E_0} * \frac{Q_2}{R}[/tex]
⇒ [tex]V_Center = \frac{1}{4\pi E_0} *( \frac{Q_1}{R} + \frac{Q_2}{R})[/tex]
⇒ 9.0 × 10⁹Nm²/C₂ ([tex]\frac{4.20*10^-12 C}{0.082m} +\frac{-25.2*10^-12C}{0.082m}[/tex])
⇒ -2.30V
The electrical potential V (center) at the center C of the circle due to the charges Q1 and Q2 is -2.30 V.
(b) From the above figure the r between each charged particle and the point P is given as:
[tex]r = \sqrt{R^{2}+D^{2} }[/tex]
In the figure above, r between each charged particle and point P is defined as: ="1662703245948 "
[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_1}{\sqrt{R^{2} + D^{2} } }[/tex] ------------------ (5)
Again, the electric potential at point P due to charge Q2 is given using equation (i) as follows:
[tex]V_Q_1 = \frac{1}{4\pi E_0} * \frac{Q_2}{\sqrt{R^{2} + D^{2} } }[/tex] -------------------- (6)
A The potential at point P due to charge Q2 is determined using equation (i): The potential of charge Q1 and the potential of charge Q2. This is given using equations (c) and (d) in equation (ii) as:
[tex]V_P = 9.0 * 10^9Nm^2/C^2 (\frac{4.20*10^-12C-6(4.20*10^-12C)}{\sqrt{(0.082m)^{2} + (0.082m)^{2} } })[/tex]
= -1.78V
The total electrical potential at the point P due to charge Q1 and Q2 , located at a distance of 6.71 cm is -1.78V.
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Finn is making muffins. The recipe calls for 1 5/6 cups of flour. If he triples the recipe, what is the total amount of flour he will need?
Responses
If the recipe calls for 1 5/6 cups of flour, and Finn triples the recipe, he will need 3 times the amount of flour.
To find the total amount of flour Finn will need, we can first convert the mixed number 1 5/6 to an improper fraction:
1 5/6 = (6 x 1 + 5)/6 = 11/6Next, we can multiply this fraction by 3 to find the total amount of flour needed:
(11/6) x 3 = 33/6We can simplify this fraction by dividing both the numerator and the denominator by 3:
33/6 = (11 x 3)/(2 x 3) = 11/2Therefore, Finn will need 11/2 cups of flour in total.
~ Zeph
3 dotted horizontal and parallel lines are shown. Point Q is at the far left side of the top line, point R is at the far right of the second line, and point S is at the far left side of the bottom line. Lines are drawn from point Q to point R and from point R to point S. The angles formed are labeled, from top to bottom: 1, 2, 3, 4.
Use the diagram to complete the statements.
The angle of depression from point R to point S is angle
.
The angle of elevation from point S to point R is angle
.
Angle 2 is the angle of elevation from
.
Angle 1 is the angle o
Angle 2 is the angle of elevation from point Q to point R.
What is angle of elevation ?
The angle of elevation is the angle formed between a horizontal line and the line of sight from the observer's eye to an object located above the observer's level. In other words, it is the angle between the horizontal and an imaginary line drawn upwards from the observer to the object being viewed. It is typically measured in degrees or radians.
Given,
Point Q is at the far left side of the top line, point R is at the far right of the second line, and point S is at the far left side of the bottom line.
Lines are drawn from point Q to point R and from point R to point S.
angle of depression from point R to point S.
The angle of depression from point S to point R is angle 3.
Therefore, Angle 2 is the angle of elevation from point Q to point R.
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Answer:
the angle of depression from point R to point S is angle 3
the angle of elevation from point S to point R is angle 4
angle 2 is the angle of elevation from point R to point Q
angle 1 is the angle of depression from point Q to point R
Step-by-step explanation:
Find the solution of the system of equations. 8x+4y= 8x+4y= \,\,-24 −24 -5x+4y= −5x+4y= \,\,-11 −11
The y-coordinate for the solution to the system of equations is 6.
What is equation?Equation is a physical and mathematical statement the describing physical phenomenon the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.
