Factor 72 + 32 in the form of a ( b + c) with A having gcf is 72 + 32 is 8(9 + 4).
To factor 72 + 32, we first need to find the greatest common factor (GCF) of 72 and 32.
The prime factorization of 72 is 2³ x 3², and the prime factorization of 32 is 2⁵.
The common factors of 72 and 32 are 1, 2, 4, 8, and 16. The greatest common factor is 8, since it is the largest factor that they both share.
So, we can write 72 + 32 as:
72 + 32 = 8 x (9 + 4)
Therefore, the factored form of 72 + 32 is 8(9 + 4).
To factor 72 + 32, we need to find the greatest common factor (GCF) of 72 and 32, which is 8. We can then use this GCF to write 72 + 32 in factored form as 8(9 + 4). This expression can also be simplified as 8(13), which equals 104. This means that 72 + 32 can be written as the product of 8 and 13, where 8 is the GCF of 72 and 32, and 13 is the sum of the quotients of 72 and 32 when divided by 8. Factoring expressions is an important skill in algebra and is used in many areas of mathematics and science.
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the average athlete is able to begin activity 90 days after having a knee operation. the standard deviation is 15 days. fifty percent of athletes are able to participate within how many days? round to the nearest day.
On average, 50% of athletes are able to begin activity 90 days after a knee operation, with a standard deviation of 15 days.
This means that the median time for 50% of athletes to be able to participate is 75 days, rounded to the nearest day.
The average time for an athlete to begin activity after a knee operation is 90 days, and the standard deviation is 15 days.
Standard deviation is a measure of how spread out the data points are in a data set; a larger standard deviation means that the data points are more spread out.
In this case, 50% of athletes can begin activity within 75 days, which is the median. By rounding to the nearest day, this would be 75 days. Therefore, 50% of athletes are able to participate within 75 days, rounded to the nearest day.
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The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis? A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries 12, 2, one-third, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries 12, 2, 0, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12.
Answer:
The correct table of values that could be used to graph g(x), a reflection of f(x) across the x-axis, is:
x f(x) g(x)
-2 1/108 12
-1 1/18 2
0 1/3 1/3
1 2 1/18
2 12 1/108
To reflect a function across the x-axis, we need to change the sign of the y-coordinate for every point on the function. Therefore, to find g(x), we take the negation of f(x) for every value of x. The second column in the third option is the negation of f(x), so it is the correct table of values for g(x).
Answer:
Its A.
Step-by-step explanation:
Other one was not clear enough lol ^
Triangle A: All sides have length 12 cm.
Triangle B: Two sides have length 10 cm, and the included angle measures 60°.
Triangle C: Base has length 15 cm, and base angles measure 40°.
Triangle D: All angles measure 60°.
Which triangle is not a unique triangle? (5 points)
a
Triangle A
b
Triangle B
c
Triangle C
d
Triangle D
triangle C
Step-by-step explanation:
If you draw it out, it looks unique
lisa and daisy work at a hair salon. the salon charges $18 fir a hair styling session with lisa and $12 for a session with daisy. the income on a certain day is projected to be $216. this situation can be represented by the equation 18x+12y=216, where x is the number of lisa's customers and y is the number of daisy's customers would lisa need to serve to attain the projected income if daisy calls in sick that day?
Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day
What is linear function ?
A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:
y = mx + b
where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.
According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:
18x = projected income
We can solve for x by dividing both sides of the equation by 18:
x = projected income / 18
Substituting the given projected income of $216, we get:
x = 216 / 18 = 12
Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.
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8. the z-table gives the area under the standard normal curve to the left of z. what does the t-table give?
Answer:
The z-Table gives the area under the standard normal curve to the left of z. What does the t-Table give? The t-Table gives the area under the t-curve with n degrees of freedom to the left of it
HOPE THIS HELPSSS!
7. Write the unknown value that makes this
statement true:
25% of is 10
Answer: 40
Step-by-step explanation:
25/100 x ? = 10
multiply both sides by 100/25
x= 10 x 100/25
x=10
Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. If she spends 3x-7 dollars on rent, how much does she spend on electricity? Use pencil and paper. For which
value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s)
She spends
(Simplify your answer.)
dollars on electricity.
The values of x is [tex]x < 39.5[/tex].
Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]
Spending of shopkeeper on rent [tex]= 3x-7[/tex]
So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
[tex]2x+21 < 100[/tex]
[tex]2x < 100-21[/tex]
[tex]2x < 79[/tex]
[tex]x < 39.5[/tex]
All the values of [tex]x < 39.5[/tex].
