Yes, the solution to the system of linear equations represented by the matrix A lies in the plane spanned by the columns of A.
If the last row of the reduced matrix is [0, 0, 0, 0], it means that the system of linear equations represented by the matrix is consistent, but not necessarily unique. This is because the last row corresponds to an equation of the form 0 = 0, which is always true.
However, the presence of a non-zero row in the reduced matrix that corresponds to a non-trivial equation (i.e., an equation that is not of the form 0 = 0) is sufficient to guarantee that the solution exists and is unique, and that the solution lies in the plane spanned by the columns of A.
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start.
answer both equation and other
The equation to illustrate this will be 600 + 28m m.
How to explain the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this situation, the owners of a recreation area are filling a small pond with water and they are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start.
The equation to illustrate this will be:
= 600 + (28 × m)
= 600 + 28m
m = number of minutes.
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start. Write the equation to illustrate this.
What is the formula for the arc length of the sector of a circle?
If PQ subtends angle at the circle's center, then let PQ be an arc with radius r and a center at O. Thus, the arc length of PQ is given by PQ = /360° (2r), where is a degree.
What is angle?A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. From the Latin word "angulus," which meaning "corner," comes the English term "angle." The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.Two lines intersect at a shared point to produce an angle. Degrees, denoted by the symbol °, are used to measure them. Acute, right, obtuse, and reflex angles are among the four crucial types of angles. 360° makes up a full circle. It has completed two full rotations if the angle is more than 720°.To learn more about angle, refer to:
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Stuck on this question
Answer:
ABD =30 +45
ABD=75
75°is the answer
refers to nondisclosure of the treatment an experimental unit is receiving.
Blinding refers to the nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.
What is Blinding?Blinding is a technique used in experimental design to reduce bias and improve the validity of results. It refers to the practice of not revealing to the experimental units (e.g., participants, animals) or the experimenters which treatment they are receiving in a controlled experiment. Blinding is used to eliminate potential sources of bias that might influence the results of the experiment.
For example, if the participants are aware of the treatment they are receiving, they might behave differently and affect the results. Similarly, experimenters might unconsciously treat participants differently based on their knowledge of the treatment, which could also affect the results.
Blinding is the practice of keeping the therapy that an experimental unit is getting a secret. In a single-blind experiment, the experimental unit (also known as the subject) is kept in the dark regarding the therapy that he or she is getting.
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Complete question:
refers to nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.
What is a 180 degree rotation?
Answer:
half a rotaoin
Step-by-step explanation:
think there is a crycle and you divide half and eat it and the secand half is 180 degree
Our point A(x,y) becomes A' when a point is rotated 180 degrees counterclockwise about the origin. All we actually do is turn both x and y negative.
What is the equivalent of 180 degrees in turns?A 180-degree rotation around the same central axis would put you in a position facing the opposite direction from where you were previously facing. As a result, 360°, or half of a full turn, is equal to the number of degrees in a half-turn. By dividing 360 degrees by two, we can get the number of degrees in a half-turn. We understand that a half-turn is 180 degrees.We require two 180° angles to complete a full turn. A full rotation or full turn is a 360-degree angle. Since 180 degrees makes up half of a 360-degree circle, a 180-degree angle multiplied by two or twice produces a full circle.To learn more about rotation, refer to:
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nasa launches a rocket at seconds. suppose its height, in meters above sea-level, as a function of time is given by . how high above sea-level does the rocket get at its peak? round your answer to 2 decimal places. the rocket peaks at meters above sea-level.
The rocket peaks at 5000 meters above sea-level.
The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:
h'(t) = -10t + 1000
h'(t) = 0 => t = 100
So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:
h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000
Therefore, The rocket peaks at 5000 meters above sea-level.
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The rocket peaks at 5000 meters above sea-level.
The height of the rocket as a function of time is given by h(t) = -5t^2 + 1000t. To find the peak, we need to find the maximum height, which can be done by taking the derivative of the function and setting it equal to zero:
h'(t) = -10t + 1000
h'(t) = 0 => t = 100
So the rocket peaks at t = 100 seconds, and to find the height at this time, we plug t = 100 into the original function:
h(100) = -5 * 100^2 + 1000 * 100 = -50000 + 10000 = 5000
Therefore, The rocket peaks at 5000 meters above sea-level.
