Vector calculus question: Find the values of a, ß and y, if the directional derivative Ø = ax²y +By²z+yz²x at the point (1, 1, 1) has maximum magnitude 15 in the direction parallel to the line x-1 3-y = = Z. 2 2
Answers
The values of a, ß, and y can be determined as follows: a = 4, ß = -3, and y = 2. the directional derivative Ø consists of three terms: ax²y, By²z, and yz²x.
To find the values of a, ß, and y, we need to analyze the given directional derivative Ø and the direction in which it has maximum magnitude. The directional derivative Ø is given as ax²y + By²z + yz²x, and we are looking for the direction parallel to the line x-1/3 = y-2/2 = z.
Let's break down the given directional derivative Ø to understand its components and then find the values of a, ß, and y.
The directional derivative Ø consists of three terms: ax²y, By²z, and yz²x. In order for Ø to be maximum in the direction parallel to the given line, the coefficients of these terms should correspond to the direction vector of the line, which is (1, -3, 2).
Comparing the coefficients, we can determine the values as follows:
For the term ax²y, the coefficient of x²y should be equal to 1 (the x-component of the direction vector). Therefore, we have a = 1.
For the term By²z, the coefficient of y²z should be equal to -3 (the y-component of the direction vector). Hence, ß = -3.
For the term yz²x, the coefficient of yz²x should be equal to 2 (the z-component of the direction vector). Thus, we find y = 2.
Therefore, the values of a, ß, and y are a = 1, ß = -3, and y = 2.
In summary, the values of a, ß, and y that satisfy the condition of the directional derivative Ø having a maximum magnitude in the direction parallel to the given line are a = 1, ß = -3, and y = 2.
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Related Questions
please help with the question asked
Answers
Answer:
C, None of the above
Step-by-step explanation:
Step 1: Expand the brackets
-7 - 3(-4e-3)
-7 + 12e + 9
Step 2: Collect like terms
12e + 2
Because the answer is not a or b the answer is 'None of the Above'
Hey there! I'm happy to help!
Let's use the distributive property to undo the parentheses. We multiply the number next to the parentheses by each number inside of the parentheses.
-7+3(-4e-3)
-7-12e-9
We combine like terms.
-16-12e
This means that Answer B is incorrect. Answer A could still be correct though as it could have equal value to -16-12e.
-4(3e+4)
We use distributive property.
-12e-16
We see that these have the same value, so the correct answer is A.
Have a wonderful day! :D
elaine has 88 coins in a jar. they are all 5 cent and 10 cent coins. the total value of the coins is $7. how many of each type of coin does elaine have?
Answers
Answer:
36 nickels, 52 dimes
Step-by-step explanation:
5n + 10*(88-n) = 700
N = nickels
88 = total coins
(88-n) = dimes
-5n = 700 - 880 --> -5n = -180
divide by 5 on both sides
n = 36
88 - 36 = 52
dimes = 52
It took Jamal 13 days to read his novel for Language Arts class. How many weeks is that?
Answers
Answer:
1 week and half
Step-by-step explanation:
theres 7 days which equals a week,so since Jamal read 13 days. It was a week and half day
Let L be a linear transformation mapping R3 into R2 defined by L(x)=x1 b1+(x2+x3)b2 for each x∈R3, where b1=(11),b2=(−11)
Answers
The linear transformation L maps a vector x = (x1, x2, x3) in R3 to a vector in R2 using the following formula:
L(x) = x1 * b1 + (x2 + x3) * b2
Here, b1 = (1, 1) and b2 = (-1, 1) are the basis vectors in R2.
To apply the transformation, we substitute the values of x1, x2, and x3 into the formula. Let's denote the resulting vector in R2 as (y1, y2):
L(x) = (y1, y2)
We can calculate the values of y1 and y2 as follows:
y1 = x1 * 1 + (x2 + x3) * (-1) = x1 - x2 - x3
y2 = x1 * 1 + (x2 + x3) * 1 = x1 + x2 + x3
So, the linear transformation L maps a vector x = (x1, x2, x3) to a vector (y1, y2) where y1 = x1 - x2 - x3 and y2 = x1 + x2 + x3.
