The required one point and two non-parallel vectors are (0, -3, 0) and (1, 0, 0), (0, 0, 1).
What is Vectors?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
According to question:One point on the plane y=-3 is (0, -3, 0).
Two non-parallel vectors that are parallel to the plane y=-3 can be obtained by taking any two vectors whose y-coordinate is 0,
since any vector with a y-coordinate of 0 lies in the x-z plane, which is parallel to the y=-3 plane.
For example, the vectors (1, 0, 0) and (0, 0, 1) are non-parallel vectors that are parallel to the plane y=-3.
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I will give brainliest and ratings if you get this correct
Hence, [tex]-\frac{a}{\sqrt{ap-c} }[/tex] is the derivative of [tex]x=b-\sqrt{ap-c}[/tex].
What is derivative?Derivatives refers to the instantaneous rate of change of a quantity with respect to the other. That is, the amount by which a function is changing at one given point.
Given, [tex]x=b-\sqrt{ap-c}[/tex]
To find [tex]\frac{dx}{dp}[/tex]:
⇒[tex]\frac{dp(b-\sqrt{ap-c)}}{dx}[/tex]
⇒0- [tex]\frac{1}{2} (ap-c)^{-1/ 2} .\frac{d}{dp}(ap-c)[/tex]
⇒[tex]-\frac{ a.dp/dp+\frac{d}{dp}(-c) }{2\sqrt{ap-c} }[/tex]
⇒[tex]-\frac{a}{\sqrt{ap-c} }[/tex]
Hence, [tex]-\frac{a}{\sqrt{ap-c} }[/tex] is the derivative of [tex]x=b-\sqrt{ap-c}[/tex].
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The lines represented by the equations 9 � − 6 � = − 18 9y−6x=−18 and 3 � − 2 � = 24 3y−2x=24 are
The lines are parallel because they have the same slope in the equation of lines
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first equation be 9y - 6x = -18 be equation (1)
Let the second equation be 3y - 2x = 24 be equation (2)
On simplifying the equation , we get
Adding 6x on both sides of the equation , we get
9y = 6x - 18
Divide by 9 on both sides of the equation , we get
y = ( 2/3 )x - 2
So , the slope of line 1 is m = 2/3
And , for the second equation ,
Adding 6x on both sides of the equation , we get
3y = 2x + 24
Divide by 3 on both sides of the equation , we get
y = ( 2/3 )x + 8
So , the slope of line 2 is m = 2/3
Since the slopes of the lines are same , they are parallel lines
Hence , the equation of lines are solved
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The complete question is :
The lines represented by the equations 9y - 6x = -18 and 3y - 2x = 24 are
a) perpendicular
b) parallel
c) none of the above
Which is true about an equilateral triangle?
no sides have equal measure
one angle is obtuse
all angle measures are equal
only two sides have equal measure
Answer: all angles are equal
Step-by-step explanation:
in a equilateral triangle all angles will be 60°
A group of 6 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.
The designated cards are: Queen of Clubs, 10 of Hearts. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)
In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?
What is the probability of a successful hand that will go all the way till everyone gets 7 cards? (Round your answer to 4 decimal places.)
Recall, while using your calculator, that E10 means to move the decimal place 10 places to the righ
a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.
b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.
Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52
Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,
a) Number of cards are in the deck that are not one of the designated cards
= 52 - 2 = 50
Number of cards that need to be dealt in order for each player to have 7 cards
= 5× 7 = 35
Thus total possible number of ways
= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.
b) Number of cards are in the deck = 52
Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35
Thus total possible number of ways
= ⁵²C₃₅ = 21945588357420
Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards
= 2250829575120/21945588357420
= 0.10256410256
Hence, required probability is 0.1026.
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What is the y-intercept of the graph of y = 2.5*?
a. 2.5
b. 1
ΟΑ
О в
О с
OD
C. 0
d. -1
OT
Ü
Please select the best answer from the choices provided
Point of y-intercept is (0,1)
What is y-intercepts?In a graph, the point where the line or curve crosses the axis is called the intercept. If a point crosses the x-axis it is x-intercepts. If a point crosses y-axis it is y-intercepts.
Given the function is [tex]y=2.5^{x}[/tex]
y-intercept is the point where the graph of the function crosses the y-axis.
To find the point of y-intercept put x=0 in the given function, we get
if x=0 then [tex]y=2.5^{0}[/tex] ⇒ y=1.
The function crosses at the point 1 in the y-axis.
Hence, point of y-intercept is (0,1)
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What is D(50) − (D(15) ∪ D(20))?
The expression "D(50) - (D(15) ∪ D(20))" refers to the set difference between the set D(50) and the union of sets D(15) and D(20).