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y varies directly with [tex](x-2)^2[/tex] and [tex]y=\frac{5}{3}[/tex] when x=4. Write the equation for y in terms of x.
As y varies directly as (x−2)² and y = 5/3 when x = 4, then the equation for y in terms of x is y = (5/12)(x - 2)²
Direct variationIf the values of y varies directly as does of x, then there is a constant say "k" that is true for them, else y does not vary directly as x.
For y = 5/3 when = 4, we can solve for the constant k as follows:
5/3 = k(4 - 2)² {we simplify the expression in the bracket}
5/3 = k2²
5/3 = k4
k = 5/(3 × 4) {cross multiplication}
k = 5/12
Therefore, as y varies directly as (x−2)² and y = 5/3 when x = 4, the equation for y in terms of x is y = (5/12)(x - 2)²
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2r²-32 quadratic equation
Answer:
r = ±4.
Step-by-step explanation:
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. To write the equation 2r^2 - 32 in this form, you can subtract 32 from both sides to get 2r^2 - 32 = -32, and then divide both sides by 2 to get r^2 - 16 = -16. Finally, you can add 16 to both sides to get r^2 = 0, which is the standard form of a quadratic equation.
So, the equation 2r^2 - 32 = 0 can be written as the quadratic equation r^2 = 16, which has two real roots, r = ±4.
what does -4xy equal to
Answer: I can not give an answer because you have not given enough information to answer it. If you could add a picture it would be greatly appreciated.
How to turn -7 37/40 into a decimal
Answer:
-7.925
Step-by-step explanation:
Write the next three terms of the geometric sequence -2, 4, -8, 16, …
Answer:
-32, 64, -128
Step-by-step explanation:
Each term is -2 times the previous term. This means the next term is
(-2) x 16 = -32
Then,
(-2) x (-32) = 64
and lastly,
(-2) x 64 = -128
In ΔABC, a = 6 inches, � m∠A=121° and � m∠B=36°. Find the length of b, to the nearest 10th of an inch.
The length of b from the given triangle ABC is 4.1 inches.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in ΔABC, a = 6 inches, m∠A=121° and m∠B=36°.
Here, sin 121°/6=sin 36°/b
0.8571/6=0.5877/b
0.8571b=0.5877×6
0.8571b=3.5262
b=3.5262/0.8571
b=4.1 inches
Therefore, the length of b from the given triangle ABC is 4.1 inches.
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collection of n < min{m, n −m } is taken out at random without replacement. for k = 0, . . . , n, give a formula for the probability that exactly k balls are red.
The formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).
Given n balls, m of which are red and n - m are blue, if a collection of n < min{m, n - m} balls is taken out at random without replacement, the probability that exactly k balls are red can be calculated using the Hypergeometric Distribution. The formula for the probability that exactly k balls are red is given by: P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n)
where C(n, k) denotes the number of combinations of n things taken k at a time, and is given by: C(n, k) = n! / (k! * (n - k)!).
Therefore, the formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:
P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).
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Evaluate the function at the specified values of the independent variable. Simplify the results. f(x) = 5x + 7 (a) f(-8) (b) f(0.6) (c) f(x + 9)
At the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
Given that the function is:
f(x) = 5x + 7
To evaluate the function at the specified values substitute the value in x:
a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33
b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10
c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52
Hence, at the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.
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A single die is rolled 100 times. List the probabilities below from leat to greatest. P(odd), P(>4), P(prime), P(8)
The probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).
What is probability?
Calculating probability is a method of determining how likely something is to occur. The probability scale runs from 0 to 1, where 0 denotes impossible and 1 denotes certainty.
We are given that a single die is rolled 100 times.