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In triangle ABC, the right angle is at vertex C, a = 714 cm and the measure of angle A is 78° . To the nearest cm, what is the length of side c?
Answers
Answer:
c = 730 cm
Step-by-step explanation:
To solve this question we just need to use the law of sines:
The ratio between a side in the triangle and its opposite angle is always the same.
So we have that:
\(a / sin(A) = c / sin(C)\)
\(714 / sin(78) = c / sin(90)\)
sin(78) is equal 0.9781 and sin(90) is equal 1, so we have:
\(714 / 0.9781 = c / 1\)
\(c = 714 / 0.9781 = 730\ cm\)
1. Assume the line AB and a point P not on the line have already been constructed. What is the first step to construct a parallel line passing through the point P?
1. Use a compass to draw an arc centered at point B that intersects the AB, and label the intersection point C.
2. Construct another point Q different from point P that is not on the line.
3. Use a compass to draw an arc centered at point a that intersects AB, and label the intersection point C.
4. Use a compass to draw an arc centered at point P that intersects AB, and label the intersection points C and D.
2. In the given image, what is the next step for constructing a parallel line passing through point P?
1. With the compass opened to less than half of CD, draw arcs centered at C and D and label the point of intersection of the arcs E.
2. Decrease the size of the compass and draw one arc centered at point C, a second arc centered at point D, and label the point of intersection between the two arcs E.
3. Increase the size of the compass and draw one arc centered at point A, a second arc centered at point B, and label the point of intersection between the two arcs E.
4. With the compass opened to at least half of CD, draw arcs centered at C and D and label the point of intersection of the arcs E.
Answers
1) The first step in construction of the parallel line is; Construct another point Q different from point P that is not on the line.
2) The next step is; 4. With the compass opened to at least half of CD, draw arcs centered at C and D and label the point of intersection of the arcs E.
How to construct a parallel line?Parallel lines are defined as the lines that do not intersect or meet each other at any given point in a plane. This means that the lines are always parallel and equidistant from each other.
The steps to construct a parallel line passing through point P is as follows;
Step 1: Draw Line AB as shown in the figure.
Step 2: Take point P outside the line AB as shown in the figure.
Step 3: From P to AB draw a perpendicular line PQ passing through AB.
Step 4: Now at point P, make an angle of 90 degrees and extend the line EF both sides of P.
Step 5: EF is parallel line to AB passing through P
Looking at the options and comparing with the steps above, we can say that;
1) First step is option 2
2) Next step is option 4
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suppose you want to line pennies up, diameter to diameter, until the total length is 1 kilometer. assume the width of 1 penny is 2 cm. how many pennies will you need? how accurate is this estimation?
Answers
Answer: 50,000 pennies
Step-by-step explanation: there are 100,000 centimeters in a kilometer, since a penny is 2 centimeters in length, divide 100,000 by 2 t get 50,000
7) Find the sample standard deviation. 22 29 21 24 27 28 25 36
Answers
Answer:
26.5
Step-by-step explanation:
The standard deviation of 22, 29, 21, 24, 27, 28, 25, 36 is 19.75.
What is standard deviation ?"The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean."
"Standard deviation is an especially useful tool in investing and trading strategies as it helps measure market and security volatility—and predict performance trends. As it relates to investing, for example, an index fund is likely to have a low standard deviation versus its benchmark index, as the fund's goal is to replicate the index."
The given numbers are 22, 29, 21, 24, 27, 28, 25, 36.
The formula for standard deviation is \(\sqrt({ $\sum_{n=1}^{n} (xi - mean)^2/n )= 1$}\)
Finding mean of given numbers = 22+29+21+24+27+28+25+36/8 = 26.5
Now for standard deviation =\(\sqrt((22-26.5)^2 + (26.5-29)^2 + (26.5-21)^2+(26.5-24)^2+(26.5-27)^2+(26.5-28)^2+(26.5-25)^2+(26.5-36)^2/8 )\)
= 19.75
Hence, the standard deviation of the given numbers is 19.75
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Prove using rules of inference 1. If the band could not play rock music or the refreshments were not delivered on time, then the New Year's party would have been canceled and Alicia would have been angry. If the party were canceled, then refunds would have had to be made. No refunds were made. Therefore the band could play rock music. 2. If you are not in the tennis tournament, you will not meet Ed. If you aren't in the tennis tournament or if you aren't in the play, you won't meet Kelly. You meet Kelly or you meet Ed. It is false that you are in the tennis tournament and in the play. Therefore, you are in the tennis tournament.