The set difference is the operation that gives you the elements that are in the first set (D(50)) but not in the second set (D(15) ∪ D(20)). Note that this prompt draws on Set Theory.
What is Set Theory?Set Theory is a branch of mathematics concerned with the study of sets, their properties, and their relationships.
In set theory, a set is a collection of distinct objects, and the set difference operation, represented by the minus sign (-), returns the elements that are in the first set but not in the second set.
The union of sets, represented by the symbol ∪, is the operation that gives you the set of all elements that are in at least one of the sets being considered.
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find the missing length, round to the nearest tenth if necessary
It is less than 21 so it has to be 19.4.
calculate the herfindahl-hirschman index for two scenarios. initially, there are four teams, and they compete for 10 years. team a wins 8 championships and team b wins 2. the other teams win none. now suppose there are eight teams. two teams win 4 championships, two win one each, and the others all win zero
The HHI is less than 1,800, which is considered a low level of market concentration. Therefore, we can conclude that both scenarios represent relatively competitive markets.
The Herfindahl-Hirschman Index (HHI) is a measure of market concentration that is commonly used to assess the degree of competition in a market. The index is calculated as the sum of the squared market shares of all the firms in the market. The HHI can range from 0 to 10,000, with higher values indicating greater market concentration.
To calculate the HHI for the two scenarios given, we need to first calculate the market shares of the teams in each scenario. In the first scenario, there are four teams with the following market shares:
Team A: 8/10 = 0.8
Team B: 2/10 = 0.2
Teams C and D: 0/10 = 0
The HHI for this scenario is calculated as:
HHI = [tex](0.8^2 + 0.2^2 + 0^2 + 0^2) \times10,000[/tex]
= 68,000
In the second scenario, there are eight teams with the following market shares:
Teams A and B: 4/10 = 0.4 each
Teams C and D: 1/10 = 0.1 each
Teams E, F, G, and H: 0/10 = 0 each
The HHI for this scenario is calculated as:
HHI = [tex](0.4^2 + 0.4^2 + 0.1^2 + 0.1^2 + 0^2 + 0^2 + 0^2 + 0^2) \times 10,000[/tex]
= 16,000
In both scenarios, the HHI is less than 1,800, which is considered a low level of market concentration. Therefore, we can conclude that both scenarios represent relatively competitive markets.
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Part III: Use the point given for line p and the slope you found in Part II to write an
equation for line p in point-slope form: Y-Y₁ = m(x-x₁). (1 point)
The slope of line q is equal to 3.
The slope of line q is equal to -1/3.
An equation for line p in point-slope form is y + 5 = -1/3(x - 6).
An equation for line p in slope-intercept form is y = -1/3x - 3.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c ....equation 1.
Where:
m represents the slope.x and y are the points.c represents the y-intercept or initial value.From the information provided, we have the following linear equation in slope-intercept form for line q:
y = 3x + 5 ....equation 2.
By comparing equation 1 and equation 2, we can logically deduce the following:
Slope (m) = 3
Since line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q;
m₁ × m₂ = -1
3 × m₂ = -1
Slope, m₂ of line p = -1/3.
At data point (6, -5), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-5) = -1/3(x - 6)
y + 5 = -1/3(x - 6)
By simplifying further, the slope-intercept form is given by;
y + 5 = -1/3(x - 6)
3y + 15 = -x + 6
3y = -x - 9
y = -1/3x - 3
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Complete Question:
Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.
Find the slope of line q.
Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)
Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)
Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b.
4 A shop sells large and small bags of rice. On Monday 57 large bags and 132 small bags were sold. a What percentage of the bags sold were large? b What percentage of the bags sold were small? On Tuesday 73 large bags and 81 small bags were sold. c What percentage of the bags sold on the two days combined was large?
Step-by-step explanation:
a. On Monday, the percentage of large bags sold was 57/(57 + 132) x 100 = 30.22%.
b. On Monday, the percentage of small bags sold was 132/(57 + 132) x 100 = 69.78%.
c. The total number of large and small bags sold on the two days combined was 130/(130 + 154) x 100 = 45.45%.
6. Write the unit rate for the following: a) Kate sews 100 dresses in a 20 day month. b) Kim runs 5 km in 30 minutes.
a) The unit rate of Kate's sewing productivity can be found by dividing the number of dresses by the number of days:
Kate sews 100 dresses in 20 days.
The unit rate is 100 dresses / 20 days = 5 dresses per day.
b) The unit rate of Kim's running speed can be found by dividing the distance by the time:
Kim runs 5 km in 30 minutes.
The unit rate is 5 km / 0.5 hour = 10 km/hour.