The y-coordinate for the solution to the system of equations is 6. This is calculated by substituting the given y-value (2/3) into the equation -x+3y=9 and solving for x. Specifically, -x+3(2/3) = 9, which reduces to -x = 3. Therefore, x = -3 and substituting this value into the first equation yields 3y = 9, which simplifies to y = 3. Therefore, the y-coordinate for the solution to the system of equations is 6.
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Which statement is true?
1) Kai's bag definitely has more pink marbles than orange marbles.
2) If Piper chooses 15 more marbles, she can expect 3 to be orange.
3) Each bag must contain at least 20 marbles.
4) There are definitely no green marbles in Kaia's bag.
The true statement is, 3) Each bag must contain at least 20 marbles.
What is the expected value?We know The expected value, also known as the expectation, average, is a generalization of the weighted average in the field of probability theory.
The anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
1. From the table, Piper's bag has definitely more pink marbles than Kai's.
2. If Piper chooses 15 more marbles he can expect (4/30)×15 = 2 orange marbles.
3. There can be green marbles in Kai's bag as the process is repeated only 20 times.
4. So, The true statement is each bag must have at least 20 marbles,
As the sum of different colored marbles is 20.
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Answer:
If Piper chooses 15 more marbles, she can expect 3 to be orange.
pleaseeee helpppppppppppppp
5) Practice: Summarizing
Find the slope of the line passing through (6, −1) and (7, 3). Let (x1, y1) = (6, −1) and (x2, y2) = (7, 3). List the coordinates, fill in the slope formula, and then simplify.
x1 = ___________ x2 = ___________ y1 = ___________ y2 = ___________
The slope is ____________.
We can fill in the given blanks as follows:
x1 =6, x2 = 7 , y1 = -1, y2 =3. The slope is 4.
What is meant by the slope of a line?
We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope. A line's steepness can be determined by looking at its slope. A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinates. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given,
(x1, y1) = (6, −1)
(x2, y2) = (7, 3)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = 3 -(-1) / 7-6 = 4/1 = 4
Therefore we can fill in the given blanks as follows:
x1 =6, x2 = 7, y1 = -1, y2 =3. The slope is 4.
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I need help with this question. 20 points?
Answer:
Step-by-step explanation:
PLEASE HELP!! 100 POINTS!!
Write equations that represent the transformed functions described below:
NOT ANSWER CHOICES
a) f(x)=√x is shifted left 4 units and vertically compressed by a factor of 1/3
b) f(x)=√x is vertically stretched by a factor of 4 and then shifted 3 units up
c) f(x)=√x is shifted left 2 and then shifted 6 units down
Answer:
a) f(x) = (1/3)√(x-4)
b) f(x) = 4√(x+3)
c) f(x) = 6 - √(x - 2)
True or false 5. An equilateral triangle has 3 equal sides and 3 acute angles.
trueeeeeeeeeeeeeeeee
Suppose we pick three people at random. For each of the following questions, ignore the special case where someone might be born on February 29th, and assume that births are evenly distributed throughout the year (a) What is the probability that the first two people share a birthday? (b) What is the probability that at least two people share a birthday?(c) What is the probability that all three people share a birthday? (d) What if there were 15 people, what is the probability that at least one pair share a birthday? (e) What if there were 23 people, what is the probability that at least one pair share a birthday?
Answer:
a) The probability that the first two people share a birthday is 0.97 or 97%.
b) The probability that at least two people share a birthday is 0.99 or 99%.
c) The probability that all three people share a birthday is 0.0015 or 0.15%.
d) The probability that at least one pair of 15 people share a birthday is 0.58 or 58%.
e) The probability that at least one pair of 23 people share a birthday is 0.87 or 87%.
A certain parrot medicine comes in 5
gram bottles. If Natalie buys one
bottle of the medicine, how many
milligrams of medicine will she have?
[?] mg
Hint: 1 g = 1,000 mg
what is solution set calculator online
A solution set calculator online is a tool used to find the set of values that satisfy an equation or system of equations.
