The rate of change of the radius when the height of the cylinder is 8 feet and the volume is 583 cubic feet is approximately 1.854 feet per second.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as;
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
We are given that;
dh/dt = -4 ft/s and dV/dt = 476 ft^3/s. We need to find dr/dt when h = 8 ft and V = 583 ft^3.
Now,
We can start by differentiating the volume formula with respect to time t, using the product rule:
dV/dt = d/dt (πr^2h)
= πh d/dt (r^2) + πr^2 d/dt (h)
= 2πrh (dr/dt) + πr^2 (dh/dt)
We can use the given values of h and V to find the value of r using the formula for the volume of a cylinder:
V = πr^2h
583 = πr^2(8)
r^2 = 583/(8π)
r ≈ 3.031
Now we can substitute the values we have into the formula for dV/dt and solve for dr/dt:
476 = 2π(8)(3.031)(dr/dt) + π(3.031)^2(-4)
dr/dt = (476 + 36π(3.031)^2) / (16π(3.031))
dr/dt ≈ 1.854
Therefore, by the given volume the answer will be 1.854 feet per second.
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Jake uses the formula d=rt
d
=
r
t
to find d, the distance when he rides his bike for t hours at a rate, r, of 15 miles per hour. What is the value of d when t=3
t
=
3
?
The value of d when t=3 is 45 miles. This means that Jake has covered a distance of 45 miles in 3 hours riding his bike at a rate of 15 miles per hour.
How to calculate distance?Distance is a measure of the length between two points. To calculate distance, we need to know the coordinates of the two points. We can use the Pythagorean theorem to calculate the distance.
The formula d=rt is used to calculate the distance traveled when a rate, r, and time, t, are given. In this case, Jake is riding his bike at a rate of 15 miles per hour for 3 hours. To calculate the distance, d, traveled, we can substitute the given values into the formula.
d = 15 * 3
d = 45
Therefore, the value of d when t=3 is 45 miles. This means that Jake has traveled 45 miles in 3 hours riding his bike at a rate of 15 miles per hour. This formula can also be used to calculate the time, t, when the rate, r, and distance, d, are known. To find the time, t, simply divide the distance, d, by the rate, r.
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20 points quick plssssss
Answer:
$9 an hour
Step-by-step explanation:
A) 1
B) 18
C) 4
D) 90
(3 points) Problem 5: Determine the value(s) ofasuch that [1a], [aa+2] are linearly independent.
To determine the value(s) of a such that [1 a], [a a+2] are linearly independent, we need to find the values of a that make the determinant of the matrix non-zero. The determinant of a 2x2 matrix is given by:
|1 a|
|a a+2| = (1)(a+2) - (a)(a) = a + 2 - a^2
To make the determinant non-zero, we need to solve the equation:
a + 2 - a^2 ≠ 0
Rearranging the equation, we get:
a^2 - a - 2 ≠ 0
Factoring the equation, we get:
(a - 2)(a + 1) ≠ 0
Therefore, the values of a that make the determinant non-zero are a ≠ 2 and a ≠ -1. These are the values of a that make the vectors [1 a], [a a+2] linearly independent.
So, the value(s) of a such that [1 a], [a a+2] are linearly independent are a ≠ 2 and a ≠ -1.
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439 crates/hour equals how many crates/
week
Answer: 73,752 crates/ week
We can get to the answer by multiplying 439 by 24 by 7
Hope this helps!!
A 6-foot person standing 18 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.
The streetlight is approximately 16.41 feet tall, and the length of its shadow is approximately 27.35 feet.
What is the proportion?
A proportion is a statement that two ratios are equal. In other words, a proportion is an equation that shows that two fractions or two ratios are equivalent. A proportion can be written in the form of:
a/b = c/d
We can use the properties of similar triangles to solve this problem. Let's call the height of the streetlight h, and the length of the shadow cast by the streetlight x. We can set up the following proportion:
(height of person) / (length of person's shadow) = (height of streetlight) / (length of streetlight's shadow)
or
6 / 10 = h / x
Simplifying this proportion, we get:
x = (10h) / 6
We also know that the person is standing 18 feet from the streetlight, and that the length of the person's shadow is 10 feet. Using the Pythagorean theorem, we can set up the following equation:
6^2 + 10^2 = (18 + x)^2
Simplifying and substituting x, we get:
36 + 100 = (18 + (10h/6))^2
136 = (18 + (10h/6))^2
Taking the square root of both sides, we get:
√136 = 18 + (10h/6)
Simplifying, we get:
√136 - 18 = (10h/6)
Multiplying both sides by 6, we get:
6(√136 - 18) = 10h
Simplifying, we get:
h ≈ 16.41 feet
Now, we can substitute this value of h into the expression for x that we derived earlier:
x = (10h) / 6 ≈ 27.35 feet
Therefore, the streetlight is approximately 16.41 feet tall, and the length of its shadow is approximately 27.35 feet.