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Jada is training for a swimming race. The more she practices, the less time it takes for her to swim one lap. Name the independent and dependent variables.
Answer:Independent = Her practice time. Dependent= Her lap time.
Step-by-step explanation: The more she practices the faster she can swim.
17 identical tasks are assigned to 7 different people. each task is assigned to exactly one person and there are no restrictions on the number of tasks that can be given to any one person. how many ways are there to assign the tasks?
There are 100,947 ways to assign the tasks to the 7 people.
This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.
Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,
The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is
(17 + 6) choose 6 = 23 choose 6 = 100947
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Kira has $2.20 in dimes and quarters. If the number of dimes
is the number of quarters, how many dimes does she have?
Answer:
There are 2 dimes in the purse that contains $2.20
What is an equation?
An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Let quarters be = x
The dimes be = 1/4 * x
25x+10x/4 = 220
(100x + 10x) /4 = 220
110x/4 = 220
110x = 220*4
110x = 880
x = 880/110
x = 8
The dimes be = 1/4 * x
The dimes be = 1/4 * 8
The dimes be = 2
Step-by-step explanation:
Pls ad brainliest!!!
i need help on this question :(((
The Polynomials that are listed in the question are the options labelled;
B, C, E
What is a polynomial?
A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.
The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.
Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.
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If you have 4 purple marbles and 8 yellow marbles in a bag. What is the probability of getting a purple marble
You have a 4/12 probability.
what is the average rate of change of f(x) from x = -3 to x = 6? f(x) = x^2 + 4x − 15 enter your answer in the blank.
The average rate of change of f(x) from x = -3 to x = 6 is 7.
What is meant by average?
The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.
To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.
For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:
[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]
The value of the function at [tex]x = 6[/tex] is:
[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]
The difference in the function values is:
[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]
The difference in the input values is:
6 - (-3) = 9
Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:
average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]
So, the average rate of change of f(x) from x = -3 to x = 6 is 7.
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assume that 20% of criminal suspects who agree to take lie detector tests are actually guilty while 80% of those who agree to take the test are innocent. of those who are guilty, 70% fail the lie detector test. of those who are innocent, only 15% fail the test. suppose a person is arrested and takes a lie detector test. given that the person fails the test, what is the probability that the person is actually innocent?
The probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.
The question asks us to calculate the probability that the person is actually innocent given that they have failed the test. The probability that the person is actually innocent is given by the formula: P(innocent | fails test) = P(innocent and fails test) / P(fails test).
Now we need to calculate the values of the probabilities on the right-hand side of this equation. P(fails test) is equal to the sum of the probabilities that a guilty person fails the test and that an innocent person fails the test. Hence, P(fails test) = P(guilty and fails test) + P(innocent and fails test). P(guilty and fails test) = 0.2 × 0.7 = 0.14P(innocent and fails test) = 0.8 × 0.15 = 0.12. Therefore, P(fails test) = 0.14 + 0.12 = 0.26.
Finally, we can calculate the probability that the person is actually innocent given that they have failed the test: P(innocent | fails test) = P(innocent and fails test) / P(fails test)= 0.12 / 0.26= 0.4615 (rounded to four decimal places).
Therefore, the probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.
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What is 3x+7y=11 equal to
(6,-1)
(1,-2)
(0,4)
The given equation 3x + 7y = 11 is equal to (1,-2).
The given equation is 3x + 7y = 11.
To find the solution of the equation, we need to consider the given options:
(6,-1)(1,-2)(0,4)
Now substitute each value of x and y in the given equation, we get,
If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11
If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11
If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11
Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).
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If the limit as n goes to infinity of the quotient of the absolute value of the quantity a sub n plus 1 times the n plus 1 power of the quantity x minus 7 and the absolute value of the product of a sub n and the nth power of x minus 7 for the power series the summation from n equals 1 to infinity of a sub n times the nth power of the quantity x minus 7, then what is the interval over which the power series converges absolutely? You do not need to consider the endpoints.
In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.
The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.
In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.
This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.
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This is due tomorrow so please help me ASAP! Thanks!
The value of the given lengths are as follows:
a.) KL = 11.1ft
LO = 5.7ft
b.) m<OMN = 45°
How to calculate the missing length of the given triangles?For Side LO ;
7/11 = 7√2/7√2+LO
7(7√2+LO) = 11×7√3
69.3+7LO = 108.9
7LO = 108.9-69.3
LO = 39.6/7
LO = 5.7 ft
For KL ;
This can be solved using the Pythagorean theorem;
c²= b²+a²
C = 5.7+7√2 = 15.6
b = 11
a²= 15.6²-11²
= 243.36 - 121
= 122.36
a= √122.36
a= 11.1ft
For angle OMN;
This can be solved using SOHCAHTOA.