So, the outcomes can be {1,2,3,4,5,6}
Now,
P(odd) = Probability of odd numbers
Odd numbers are 1, 3 and 5
So, P(odd) = 3/6 = 1/2
P(>4) = Probability of numbers greater than 4
Numbers greater than 4 are 5 and 6
So, P(>4) = 2/6 = 1/3
P(prime) = Probability of prime numbers
Prime numbers are 1, 2, 3 and 5
So, P(prime) = 4/6 = 2/3
P(8) = Probability of number 8
In a dice, the maximum number is 6
So, P(8) = 0
Hence, the probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).
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What is the boundary condition at a perfectly insulated surface expressed mathematically? (Check all that apply.) Check All That Apply эт (0,) k 0 эт (0, ) -k- 1 эт (0,) -k = 0 эт (),) 1
the boundary condition at a perfectly insulated surface is expressed mathematically as (0) -k = 0 depending on the physical characteristics of the surface.
A boundary condition is a mathematical expression that describes the behavior of a physical system at its boundaries, such as a surface.
Mathematically, a perfectly insulated surface is represented as an isothermal surface, meaning that the temperature is constant across the surface.
This is described by the equation (0) = 0, where эт represents the rate of heat transfer at the surface.
In other words, a perfectly insulated surface does not allow heat to flow through it.
This equation shows that the heat transfer is in the opposite direction of the temperature gradient at the surface.
Finally, the boundary condition at a perfectly insulated surface can also be expressed as эт (0,) -k = 0, which means that the heat transfer at the surface is equal to zero and there is no net heat transfer at the surface.
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Show whether each logical expression is a tautology, contradiction or neither.
(a) (p ⨠q) ⨠(q â p)
(b) (p â q) â (p ⧠¬q)
(c) (p â q) â p
(d) (p â q) ⨠p
(e) (¬p ⨠q) â (p ⧠¬q)
(f) (¬p ⨠q) â (¬p ⧠q)
The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.
(a) Neither - This expression can be written as ¬(p ∨ q) ∧ (q ∨ ¬p), which is neither a tautology nor a contradiction.
(b) Contradiction - This expression can be written as (p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.
(c) Tautology - This expression can be written as (p ∨ q) ∧ p, which is a tautology because it is equivalent to p, which is always true.
(d) Contradiction - This expression can be written as (p ∨ q) ∧ ¬p, which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.
(e) Contradiction - This expression can be written as (¬p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (¬p ∨ q) ∧ (¬p), which is a false statement.
(f) Tautology - This expression can be written as (¬p ∨ q) ∧ (¬p ∨ q), which is a tautology because it is equivalent to (¬p ∨ q), which is always true.
The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.
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A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75. 5 psi and standard deviation 3. 5 psi. How is the standard deviation of the sample mean changed when the sample size is increased from?
The standard deviation of the sample mean decreases as the sample size increases. This is because the larger the sample size, the more accurately it reflects the population mean.
The standard deviation of the sample mean is a measure of how close the sample mean is to the population mean. The sample mean is an estimate of the population mean, and the standard deviation of the sample mean is a measure of how accurate that estimate is. When the sample size is increased, the sample mean becomes a more accurate estimate of the population mean, thus the standard deviation of the sample mean decreases. This is because the larger the sample size, the more accurately it reflects the population mean, and the closer the sample mean is to the population mean, the lower the standard deviation of the sample mean. The decrease in the standard deviation of the sample mean as the sample size increases is called the law of large numbers.
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Please help me with math problem!! Will give brainliest!! :) It's due tonight!! 20 POINTS!!!
Answer:
Step-by-step explanation:
im sorry Im only in 6th grade and I cant help you
How do you find the t value of a 95 confidence interval?
With a significance level of 0.05 (i.e., a confidence level of 95%), the confidence interval is calculated using the T function.
As a result, the range between 190,078.9152 and 209,921.0852 is represented by the confidence interval of 200,000 9921.0848.
What is the 95 percent confidence interval's t critical value?Find the 0.025 critical value t* for 129 degrees of freedom in order to determine a 95% confidence interval for the mean based on the sample mean of 98.249 and sample standard deviation of 0.733. The critical value for 100 degrees of freedom is roughly 1.962.