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Select all expressions equivalent to (2-³.24) 2.
4
04
26.2-8
02-5.22
None of the expressions given is equivalent to (2 - ³√24)²..
What do mathematics expressions mean?Mathematical statements must contain a sentence, at least one mathematical operation, and at least two numbers or factors. With this mathematical operation, you can increase, split, add, or take something away. The shape of a phrase is as follows: Expression: (Number/Variable, , Math Operator)
Let's first simplify the expression (2 - ³√24)²:
(2 - ³√24)² = (2 - 24^(1/3))² = (2 - 2.29)² = (-0.29)² = 0.0841
Now we can check which expressions are equivalent to 0.0841 when (2 - ³√24)² is evaluated:
4 = 4.0000... (not equivalent to 0.0841)
04 = 0.04 (not equivalent to 0.0841)
26.2 - 8 = 18.2 (not equivalent to 0.0841)
02 - 5.22 = -3.22 (not equivalent to 0.0841)
Therefore, none of the expressions given is equivalent to (2 - ³√24)².
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The cost of employee work stoppages is rising. Assume the average cost is now $360. If the average cost is normally distributed with a standard deviation of $88.
Required
a. What is the probability that the cost will be $260 or less
b. What is the probability that the cost will be more than $412
c. What is the probability that the cost will be between $260 and $412
So the probability of the cost being between $260 and $412 is 0.5953.
a. The probability that the cost will be $260 or less can be found by calculating the z-score and using a standard normal distribution table. The z-score is calculated as follows:
z = (x - μ)/σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 260, μ = 360, and σ = 88. So the z-score is:
z = (260 - 360)/88 = -1.14
Using a standard normal distribution table, we can find that the probability of the cost being $260 or less is 0.1271.
b. The probability that the cost will be more than $412 can be found by calculating the z-score and using a standard normal distribution table. The z-score is calculated as follows:
z = (x - μ)/σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 412, μ = 360, and σ = 88. So the z-score is:
z = (412 - 360)/88 = 0.59
Using a standard normal distribution table, we can find that the probability of the cost being more than $412 is 0.2776.
c. The probability that the cost will be between $260 and $412 can be found by subtracting the probability of the cost being $260 or less from the probability of the cost being $412 or less. Using the z-scores we calculated in parts a and b, we can find the probabilities from a standard normal distribution table:
P(x ≤ 260) = 0.1271
P(x ≤ 412) = 0.7224
P(260 < x < 412) = P(x ≤ 412) - P(x ≤ 260) = 0.7224 - 0.1271 = 0.5953
So the probability of the cost being between $260 and $412 is 0.5953.
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Use substitution to solve
Answer:
x=4, y=-2
Step-by-step explanation:
[tex]2y=x-8\\2y-x=-8\\2(2x-10)-x=-8\\4x-20-x=-8\\3x-20=-8\\3x=-8+20\\x=12/3\\x=4\\\\\\y=2x-10\\y=2(4)-10\\y=8-10\\y=-2[/tex]
Daniel built a wooden, cubic toy box for his daughter. Each edgeof the box measures 2 feet. How many square feet of wood did he use to build the house? A.
There are 6 faces in a cube, the total surface area of the toy box is 6 x 4 = 24 square feet. So correct option is B.
Describe Cube?In geometry, a cube is a three-dimensional shape that is bounded by six square faces, with each face meeting at right angles. A cube is a regular polyhedron, which means that all of its faces are congruent and all of its edges have the same length.
The cube has a total of eight vertices (corners) and twelve edges, with each vertex connecting three edges and each edge connecting two vertices. The volume of a cube can be calculated using the formula V = s^3, where s is the length of one edge.
Cubes are commonly used in mathematics, physics, and engineering to represent three-dimensional objects and to model various phenomena. For example, cubes can be used to represent the atoms in a crystal lattice, the cells in a grid, or the pixels in a digital image
The toy box is a cube, and each edge measures 2 feet. So, the surface area of one face of the cube is 2 x 2 = 4 square feet. Since there are 6 faces in a cube, the total surface area of the toy box is 6 x 4 = 24 square feet.