Sin∅ = opposite/hypotenuse
opposite = 7
hypotenuse = 7√2
sin∅ = 7/7√2
sin∅ = 0.707106781
∅= sin-1 0.707106781
∅ = 45°
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Solve for z.
d³ = −27
ANSWER FAST PLEASE
Answer:
d=-3
Step-by-step explanation:
d^3=-27
d=[tex]\sqrt[3]{-27} \\[/tex]
d=-3
Answer:
d=-3
Step-by-step explanation:
You must that 3rd root of -27, which is -3
the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. a. false b. true
The given statement "the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size" is True as it is proved by the central limit theorem.
The central limit theorem (CLT) states that for large enough sample sizes, the distribution of the sample means approximates a normal distribution regardless of the shape of the initial population distribution.
It is a statistical theory that clarifies how the mean of a random sample of independent observations drawn from a non-normal population converges in distribution to a normal population.
According to this theory, the sample size should be at least 30 for the sample mean to have an approximately normal distribution. The following are the fundamental assumptions of the central limit theorem:
A large enough sample size is requiredPopulation must be random and independentThe variance of the population must be finiteThe sampling must be done with replacement.Therefore, we can say that the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. The statement is true.
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Which expression is equivalent to the following complex fraction?
The expression that is equivalent to the following complex fraction is this: B. -2y + 5x/3x -2y.
What is an equivalent expression?An equivalent expression is one that produces the same result as the given one when simplified. To get the equivalent expression, we simply need to simplify the expression above and the one underneath.
After finding the lowest common multiples of the figures underneath and the ones above, the next thing to do will be to multiply by the numerators.
-2/x + 5/y = -2y + 5x
Also:
3/y - 2/x = 3x - 2y
So, option B is an equivalent expression of the complex fraction.
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The diagram shown is two intersecting lines. The measure of <5 is 42°.
Two intersecting lines. Not perpendicular. Angles labeled from far left counterclockwise are labeled 5 then 6 then 7
What is the measure of <7 ? How do you know. Explain your answer in complete sentences.
Suppose the measure of <6 can be represented by(3x-9). What equation can be written to solve for the value of x?
What is the value of x?
Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.
what is angle ?The distance between two intersecting lines or planes is measured in terms of angles. The amount of rotation required to align one of the lines or planes with the other is usually expressed in terms of degrees. The range of an angle is 0 degrees (i.e., no rotation) to 360 degrees (corresponding to a complete rotation).
given
As angles 5 and 7 are a pair of linear angles, their sum must be 180 degrees. Angle 7 therefore has a measure of 180 - 42 = 138 degrees.
We can use the fact that angles 6 and 7 are vertical angles and have the same measure to find the value of x. As a result, we can set the following phrase to indicate that the measure of angle 6 is equal to angle 7:
3x - 9 = 138
In order to find x, we add 9 to both sides and divide the result by 3:
3x = 147
x = 49
Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.
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1. A rain barrel collects water off the roof of a house during three hours of heavy rainfall. The height of the water in the barrel increases at the rate of r(t) = 47-15 feet per hour, where is the time in hours since the rain began. At time t = 1 hour, the height of the water is 0. 75 foot. What is the height of the water in the barrel at time = 2 hours? (A) 1. 361 ft (B) 1. 500 ft (C) 1. 672 (D) 2. 111
As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).
The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.
In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.
∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922
So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:
0.75 + 0.922 = 1.672 feet
Therefore, the correct option is (C).
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I tried and it did not make sense help
Answer: D) -20.99
Step-by-step explanation:
-4.97-2.36+-5.19-8.47 = -20.99
Find the measure of the indicated angle to the nearest degree.
8)
7)
28
25
I
Find the area of each.
9)
5m
6.7 m
10)
8 km
46
9.6 km
22
The given angles and measures is given below:
What is an Angle?In mathematics and geometry, an angle is a measure of the space between two intersecting lines, rays, or line segments, usually expressed in degrees, radians, or grads. It is the measure of the opening between two lines that intersect at a common point, called the vertex of the angle.
5) tan x = 153 / 41
x = tan^-1 ( 153 / 41 )
75 degrees
6) tan y = 25/25
y = tan^-1 ( 25/25 )
45 degrees
7) sin z = 10/28
z= sin^-1 ( 10/28 )
21 degrees
8) cos a = 47/50
a = cos^-1( 47/50)
20 degrees
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a line segment has endpoints (0, 5) and (6, 5). after the line segment is reflected across the x-axis, how long will it be?