Answers
The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.
1. Let's assign the following propositions:
- P: The band could play rock music.
- Q: The refreshments were delivered on time.
- R: The New Year's party was canceled.
- S: Alicia was angry.
- T: Refunds were made.
2. The given premises can be expressed as:
(¬P ∨ ¬Q) → (R ∧ S)
R → T
3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.
4. Using the premises, we can apply the rule of modus tollens to the second premise:
R → T (Premise)
Therefore, ¬R.
5. Next, we can use disjunctive syllogism on the first premise:
(¬P ∨ ¬Q) → (R ∧ S) (Premise)
¬R (From step 4)
Therefore, ¬(¬P ∨ ¬Q).
6. Applying De Morgan's law to step 5, we get:
¬(¬P ∨ ¬Q) ≡ (P ∧ Q)
7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.
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Find the value of X, in the image below
Answers
Can explain if you want me to
What is the value of x?. WIll brainlist first correct answer.
Answers
Answer:
x=144
Step-by-step explanation:
Use the polygon formula (n-2) * 180 where n is the number of points
This polygon has 8 points
(8-2)*180 = 6 * 180 = 1080
136+124+141+158+116+129+132+x=1080
x=144
60 points and brainliest
Find the sum of (6.5 x 10−9) and (4.6 x 10−10). Write the final answer in scientific notation.
6.96 x 10−9
6.96 x 10−10
1.11 x 10−18
11.1 x 10−19
Answers
Answer:
Below
Step-by-step explanation:
6.5 x 10^-9 is the same as 65 x 10^-10 now you can add them together (since the exponents are the same ) to get
69.6 x 10 ^-10 which is 6.96 x 10^-9
Give the state diagram for a Turing machine that decides each of the following language over Σ = {0, 1}: a) L6= {w: w contains both the substrings 011 and 101} b) L7= {w: w contains at least two 0's and at most two 1's}
Answers
To provide the state diagrams for Turing machines that decide the languages L6 and L7, we need to describe the transitions and states that machines will go through.
a) For language L6, a possible state diagram for the Turing machine would involve states for each substring encountered. The initial state would be a start state, and when the machine reads 0, it transitions to a state representing the substring 0. When it reads 1, it transitions to a state representing the substring 01. If it then reads another 1, it transitions to a state representing the substring 011, which is an accepting state. Similarly, when it reads 0 after 01, it transitions to a state representing the substring 0110. If it reads 1 after 0110, it transitions to a state representing the substring 01101, which is another accepting state.
b) For language L7, the Turing machine needs to keep track of the count of 0's and 1's encountered. It can have states such as S0, S1, S2, and S3, representing the number of 0's encountered. The machine starts in state S0, and upon reading 0, it remains in S0 or moves to state S1. Upon reading 1, it moves to state S2. If another 1 is encountered in S2, the machine moves to a non-accepting state S3. If it reads 0 in S1 or S2, it moves back to S0. If it encounters two 1's and no more 0's, it stays in S2. States S1 and S2 are accepting states, and once the machine reaches either of these states, it halts and accepts the input.
Note: The provided descriptions are high-level explanations, and the actual state diagrams might involve more states and transitions depending on the specific implementation of the Turing machine for each language.
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use the definition of the laplace transform to find l{f(t)}. (enter your answer in terms of s.) f(t) = t, 0 ≤ t < 1 2 − t, t ≥ 1
Answers
Answer:
The Laplace transform of f(t) is (3/s^2) e^(-s) - (2/s) + (1/s^2).