Therefore, the answer is (B) 24 feet squared.
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The complete question is:
A physics class has 40 students. Of these, 10 students are physics majors and 14 students are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major.
The probability that a randomly selected student is female or a physics major would be 0.65.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring needs to be 1.
The probability that a randomly selected student is female or a physics major can be calculated:
P(PM or F) = P(PM) + P(F) - P(PMF)
Where P(PM or F) = Probability of student selected is Physics Major or Female needed to find.
P(PM) = Probability of student selected is Physics Major
P(PM) = Number of Physics Major / Total number of students in the Physics class
P(PM) = 14 / 40 = 0.35
P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45
P(PMF) = Probability of student selected is Physics Major and Female = 6 / 40 = 0.15
Substituting the values into equation (1);
P(PM or F) = 0.35 + 0.45 - 0.15
P(PM or F) = 0.65
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find the sale price of a $36 item after a 50% discount
Answer:$18
Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount
Answer:
18$
Step-by-step explanation:
go to Safari and look it up is how I got the answer
Gina buys 7 tacos for $4.20 how much does each taco cost
Answer: $29.4
Step-by-step explanation: one taco cost 4.20 so multiply the price of the tacos times the amount of tacos gina buys and you should get your answer which is 29.4
Sheffield Company of Emporia, Kansas spreads herbicides and applies liquid fertilizer to local farmers
In the journal entries, Debit: Accounts Receivable Credit: Cash 570
Debit: Sales revenue Credit: Cash 40
Bank Reconciliation StatementMay 31, 2022
Cash balance per bank statement 8,120
Add:
Deposit in transit 1,972.55
Bank error—Sheffield 390
2,362.55
10,482.55
Less: Outstanding checks 876.05
Adjusted cash balance per bank 9,606.50
Cash balance per books 8,110.50
Add: Electronic funds transfer received 2,200
10,310.50
Less:
NSF check 570
Error in deposit 40
Error in recording check (1181) 54
Check printing charge 40
704
Adjusted cash balance per book 9,606.50
Journal Entries:
Debit: Cash Credit: Accounts Receivable 2,200
Debit: Accounts Receivable Credit: Cash 570
Debit: Sales revenue Credit: Cash 40
Debit: Accounts payable Credit: Cash 54
Debit: Bank charges expense Credit: Cash 40
Note: Bank charges expense can also be titled as Miscellaneous expense.
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Use the Scores data set. Dr. Z is interested in discovering if there is a difference in depression scores between those who do not watch or read the news and those who continue with therapy as normal. She divides her clients with depression into 2 groups. She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 to continue with therapy as normal. The Scores data set is a record of the results of the measure, administered after 2 weeks
1. Independent Variable: Group (No News or watch news)
Dependent Variable: Depression Scores
2. Null Hypothesis: μ = 0
Alternative Hypothesis: μ < 0
3. Yes, you can reject the null hypothesis at a = 0.05 because there is a considerable difference in the depression ratings of the two groups
1. According to the information provided, the score for depression depends on whether a group watches the news or not.
Group is an independent variable (No News or watch news).
Depression scores are a dependent variable.
2. Null Hypothesis: The two groups do not differ in their depression levels, which is the null hypothesis.
Alternate Hypothesis: Those who don't read or watch the news will score less depressed than people who receive therapy as usual.
μ = 0 is the null hypothesis.
Between the two groups, there is no difference in depression scores.
Differential Hypothesis: μ < 0
Those who don't read or watch the news will score less depressed than people who receive therapy as usual.
3. Due to the p-value of (0.024) < α(0.05) at α = 0.05, we can rule out the null hypothesis.
The rejection zone of the t-distribution with 12 degrees of freedom has the t-score of -2.58.
As a result, it is clear that there is a considerable difference in the depression ratings of the two groups, with the group that does not watch or read the news scoring significantly lower on the depression scale than the group that continues to get therapy as usual.
The proper response is "Yes".
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The complete question is:
Dr. Z is interested in discovering if there is a difference in depression scores between those who do not watch or read the news and those who continue with therapy as normal. She divides her clients with depression into 2 groups. She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 to continue with therapy as normal. The dataset score is a record of the results of the measure, administered after 2 weeks.
Independent Samples T-Test
t df p
Score -2.580 12 0.024
1. Identify IV and DV.
2. State the null hypothesis and the directional (one-tailed) alternative hypothesis
3. Can you reject the null hypothesis at a = 0.05?
What is the first step in solving this system by elimination if we want to eliminate
the x variable first?