It is useful in a variety of mathematical fields such as algebra, calculus, and linear algebra. The calculator takes in the equation(s) and returns the solution set, which is the set of values that satisfy the equation(s). These calculators can be used for both linear and nonlinear equations, and can help in finding the solutions to problems that are difficult or time-consuming to solve by hand.
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What is one solution to the trigonometric equation sinx − cos^2 x - 1 = 0 in the interval [0, 2π]?
The solution to the trigonometric equation given in the task content is; π / 2.
What is a solution to the given trigonometric equation?Given; sin x − cos² x - 1 = 0 in the interval [0, 2π].
Recall; cos² x = 1 - sin² x
Therefore; sin x − 1 + sin² x - 1 = 0
sin² x + sin x - 2 = 0
Let, y = sin x;
y² + y - 2 = 0
y = -2 or y = 1
Therefore, the valid value of y is; y = 1.
Therefore; 1 = sin x
x = sin-¹ (1)
x = 90° = π/2.
Consequently, the one solution which represents the solution as required is; π / 2.
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Determine if the sequence is geometric. If it is, find the common ratio. If there is no ratio, write none. −3, −15, −75, −375,
Answer:
Common Ratio = 5
Step-by-step explanation:
See picture below :)
The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic
The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.
The conditions for performing a significance test using a z-statistic require a sample size large enough to satisfy the Central Limit Theorem, which means that the sample should be approximately normal. In this case, the expected number of adults who own a motorcycle in the sample is only 1, which is less than the threshold of 10 needed for approximate normality. Therefore, the sample distribution is not normal, and a z-statistic cannot be used for hypothesis testing. The other conditions, such as random sampling and independence, are not relevant to this particular issue.
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Complete question:
The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic
The sample is not large enough because (50) (1-0.02) is not equal to or greater than 10.
The sample was not randomly selected.
The sample does not have independence.
The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.
What is the conversion of 29 c to f ?
The conversion of 29 Celsius to Fahrenheit is 84.2.
Celsius and Fahrenheit are two common units of temperature measurement.
Celsius, also known as centigrade, is a temperature scale used in the metric system. It is defined by setting the freezing point of water at 0 degrees Celsius and the boiling point of water at 100 degrees Celsius at standard atmospheric pressure.
To convert 29 Celsius to Fahrenheit, you can use the following formula,
°F = (°C × 9/5) + 32
Plugging in the value of 29 Celsius, we get,
°F = (29 × 9/5) + 32
°F = (261/5) + 32
°F = 52.2 + 32
°F = 84.2
Therefore, 29 Celsius is equivalent to 84.2 Fahrenheit.
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Correct Question :
What is the conversion of 29 Celsius to Fahrenheit ?
what is 2 sample t-test of null hypothesis?
The two-sample t-test is a statistical test used to compare the means of two independent groups to determine if they are significantly different from each other.
The null hypothesis in a two-sample t-test states that there is no significant difference between the means of the two groups.
The test is performed by calculating the t-statistic, which is a ratio of the difference between the means of the two groups and the standard error of the difference. The t-statistic is then compared to a critical value from the t-distribution with degrees of freedom equal to the sum of the sample sizes minus 2.
If the calculated t-statistic is greater than the critical value, then the null hypothesis is rejected, and it is concluded that there is a significant difference between the means of the two groups. If the calculated t-statistic is less than the critical value, then the null hypothesis is not rejected, and it is concluded that there is not enough evidence to suggest a significant difference between the means of the two groups.
Therefore, the 2 sample t-test of null hypothesis has been explained
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What is factors of 20 ?
The factors of 20 are 1, 2, 4, 5, 10 and 20. A number that divides 20 exactly without producing a remainder is said to be one of its factors.
In other words, the factors of 20 are the numbers that, when multiplied in pairs, result in the number 20. 20 has many factors besides 1 and 20 because it is an even composite number. Thus, 1, 2, 4, 5, 10, and 20 are the factors of 20.
By dividing 20 by various integers, the division method allows one to discover the factors of the number 20. The integers are the factors of 20 if they divide 20 precisely with a remainder of 0. Let's discuss the factors of 20 using the division method now.