Use the crucial value of t to determine a confidence interval for a mean by doing the following four steps:Depending on the degree of confidence you want to have, choose the significance level. The two-tailed t table's =.05 corresponds to the most typical confidence level of 95%.
In the two-tailed t table, determine the critical value of t.
Add s/n to the crucial value of t.
Calculate the top limit of the confidence interval by adding this value to the mean, and the lower limit by deducting this value from the mean.
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if+x+grows+by+2%,+and+y+grows+by+3%,+then+z=xy+will+grow+approximately+by
The final value of z = xy will be 1.05 times the original value.
The formula for calculating the growth rate of z = xy is z’/z = (x’/x)+(y’/y). The prime symbol (‘) denotes the rate of growth. In this case we can substitute the given rates of growth of x and y: x’/x = 2% and y’/y = 3%. By substituting these values into the formula we can calculate the rate of growth of z. z’/z = (2% + 3%) = 5%.
Therefore z = xy will grow approximately by 5%. To calculate the exact change in z, we can use the formula for compound growth: z’ = z (1 + r/100)^t, where r is the rate of growth and t is the number of time periods. In this case, r = 5% and t = 1 (as the growth rate is per period). Therefore, z’ = z (1 + 5/100)^1 = z (1.05) = z * 1.05. This means that the final value of z = xy will be 1.05 times the original value.
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Two friends shop for fresh fruit. Jackson buys a watermelon for $7.85 and 3 pounds of cherries. Tim buys a pineapple for $3.25 and 2 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Jackson spent.
(please its due Wednesday!!!!)
Jackson spent 4.60+p more than Tim in buying fruits.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, two friends shop for fresh fruit. Jackson buys a watermelon for $7.85 and 3 pounds of cherries.
Let the variable p to represent the price, in dollars, per pound of cherries.
So, the total cost is 7.85+3p
Tim buys a pineapple for $3.25 and 2 pounds of cherries.
Here, the total cost is 3.25+2p
Difference in there price is 7.85+3p -(3.25+2p)
4.60+p
Therefore, Jackson spent 4.60+p more than Tim in buying fruits.
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Can someone PLEASE help? I will give brainliest if possible and lots of points. Show work please
Match the angle measure in the left column with its complementary angle measure in the right column. Click on the image
Answer:
Solution
or, 11°=90° {being complementary angle}
or,90°-11°
79°
Answer is 79°
Alex drew two lines and two transversals. He wants to know the measures of angles 1, 2, and 3. Identify the measure of each angle and the relationship used to find the angle measure.
2 vertical parallel lines, M and N, intersected by 2 transversal lines P and Q. Lines P and Q intersect each other on line N. Between lines M and N, the 2 angles formed by lines M and P are labeled 1 and one hundred thirty-five degrees, and the smaller angle formed by lines M and Q is labeled 3. The non-adjacent angles formed by lines P and Q are labeled 2 and ninety-five degrees.
m∠
1=
° because ∠
1 and the angle measuring 135° are
Choose...
angles.
m∠
2=
° because ∠
2 and the angle measuring 95° are
Choose...
angles.
m∠
3=
° because ∠
1, ∠
2, and ∠
3 form a
Choose...
.
<1 = 45 degrees- are supplementary angles.
<2 = 95 degrees - vertical angles.
<3 = 40 degrees because 1, 2, and 3 form a triangle.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Using the provided figure, we can
Because <1 and the angle with a measure of 135 degrees are supplementary angles, m<1 = 45 degrees.
and, Because <2 and the angle measuring 95 degrees are vertical angles, m<2 = 95 degrees.
Also, Because 1, 2, and 3 make a triangle, m<3 = 40 degrees.
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The measures of the angles in triangle UVW are shown in the diagram.
What is the value of x ?
Answer:
3x-9+34+24=180 (because the sum of angle of triangle is 180 )
3x+49=180
3x=180-49
3x=131
x=131÷3
x=43.67
use the root test to determine whether the series is convergent or divergent. [infinity] n = 1 4 1 1 n n2 identify an. evaluate the following limit. lim n → [infinity] n |an| since lim n → [infinity] n |an| ? 1,
In this case, the limit is 0, so the series is indeed convergent.