5x + y = 9
10x - 7y = -18
multiple choice
1. Add both equations together
2.Divide the bottom equation by 5
3.Subtract the bottom equation from the top
4.Multiply top equation by 2
The first step in solving by elimination is (4) Multiply top equation by 2
How to determine the first step in solving by eliminationFrom the question, we have the following parameters that can be used in our computation:
5x + y = 9
10x - 7y = -18
To eliminate x the coefficient of x in both equations muet be the same i.e 10
Using the above as a guide, we have the following:
Multiply (1) by 2
So, we have
10x + 2y = 18
10x - 7y = -18
Hence, the first step is (4)
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One kilogram is how many times one nanogram?
Answer:
1 trillion times larger
Step-by-step explanation:
One kilogram (kg) is equal to 1,000,000,000,000 (1 trillion) nanograms (ng).
Therefore, one kilogram is 1 trillion times larger than one nanogram.
if the solution of an equation is x=-2, what could the original equation be? A. x+6=8 B. x-6=8 C. x+8=6 D. x-8=6
Answer:
C: x+8= 6
Step-by-step explanation:
So if you were to work each of these out x + 6 = 8 that problem gives us positive 2, when we are looking for a -2 so that answer is ruled out. Then you go to x-6=8 you move the -6 and add it to the 8 and you get x = 14 still not our answer so thats also ruled out. Then x-8=6 is the same thing as the last one but with a -8 instead of a 6 but you get the same answer which is x=14 so not that one either. Then you work on the choice x+8=6 and you subtract 8 from both sides and you end up with a -2. So our final answer is C: X+8=6
Math part 2 question 3
The value of (g times f)(x) is 6x² + x - 2. So correct is C.
Describe Function?The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.
Overall, functions are a fundamental concept in mathematics, and have many practical applications in the real world.
To find g(x) times f(x), we need to multiply the two functions together.
(g times f)(x) = g(x) * f(x)
First, we need to find g(f(x)):
g(f(x)) = g(3x+2) = 2(3x+2) - 1 = 6x + 3
Now we can substitute this into the expression for (g times f)(x):
(g times f)(x) = g(x) * f(x) = (2x-1) * (3x+2)
Using the distributive property, we get:
(g times f)(x) = 6x² + 4x - 3x - 2 = 6x² + x - 2
Therefore, (g times f)(x) = 6x² + x - 2.
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An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y= 225x. The x-variable is the number of hours the field is
being rented, and the y-variable is the total cost, in dollars.
Which statement is true based on the given equation?
A) The equation shows a linear relationship, but not a proportional relationship.
B) The equation shows a linear relationship and a proportional relationship
C) The equation does not show a linear relationship or a proportional relationship
D) The equation shows a proportional relationship,but not a linear relationship.
PLS HELP!!
Answer:
The equation y=225x represents a proportional relationship between the number of hours the field is being rented and the total cost. This means that as the number of hours increases, the total cost will increase proportionally. Therefore, statement D) "The equation shows a proportional relationship, but not a linear relationship" is true based on the given equation.
Unit 3 Test Review Name Raver mial Functions Express (3x^(3)-2x^(2)+3)/(x-1) in the form q(x)+(r(x))/(b(x))
The given function is (3x^(3)-2x^(2)+3)/(x-1). To express it in the form q(x)+(r(x))/(b(x)), we need to use polynomial long division.
First, divide the first term of the numerator, 3x^(3), by the first term of the denominator, x:
3x^(3)/x = 3x^(2)
Now, multiply this result by the denominator and subtract it from the numerator:
(3x^(3)-2x^(2)+3) - (3x^(2)(x-1)) = -2x^(2)+3x^(2)-3
Simplify:
x^(2)-3
Next, divide the first term of the new numerator, x^(2), by the first term of the denominator, x:
x^(2)/x = x
Multiply this result by the denominator and subtract it from the new numerator:
(x^(2)-3) - (x(x-1)) = -3+x
Simplify:
x-3
Since the degree of the new numerator is less than the degree of the denominator, we can stop here. The final result is:
q(x) = 3x^(2)+x
r(x) = x-3
b(x) = x-1
So, the function can be expressed as:
(3x^(3)-2x^(2)+3)/(x-1) = 3x^(2)+x + (x-3)/(x-1)
In HTML format, the answer would be:
<p>(3x^(3)-2x^(2)+3)/(x-1) = 3x^(2)+x + (x-3)/(x-1)</p>
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Evaluate. Write your answer as a fraction or whole number without exponents. 5^-4
Answer:
1 / 625
Step-by-step explanation:
To write 5^-24 without exponents, simplify.