20/1 equals 20 (factor 1; remainder 0).
20/2 = 10 (Factor is 2 and Remainder is 0)
20/4 equals 5 (the factor is 4 and the remainder is 0).
20/5 equals 4 (the factor is 5 and the remainder is 0).
20/10 equals 2 (factor is 10; remainder is 0).
20/20 = 1 (20 is the factor and 0 is the remainder).
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Please answer the following question.
For dinner, Javier will choose one of the four fish options and one of the three side dishes.
(a) Here's a tree diagram for the sample space of all dinner combinations:
The Tree DiagramFish
/ | \
/ | \
Salmon Trout Halibut
/ | \ / | \ / | \
Fries Carrots Coleslaw Fries Carrots Coleslaw
(b) To determine the total number of dinner combinations, we can multiply the number of fish options by the number of side dish options:
3 fish options * 3 side dish options = 9 dinner combinations
Therefore, Javier has 9 choices for dinner combinations.
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For dinner, Javier will choose one of three fish options and one of three side dishes. His choices for fish are salmon, trout, and halibut. His choices for side dishes are fries, cooked carrots, or coleslaw.
(a)Draw a tree diagram for the sample space of all dinner combinations.
(b)How many choices for dinner combinations does Javier have?
Answer:
How to convert 1.77 meters to feet?
After converting 1.77 meters to feet its value is equal to 5.8071 feet ( approximately ) .
Conversion of meters to feet we get,
Meter and feet both are the units used to measure length.1 meter is equal to 3.28084 feet
Substitute the value given meters to convert into feet.
Now convert 1.77 meters to feet
⇒ 1.77 meters = ( 1.77 ) × ( 3.28084 ) feet
⇒ 1.77 meters = 5.8070868 feet
⇒ 1.77 meters = 5.8071 feet ( approximately )
Therefore, the conversion unit of 1.77 meters to feet is given by 5.8071 feet ( approximately ) .
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Solve for the variable.
B.
3x
A
4x - 1
О
F
x2-x-2
D
The value of the variable x in the trapezium is 6 .
How to find variable in a trapezium?The diagram above is a trapezium. The mid segment of the trapezium is EF. The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.
Therefore, using the mid segment rule,
EF = 1 / 2 (AB + CD)
EF = 4x - 1
AB = 3x
CD = x² - x - 2
Therefore,
4x - 1 = 1 / 2(3x + x² - x - 2)
4x - 1 = 1 / 2 (x² + 2x - 2)
8x - 2 = x² + 2x - 2
x² + 2x - 8x = 0
x² - 6x = 0
x² = 6x
x = 6
Therefore,
x = 6
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PLEASE HELP ME
Which is a correct classification for this triangle?
Responses
obtuse triangle
equiangular triangle
acute triangle
right triangle
Answer:
This is an obtuse triangle.
Step-by-step explanation:
Sure that are 2 acute angle but it is not acute, if it was acute, then it would have 3 acute angles. It might look like a right triangle, but the angle on the bottom left is actually past 90º. So it is an obtuse triangle. Hope this helped! Have a good day!
I need help with this please
Answer: 9. False
10. True
11. False
12. False, it is called an isosceles triangle
Step-by-step explanation:
how to make 220 lb to kg?
220 lbs is approximately equal to 99.7903 kg ( rounded to four decimal places )
The conversion factor to convert lbs to kilogram is 0.453592
1 lbs = 0.453592 kg
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in kg = The mass in lbs × conversion factor
Substitute the values in the equation
1 lbs = 0.453592 kg
220 lbs = 220 × 0.453592
Multiply the numbers
= 99.7903 kg ( rounded to four decimal places )
Therefore, 220 lbs is 99.7903 kg
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The Tabletop Games club, a student-led campus group, hosted a virtual concert last week to raise awareness about their club and bring community members together. They sold full-price tickets for
$7. 00, tickets for senior citizens were $5. 25
and student tickets cost $5. 50.
After the concert, they counted up the totals. There were a total of 215 tickets sold, and ticket sales brought in $1,214. 00
. It was noted that there were 3 times as many senior citizen tickets sold as there were full-price tickets.