The length of the reflected line segment is approximately 11.66 units.
The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.
Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.
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a run test is conducted for a process. the z-test value is calculated to be -1.5. if the run test acceptable limits are /- 2sigma you would conclude?
The conclusion of the test is the calculated z-test value of -1.5 falls within the acceptable limits of +/- 2 sigma.
To interpret the results of the run test, we need to compare the calculated z-test value with the acceptable limits for the test. The acceptable limits for the run test are +/- 2 sigma, which means that the process is considered acceptable if the z-test value falls within this range.
Since the z-value of -1.5 falls within the acceptable limits of +/- 2 sigma, we can conclude that the process is acceptable according to the run test. This means that there is no evidence of non-randomness or nonconformity in the process, and the process is functioning as expected.
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A quadratic equation is usually written in the form ax² + bx+c = 0. What are a, b, and c for the following quadratic equations? Separate your answers with a comma. (a) 13x²14x + 5 = 0 a, b, c (b) 5x² 13x - 10 = 0 (c) x² - 4 = 0 (d)-9x² = 0
Answer:
a) a is 13
b is 14
c is 5
b) a is 5
b is 13
c is-10
c) a is 1
b is 0
c is -4
d) a is -9
b is 0
c is 0
Step-by-step explanation:
hope this will be helpful:)
Determine if the given functions are even, odd or neither f(x)=x^2-7
The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.
To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.
Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).
f(-x) = (-x)² - 7 // substitute -x for x
= x² - 7 // simplify
Comparing f(-x) to f(x), we can see that they are not equal:
f(-x) = x² - 7
f(x) = x² - 7
Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.
f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term
= 2x² - 14
Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.
Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.
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I need the questions 25,28 and 29
Using the given values, the values of the expression and equations are:
25. -0.8
28. S ≈ 137.22
29. V ≈ 50.94
Evaluating an expressionFrom the question, we are to evaluate each of the expressions for the given values
25.
[-b + √(b² -4ac)]/2a
a = 2, b = 8, c = 5
Substituting the values into the expression
[-b + √(b² -4ac)]/2a
= [-8 + √((8)² - 4(2)(5))]/2(2)
= [-8 + √(64 - 40)]/4
= [-8 + √(24)]/4
= [-8 + 2√6]/4
= -2 + 1/2(√6)
= -0.775
≈ -0.8
28.
S = 2πrh + 2πr²
r = 2.3, h = 7.1 (Take π = 3.14)
Thus,
S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²
S = 103.9968 + 33.2212
S = 137.218
S ≈ 137.22
29.
V = 4/3 πr³
r = 2.3(Take π = 3.14)
V = 4/3 × 3.14 × (2.3)³
V = 50.939
V ≈ 50.94
Hence, the value of V is 50.94
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DUE TOMORROW PLEASE HELP!!!!
The center of an airplane propeller is 13 feet off the ground and the radius of the propeller is 3 feet. The blades of the propeller are set at π/6, 5π/6, and 3π/2 radians from 0 radians directly to the right of the center of the propeller.
What is the height of the tip of each propeller in this position?
The heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.
What is the equation of a circle in parametric form?
The equation of a circle in parametric form is given by x=acosθ,y=asinθ.
We can use the equation for a circle in standard form:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
In this case, the center of the propeller is (0, 13) and the radius is 3. So the equation of the circle is:
x² + (y - 13)² = 9
We can use this equation to find the x and y coordinates of the tip of each propeller.
For the blade at π/6 radians, we can use the parametric equations for a circle:
x = r cos(t) + h
y = r sin(t) + k
where t is the angle in radians.
Substituting r = 3, h = 0, k = 13, and t = π/6, we get:
x = 3 cos(π/6) + 0 = 3√3/2
y = 3 sin(π/6) + 13 = 13 + 3/2 = 15.5
So the height of the tip of the propeller blade at π/6 radians is 15.5 feet.
Using the same method for the blades at 5π/6 and 3π/2 radians, we get:
Blade at 5π/6 radians:
x = 3 cos(5π/6) + 0 = -3√3/2
y = 3 sin(5π/6) + 13 = 13 - 3/2 = 11.5
Height of tip: 11.5 feet
Blade at 3π/2 radians:
x = 3 cos(3π/2) + 0 = 0
y = 3 sin(3π/2) + 13 = 10
Height of tip: 10 feet
Therefore, the heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.
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