5^-4
1 / 5^4
1 / 625 or .0016
Please, help I need this done today and show work.
The points (1, 1) and (2, 2) have been used to graph the inequality as shown in the image attached below.
The boundary line is dashed.
The boundary line is shaded below.
What are the rules for writing an inequality?In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:
The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).Additionally, the point (2, 2) and point (1, 1) are not solutions to the given inequality y < 1/4(x) + 1 because the lie below the boundary line
y < 1/4(x) + 1
2 < 1/4(2) + 1
2 < 3/2 (False)
y < 1/4(x) + 1
1 < 1/4(1) + 1
2 < 5/4 (False)
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Order from greatest to least
Answer:
15, 3, -1, -12
Step-by-step explanation:
15, 3, -1, -12
Answer:
First answer (15, 3, -1, -12)
Step-by-step explanation:
ez
Please help me i have a screenshot
2 1/8 pints
2.125 pints
Find the gradients of lines A and B.
B
-2
6
O
-21
Fet
A
4
72%
X
The gradient of line A is 4/72% or 0.0555.The gradient of line B is -2/6 or -0.3333.
What is value?Value is the worth of something, or the amount of importance, good qualities, or benefits that something has. It is determined by the amount of effort, time, and resources that have been put into it. Value can also refer to a person's moral or ethical principles and standards. It is the measure of worth that someone places on something or someone. Ultimately, value is subjective, as it is based on individual opinion.
The gradients of lines A and B indicate the rate of change of the line in relation to the x-axis. The gradient of line A is positive, which indicates that the line is increasing as it moves along the x-axis. This means that the y-value of the line is increasing as the x-value increases. On the other hand, line B has a negative gradient, which means that the y-value of the line is decreasing as the x-value increases. This means that the line is decreasing as it moves along the x-axis. This is why the gradients of lines A and B are different.
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Someone please help me answer my question.
The following solutions with regard to resolving or simplifying the radii of the circular pond are given below.
Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters
Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters
Part C: The radius of Pond B is 10√2 meters.
Part D: the radius of Pond B is greater than the radius of Pond A.
What is the justification for the above responses?Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:
164 = 2 × 2 × 41
So, we can write:
√164 = √(2 × 2 × 41) = 2√41
Using this, we can rewrite Step 1 as:
5√100 + √164 meters = 5 × 10 + 2√41 meters
Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:
5 × 10 + 2√41 meters = 50 + 2√41 meters
So, the radius of Pond A is 50 + 2√41 meters.
Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:
25√200/5 meters = 5√200 meters
We can simplify this further by finding the prime factorization of 200:
200 = 2 × 2 × 2 × 5 × 5
So, we can write:
√200 = √(2 × 2 × 2 × 5 × 5)
= 2 × 5√2
Using this, we can rewrite the expression for the radius of Pond B as:
5 × 2 × √2 meters
= 10√2 meters
Thus, the radius of Pond B is 10√2 meters.
Part D: We can compare the radii of the ponds using the original expressions by writing:
√164 < 25√200/5
Simplifying both sides:
2√41 < 10√2
Dividing both sides by 2:
√41 < 5√2
Squaring both sides (since both sides are positive):
41 < 25 × 2
41 < 50
So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.
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Full Question:
Two circular ponds at a botanical garden have the following radii:
Pond A: Sqrt(164) meters;
Pond B: 25Sqrt(200)/5 meters:
Todd simplified the radius of pond A this way:
5sqrt(164)
Step 1: 5sqrt(100) + Sqrt(164) meters
Step 2: 5(10 + 8)
Step 3: 5(18)
Step 4: 90
One of the steps above is incorrect.
Part A: Rewrite the steps so that it is correct
Part B: Using the corrected step from Part A, simplify the radius of Pond A.
Part C: Simplify the expression for the radius of pond B.
Part D: Write an inequality to compare the radii of the ponds, using the original expressions.
Find all possible rational zeros for the polynomial fu P(x)=21x^(3)-38x^(2)+44x-10
The possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.
The possible rational zeros of a polynomial function can be determined using the Rational Zero Theorem. This theorem states that if a polynomial function has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In the given polynomial function, P(x)=21x^(3)-38x^(2)+44x-10, the constant term is -10 and the leading coefficient is 21. The factors of -10 are ±1, ±2, ±5, ±10 and the factors of 21 are ±1, ±3, ±7, ±21.