Write and solve a linear system to determine how many of each type of ticket were sold.
There were _____
full-price tickets.
There were ____
senior citizen tickets.
There were ____
student tickets
A system of three linear equations: for the total number of tickets sold is 215 is f + s + t = 215, for the total revenue from ticket sales is $1214 is 7f + 5.25s + 5.5t = 1214, for three times as many senior citizen tickets were sold as full-price tickets is s = 3f.
There were approximately 11 full-price tickets sold. There were 33 senior citizen tickets sold. There were 171 student tickets sold.
Let f, s, t be the number of full-price tickets sold, senior citizen tickets sold, student tickets sold.
Firstly, write a system of three linear equations based on the given information and mark the equation number.
f + s + t = 215 (1) (the total number of tickets sold is 215)
7f + 5.25s + 5.5t = 1214 (2) (the total revenue from ticket sales is $1214)
s = 3f (3) (three times as many senior citizen tickets were sold as full-price tickets)
solve this system by substitution. Using equation (3), we can substitute 3f for s in equations (1) and (2):
f + 3f + t = 215
7f + 5.25(3f) + 5.5t = 1214
Simplifying these equations gives:
4f + t = 215 (4)
24.75f + 5.5t = 1214 (5)
We can solve equation (4) for t to get:
t = 215 - 4f
We can substitute this expression for t in equation (5) and solve for f:
24.75f + 5.5(215 - 4f) = 1214
24.75f + 1182.5 - 22f = 1214
2.75f = 31.5
f = 11.45 ≈ 11
Therefore, approximately 11 full-price tickets were sold. Using equation (3), we can find the number of senior citizen tickets sold:
s = 3f = 3(11) = 33
Therefore, 33 senior citizen tickets were sold. Finally, we can use equation (1) to find the number of student tickets sold:
f + s + t = 215
11 + 33 + t = 215
t = 171
Therefore, 171 student tickets were sold.
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what is the instantaneous rate of change calculator?
The instantaneous rate of change calculator is the tool that displays the rate of change
The change in the rate at a certain point is referred to as the instantaneous rate of change in mathematics. It is equivalent to the rate of change in a function's derivative value at a particular location. The obtained graph is identical to the slope of the tangent line if a graph for the instantaneous rate of change at a particular point is drawn.
A free online tool known as the Instantaneous Rate of change calculator shows the rate of change, the first-order differential equation for the specified function. This tool speeds up the calculation and shows the rate of change at a particular position in a split second. With time, the tool is now widely accepted and is often used is variety of calculations.
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You arrive at your relatives house 45 seconds after leaving you home which is 90 meters away. How fast did you travel?
If you arrived at a relative's house 45 seconds after leaving home, traveling 90 m, the speed was 2 meters per second.
To find out how fast you traveled, you need to use the formula for speed, which is distance divided by time. In this case, the distance is 90 meters and the time is 45 seconds.
So, you can plug these values into the formula to find your speed:
Speed = Distance / Time
Speed = 90 meters / 45 seconds
Speed = 2 meters per second
Therefore, you traveled at a speed of 2 meters per second. This means that you covered 2 meters in just one second. This is a relatively fast speed, especially if you were walking or running.
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Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) A. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. B. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has more than one solution. Therefore, the columns of A form a linearly independent set. C. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has more than one solution. Therefore, the columns of A do not form a linearly independent set. D. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.
The correct answer is (D) If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.
What is a matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.
Mathematically, assume that B = {v₁, v₂, v₃, ........} is the set of vectors. Then B will be linearly independent if the vector equation
y₁v₁ + y₂v₂ + y₃v₃ + ........ = 0 possesses the trivial solution such that
y₁ = y₂ = y₃ = ........ = 0.
Let A be a matrix, then columns of A will be linearly independent if the equation Ax = 0 possesses the trivial solution. In other words, The row space of matrix A is the span of its rows. The column space denoted by
C(A) is the span of A’s columns. The dimension of the row and column spaces is always the same, which is known as the rank of A.
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