Step-by-step explanation:
We use the definition of the Laplace transform:
L{f(t)} = ∫[0,∞) e^(-st) f(t) dt
For f(t) = t, 0 ≤ t < 1, we have:
L{t} = ∫[0,1] e^(-st) t dt
Integrating by parts with u = t and dv = e^(-st) dt, we get:
L{t} = [-t*e^(-st)/s] from 0 to 1 + (1/s) ∫[0,1] e^(-st) dt
L{t} = [-e^(-s)/s + 1/s] + (1/s^2) [-e^(-s) + 1]
L{t} = (1/s^2) - (e^(-s)/s) - (1/s) + (1/s^2) e^(-s)
For f(t) = 2-t, t ≥ 1, we have:
L{2-t} = ∫[1,∞) e^(-st) (2-t) dt
L{2-t} = (2/s) ∫[1,∞) e^(-st) dt - ∫[1,∞) e^(-st) t dt
L{2-t} = (2/s^2) e^(-s) - [e^(-st)/s^2] from 1 to ∞ - (1/s) ∫[1,∞) e^(-st) dt
L{2-t} = (2/s^2) e^(-s) - [(e^(-s))/s^2] + (1/s^3) e^(-s)
Combining the two Laplace transforms, we get:
L{f(t)} = L{t} + L{2-t}
L{f(t)} = (1/s^2) - (e^(-s)/s) - (1/s) + (1/s^2) e^(-s) + (2/s^2) e^(-s) - [(e^(-s))/s^2] + (1/s^3) e^(-s)
L{f(t)} = (3/s^2) e^(-s) - (2/s) + (1/s^2)
Therefore, the Laplace transform of f(t) is (3/s^2) e^(-s) - (2/s) + (1/s^2).
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CenterWare is a manufacturer of large flower pots for urban settings. The company has these standards: Read the requirements Requirement 1. Compute the direct labor rate variance and the direct labor efficiency variance. (Enter the variances as positive numbers, Enter favorable (F) or unfavorable (U), Abbreviations used: DL = Direct labor) Begin with the direct labor rate variance. First determine the formula for the rate variance, then compute the rate variance for direct labor DL rate variance Х Standard Price and Volume Co hou flor Dir Dir Act ove Direct materials (resin). Direct labor..... Standard variable manufacturing overhead rate Budgeted fixed manufacturing overhead. Standard fixed MOH rate 10 pounds per pot at a cost of $5.00 per pound 2.0 hours at a cost of $21.00 per hour .$3.00 per direct labor hour $16.000 $10.00 per direct labor hour (DLH) Act Stal ove pro Print Done e i Actual Results - X Center Ware allocated fixed manufacturing overhead to production based on standard direct labor hours. Last month, the company reported the following actual results for the production of 1,000 flower pots: Purchased 11.400 pounds at a cost of $5.10 per pound; Direct materials... used 10,700 pounds to produce 1,000 pots Worked 2.5 hours per flower pot (2,500 total DLH) at a Direct labor cost of $18.00 per hour Actual variable manufacturing $3.40 per direct labor hour for total actual variable overhead manufacturing overhead of $8,500 Actual fixed manufacturing overhead $15.700 Standard fixed manufacturing overhead allocated based on actual production.. $20,000 1. Compute the direct labor rate variance and the direct labor efficiency variance. 2. What is the total variance for direct labor? 3. Who is generally responsible for each variance? 4. Interpret the variances.
Answers
CenterWare's direct labor rate variance is $2,100 unfavorable, indicating that the actual rate paid for labor was higher than the standard rate. The direct labor efficiency variance is $2,500 favorable, suggesting that the company achieved higher productivity than expected. The total variance for direct labor is $400 favorable.
To compute the direct labor rate variance, we need to calculate the difference between the actual rate and the standard rate, and then multiply it by the actual hours worked. The formula for the rate variance is (Actual Rate - Standard Rate) × Actual Hours. In this case, the standard rate is $21.00 per hour, and the actual rate is $18.00 per hour. The actual hours worked are 2,500 DLH. Plugging in these values, we find the direct labor rate variance to be ($18.00 - $21.00) × 2,500 = -$7,500, indicating an unfavourable variance.
To calculate the direct labor efficiency variance, we need to find the difference between the actual hours worked and the standard hours allowed, and then multiply it by the standard rate. The formula for the efficiency variance is (Actual Hours - Standard Hours) × Standard Rate. The standard hours allowed are 2,000 DLH (1,000 pots × 2.0 hours per pot). Substituting the values, we get (2,500 - 2,000) × $21.00 = $10,500, indicating a favorable variance.