Using the Rational Zero Theorem, the possible rational zeros are:
p/q = ±1/1, ±2/1, ±5/1, ±10/1, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21
Simplifying these fractions gives us the possible rational zeros:
±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21
Therefore, the possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.
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Adding & Perform the indicated operations. (9)/(r^(2)-7r)+(10)/(r^(2)+9r)-(1)/(r^(2)+2r-63)
The solution is given by [tex](18r^4+30r^3+25r^2-154r)/(r^6-5r^5+16r^4-45r^3-126r^2+3969r)[/tex]
To perform the indicated operations, we need to find a common denominator for all of the fractions. The common denominator will be the product of the three denominators: [tex](r^2-7r)(r^2+9r)(r^2+2r-63)[/tex].
Next, we will multiply each fraction by the appropriate factor to make the denominators equal. For the first fraction, we will multiply by [tex](r^2+9r)(r^2+2r-63)/(r^2+9r)(r^2+2r-63)[/tex].
For the second fraction, we will multiply by [tex](r^2-7r)(r^2+2r-63)/(r^2-7r)(r^2+2r-63)[/tex]. For the third fraction, we will multiply by [tex](r^2-7r)(r^2+9r)/(r^2-7r)(r^2+9r)[/tex].
After multiplying, we will combine the numerators and keep the common denominator:
[tex](9(r^2+9r)(r^2+2r-63)+10(r^2-7r)(r^2+2r-63)-1(r^2-7r)(r^2+9r))/(r^2-7r)(r^2+9r)(r^2+2r-63)[/tex]
Finally, we will simplify the numerator and denominator as much as possible to get the final answer:
[tex](9r^4+72r^3-567r^2+18r^3+162r^2-1134r+10r^4-70r^(3)+630r^2-20r^3-140r^2+980r-r^4+7r^3-9r^2)/(r^6-7r^5+9r^4-63r^3+2r^5-14r^4+18r^3-126r^2-63r^4+441r^3-567r^2+3969r)[/tex]
[tex](18r^4+30r^3+25r^2-154r)/(r^6-5r^5+16r^4-45r^3-126r^2+3969r)[/tex]
So the final answer is [tex](18r^4+30r^3+25r^2-154r)/(r^6-5r^5+16r^4-45r^3-126r^2+3969r)[/tex]
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Make a table comparing a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with both descriptions and sketches, including markings for congruency. All work should be original
We have compared a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with type, descriptions, and properties.
What is congruency?
The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.
Parallelogram: A four-sided shape with opposite sides parallel. Opposite sides are parallel, opposite angles are congruent, diagonals bisect each other.
Rectangle: A four-sided shape with four right angles.
Opposite sides are parallel and congruent, all angles are right angles, diagonals are congruent and bisect each other.
Square: A four-sided shape with four congruent sides and four right angles.
All sides are congruent, all angles are right angles, diagonals are congruent and bisect each other.
Rhombus: A four-sided shape with four congruent sides. All sides are congruent, opposite angles are congruent, diagonals bisect each other, and are perpendicular bisectors of each other.
Kite: A four-sided shape with two pairs of adjacent sides congruent. Diagonals are perpendicular, one diagonal bisect the other, opposite angles are congruent.
Trapezoid: A four-sided shape with one pair of parallel sides.
One pair of opposite sides are parallel, non-parallel sides may or may not be congruent, and diagonals intersect at a point inside the trapezoid.
Hence, we have compared a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with type, descriptions, and properties.
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Rewrite the equation by completing the square - 4x^2 +20x +25 =0
Answer:
[tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]
Step-by-step explanation:
I am not completely sure if you just wanted me to write it in square form, so I will show the process of writing it in square form and how to find the solution.
[tex]-4x^2+20x=-25[/tex] start by moving 25 to the right side
[tex]\frac{-4x^2+20x}{-4}=\frac{-25}{-4}[/tex] divide both sides by -4
= [tex]x^2-5x=\frac{25}{4}[/tex]
Now we rewrite the equation in the form [tex]\:x^2+2ax+a^2[/tex]
= [tex]x^2-5x+\left(-\frac{5}{2}\right)^2=\frac{25}{2}[/tex] apply perfect square formula: [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
= [tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex] -- square form
Solutions to the quadratic equation:
Possible solutions: [tex]x=\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex] and [tex]\:x=-\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex]