The Root Test is used to determine the convergence or divergence of a series. and it is used the Root Test, we start by finding the nth root of each term in the series.
In this case, the series is
=> [∞] n = 1 4 1 1 n n²,
so we calculate the nth root of each term:
[tex]= > (1/n^{2} )^{1/n}[/tex]
Then, we take the limit of this expression as n approaches infinity, to find the value of the root.
If this limit is less than 1, the series is convergent. If the limit is greater than or equal to 1, the series is divergent.
In this case, the limit of [tex](1/n^{2} )^{1/n}[/tex] as n approaches infinity is 0, which is less than 1. This means that the series is convergent.
To confirm this, we can evaluate the limit of the absolute value of each term as n approaches infinity, using the formula
=> lim n → [∞] n |aⁿ|.
If this limit is finite, then the series is convergent.
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A cla recorded the mae,in gram,of 20 bag of rice. Their reult are hown on the right. Explain how all three tudent could be correct?
All three students could be correct if they recorded the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces.
In order for all three students to be correct, they would have to be recording the mass of the 20 bags of rice in different units. For example, one student could have recorded the mass in kilograms, another student could have recorded the mass in pounds, and the third student could have recorded the mass in ounces. This would explain why each student has a different answer, as they are all measuring the mass in different units. The only way to ensure accuracy would be to measure the mass in the same unit of measurement, so that all students have the same answer.
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What is the Side Angle Side Formula?
Side angle side formula is used to prove congruent triangles.
What are congruent triangles?
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has a symbol ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
Side angle side rule:
The triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
There are four rules of congruent triangles.
1) Side angle side
2) Side side side
3) Angle angle angle
4) Angle side angle
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Find the values of the trigonometric functions of t from the given information. tan(t) = -12/5 , sin(t) > 0 ,sin(t),cos(t),csc(t),sec(t),cot(t).
Find the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5
π
/7 rad. (Round your answer to two decimal places.)
The values of the trigonometric functions of t are Sin(t)=0.2, Cos(t) = -5/12, Csc(t) = 5,Sec(t) = -12/5, Cot(t) = -5/12 and the radius r of the circle if an arc of length 20 m on the circle subtends a central angle of 5π/7 rad is 8.86 m
To find the values of the trigonometric functions of t, the tan(t) value was used to calculate the sin(t) value by using the relationship sin²(t) + cos²(t) = 1. The other trigonometric functions were calculated by using the relationship among the trigonometric functions.
Sin(t) = √(1 - (tan(t))^2) = √(1 - (-12/5)^2) = √(1 - 144/25) = √(25/25 - 144/25) = √(1/25) = 0.2
Csc(t)= 1/0.2= 5
The radius of the circle was then determined by using the arc length and the angle subtended at the center. The arc length was divided by the subtended angle to find the radius. The result was rounded off to two decimal places.
Radius r = (20m)/(5π/7) = (20m*7)/(5π) = 28/π = 8.86 m
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A woman drives to her office 10 km away from her house at 9 a. M. And reaches her office at 9:20 a. M. She stays in the office until 6 p. M. And then returns home at 6:25 p. M. Which answer gives the correct distance and displacement at 6:25 p. M. ?.
Distance is a scalar quantity that represents the total length of the path traveled by an object . It can be thought of as the magnitude of the displacement, which is the change in position of an object.
Displacement, on the other hand, is a vector quantity that represents the change in position of an object, taking into account the direction of travel. It is the shortest distance between the initial and final position of an object.
The distance traveled by the woman is the total length of her trip from her house to her office and back. It is equal to 2 * 10 km = 20 km.
Displacement is the final position of an object relative to its initial position, taking into account only the direction, and not the distance traveled. At 6:25 PM, the woman is back at her house, which is her initial position, so her displacement is 0 km.
So the correct answer is:
Distance traveled = 20 km
Displacement = 0 km
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