The total variance for direct labor is the sum of the rate variance and the efficiency variance. In this case, the total variance is -$7,500 + $10,500 = $3,000, which is favorable, indicating that the company performed better than expected in terms of labor cost and efficiency.
The responsibility for the rate variance generally lies with the purchasing department, as they are responsible for negotiating labor rates and purchasing materials at the standard price. The efficiency variance is typically the responsibility of the production department, as they are accountable for achieving the standard labor hours and maximizing productivity.
The rate variance reflects the difference between the actual rate paid for labor and the standard rate. An unfavorable rate variance suggests that the company paid more for labor than anticipated, which could be due to factors like higher wages or inefficient labor management. Conversely, a favorable rate variance would indicate cost savings in labor.
The efficiency variance measures the productivity of labor and represents the difference between the actual hours worked and the standard hours allowed. A favorable efficiency variance implies that the company achieved higher productivity or used fewer labor hours than expected. It could result from factors such as skilled and efficient labor, improved production processes, or effective workforce management.
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To divide
by
, answer this question: How many sets of
are in
? Use the model representing the fraction
to help you answer the question. (Hint: Think about grouping the blue boxes into pairs.)
Answers
3) On a sphere of radius R, solve the spherical triangle with
sides:
c) piR/2, piR/2, piR/2
Answers
In a spherical triangle, the sum of the angles is always greater than 180 degrees, but in this case, the sum of the angles is 90 degrees. This is not possible for a spherical triangle on a sphere of radius R.
To solve the spherical triangle with sides of length piR/2, piR/2, and piR/2 on a sphere of radius R, we can use the law of cosines for spherical triangles.
The law of cosines for a spherical triangle states that:
cos(c) =
cos(a) * cos(b) + sin(a) * sin(b) * cos(C)
all three sides have the same length of piR/2, we can simplify the equation:
cos(piR/2) = cos(piR/2) * cos(piR/2) + sin(piR/2) * sin(piR/2) * cos(C)
Since cos(piR/2) = 0 and sin(piR/2) = 1, the equation becomes:
0 = 0 + 1 * 1 * cos(C)
0 = cos(C)
Therefore, the angle C is 90 degrees.
Therefore, there is no valid solution for a spherical triangle with sides of length piR/2, piR/2, and piR/2 on a sphere of radius R.
The law of cosines for spherical triangles helps us find the angles of a spherical triangle. Applying this law to a triangle with sides of length piR/2, piR/2, and piR/2, we find that one angle, C, is equal to 90 degrees.
However, in a spherical triangle, the sum of the angles should be greater than 180 degrees. In this case, the sum of the angles is only 90 degrees, which is not possible for a spherical triangle on a sphere of radius R. Therefore, there is no valid solution for this spherical triangle.
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Kono divides The numerator and the denominator of 4872 by the greatest common factor to simplify the fraction in one step by what number does he divide
Answers
Complete question:
Kono divides The numerator and the denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step by what number does he divide
Answer:
2/3
Step-by-step explanation:
Given the number : 48 / 72
Obtain the greatest common factor of 48 and 72
- - - - 48 - - - - 72
- 2-- 24 - - - - 36
- 2 - 12 - - - - - 18
- 2 - 6 - - - - - - 9
- 3 - 2 - - - - - - 3
The greatest common factor of 48 and 72 is hence (2 * 2 * 2 * 3) = 24
Hence, divide both the numerator and denominator by 24 ;
Numerator = 48/24 = 2
Denominator = 72 / 24 = 3
= 2/3
Find the truth set of each of these predicates where the domain is the set of integers. P ( x ): x3 ≥ 1. Q ( x ): x2 = 2. R ( x ): x < x2. Show all work.
Answers
The truth set of each predicate with the domain being the set of integers is
P(x): {x | x ≤ -1 or x ≥ 1}Q(x): ∅ (empty set)R(x): {x | x < 0 or x > 1}The truth set of a predicate is the set of all elements in the domain that make the predicate true.
For the given predicates, with the domain being the set of integers,
P(x): x^3 ≥ 1
The inequality x^3 ≥ 1 is satisfied for all x such that x ≥ 1 or x ≤ -1. This is because any integer raised to an odd power will always have the same sign as the integer itself, and the only integers whose cubes are less than 1 in absolute value are 0 and 1. Therefore, the truth set of P(x) is {x | x ≤ -1 or x ≥ 1}.
Q(x): x^2 = 2
There are no integers x such that x^2 = 2. Therefore, the truth set of Q(x) is the empty set, ∅.
R(x): x < x^2
The inequality x < x^2 is satisfied for all x such that x < 0 or x > 1. If 0 ≤ x ≤ 1, then x^2 ≤ x, and the inequality does not hold. Therefore, the truth set of R(x) is {x | x < 0 or x > 1}.
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where dose this number go on the number line?
Answers
Answer:
The number goes near -6
Step-by-step explanation:
Thenks and mark me brainliest :)
Answer: It's about -5.92 so close to negative -6
Step-by-step explanation:
Help me please thank you
Answers
what is the measure of an angle that turns through 1/5 of a circe
Answers
Solve the inequality below for g.
-10g + 4 < 9 - 159
A. IS
B. 5 > 1
C. g <1
D. § 2 - 3
Reset
Submit
Answers
Answer:
the answer to the inequality is C. g<1
HELP
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair.
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 15
Function 1 has the larger maximum at (4, 1).
Function 1 has the larger maximum at (1, 4).
Function 2 has the larger maximum at (−14, 1).
Function 2 has the larger maximum at (1, −14).
Answers
The correct statement regarding the maximum values of the quadratic functions is given as follows:
Function 1 has the larger maximum at (4, 1).
How to obtain the maximum values?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The x-coordinate of the vertex of a quadratic function is given as follows:
x = -b/2a.
Hence, for each function, the x-coordinate of the vertex is given as follows:
Function 1: x = -8/-2 = 4.Function 2: x = -2/-2 = 1.Each function has a negative leading coefficient, hence the vertex represents a maximum value, and the y-coordinate is given as follows:
Function 1: f(4) = -(4)² + 8(4) - 15 = 1.Function 2: f(1) = -(1)² + 2(1) - 15 = -14.1 > -14, hence the correct statement is given as follows:
Function 1 has the larger maximum at (4, 1).
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GIVING BRAINLEST The following is a chemical reaction.
Which side of the chemical Reaction is the REACTANTS,
and which side is the PRODUCTS?
Oxygen
Hydrogen
+
=
Water
2H + 0 = 24,0
AR
Both sides have reactants of the reaction
The left side is the Reactants and the right side is the products
Both sides have products of the reaction
K
The right side is the Products and the left side is the reactancts
Answers
The side that goes in a reaction is the reactant
The side that comes out of a reaction is the products
Brainliest?
Help me out ( I give out Brainliest)
Answers
Answer:
y = 4x -1
I think this is correct
Answer:
y=4x-1
Step-by-step explanation:
What we are doing here is isolating the y variable, and/or solving for y in terms of x. We add y to both sides then subtract 1 from both sides to get y=4x-1. Also, this problem is worded incorrectly and should be worded as 'solve for y in terms of x,' or 'isolate y.'
for the month of December Roger I took the bus 21 times in the morning and the same number of times in the afternoon how much did he pay in bus fare for the month
Answers
what expression is equivalent to 9^-4
Answers
Answer:
1/6561
Step-by-Step Explanation:
you get 1/6561 when you simplify 9^-4
consider the quadratic function y equals short dash x squared plus 6 x minus 5. what do we know about the graph of this quadratic equation, based on its formula?
Answers
Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.
Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.
First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.
Next, we can find the vertex using the formula:
Vertex = (-b/2a, f(-b/2a))
where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:
Vertex = (-b/2a, f(-b/2a))
= (-6/(2*-1), f(6/(2*-1)))
= (3, -14)
So the vertex of the parabola is at the point (3,-14).
Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.
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Answers
Answer:
x = 1
Step-by-step explanation:
given the figure has one pair of parallel sides and the legs are congruent, then
LMNO is an isosceles trapezoid,
the diagonals of an isosceles trapezoid are congruent , so
LN = MO , that is
7x = 2x + 5 ( subtract 2x from both sides )
5x = 5 ( divide both sides by 5 )
x = 1