Therefore, the unit rate for Kate's sewing productivity is 5 dresses per day, and the unit rate for Kim's running speed is 10 km/hour.
-5 < 9 -6x???????????
Answer:
7/3>x
Step-by-step explanation:
-5<9-6x
subtract 9 from both sides
-14<-6x
divide by 6
14/6<x
simplified its 7/3<x
but since we divided by a negative we switch the sign
final answer is 7/3>x
PLEASE HELP FAST!!!! IT IS URGENT!!!! The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 30 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. Do the data provide convincing evidence at the level that the mean salary for the baseball players on the East Coast is different from $3.2 million? What hypotheses should the analyst use to conduct a significance test?
The hypothesis tested are given as follows:
[tex]H_0: \mu = 3.2, H_a: \mu \neq 3.2[/tex]
What are the null and alternative hypothesis?The claim for this problem is given as follows:
"The mean salary for the baseball players on the East Coast is different from $3.2 million".
At the null hypothesis, we test if the claim is false, that is, if the mean salary is equals to 3.2 million, hence:
[tex]H_0: \mu = 3.2[/tex]
At the alternative hypothesis, we test if the claim is true, that is, if the mean salary is different of 3.2 million, hence:
[tex]H_a: \mu \neq 3.2[/tex]
The [tex]\mu[/tex] symbol, without the bar, is used, as we are testing for the population mean, not sample mean, hence the first option is the correct option.
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Malcolm trains on his kayak every weekend. He paddles upstream (against current) for 3 ½ hours and then returns downstream (with current) in 2hrs 6 minutes. If the river flows at 3km/ h, find:
* The paddling speed in still water
* The distance he paddles upstream.
The probability she pulls out a purple piece of candy would be 0.22.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is Sam's fathers collection.
We can write the equations for upstream and downstream as -
x - y = 7/2
x + y = 21/10
Solving the equations graphically -
{x} = 2.8
{y} = 0.7
In still water, the speed would be -
S = 3 - 0.7
S = 2.3 Km/h
Distance peddled upstream -
D = 2.8 x 3.5 = 9.8 Km
Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.
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Use the expression (8x + 2) + (-9x + 7).
a. Find the sum.
b. Reasoning Explain how you know when to combine terms with variables.
Answer:
-x + 9
Step-by-step explanation:
Addition of expression:a)
8x + 2 + (-9x + 7) = 8x + 2 - 9x + 7
= 8x - 9x + 2 + 7
= -x + 9
b) We can combine like terms. Like terms have same variable with same power. Here 8x and (-9x) have same variable 'x'. so, combine the coefficients of the like terms which give (-1).
8x - 9x = -1
Combine the constants. 2 + 7= 9
For the following exercises, determine whether each of the following relations is a function_ 1.y =2x + 8 2. {(2, 1), (3,2), (-1,1), (0, -2)}
For the following exercises, evaluate the function f(x) = -3x2 + 2x at the given input: 3. f(-2) 4. f(a)
The value of the evaluated function f(x) = -3x² + 2x at
(i) f(-2) is -16 ;
(ii) f(a) is -3a² + 2a .
The Function is represented as : f(x) = -3x² + 2x ;
(i) We have to evaluate the above function at f(-2),
So, we substitute x = -2 into the function:
we get ;
⇒ f(-2) = -3(-2)² + 2(-2)
⇒ f(-2) = -12 - 4 = -16 .
So , f(-2) = -16 .
(ii) Next we have to evaluate f(a),
So , we substitute x = a into the function:
⇒ f(a) = -3a² + 2a
So , f(a) = -3a² + 2a .
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The given question is incomplete , the complete question is
For the following exercises, evaluate the function f(x) = -3x² + 2x ; at the given input: (i) f(-2) (ii) f(a) .
In the ratio of yellow marbles to blue marbles, 6:2, the quantities 6 and 2 are called?
The quantities 6 and 2 are called proportions
How to determine the name of the quantitiesFrom the question, we have the following parameters that can be used in our computation:
In the ratio of yellow marbles to blue marbles, 6:2,
This means that
Yellow : Blue = 6 : 2
Using the above as a guide, we have the following:
For every 6 yellow marbles, there are 2 blue marbles
This means that 6 and 2 are the proportions
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find the value of x. SIMPLEST RADICAL FORM
Answer:
Step-by-step explanation:
56
Suppose x is a normally distributed random variable with μ=10 and σ=2. Find each of the following probabilities.
a. P(x ≥ 12.5) b. P(x ≤ 9) c. P(10.88 ≤ x ≤ 15.3) d. P(4.72 ≤ x ≤ 12.46)
The value of the probabilities are
a. P(x ≥ 12.5) is 6.68%
b. P(x ≤ 9) is 2.28%
c. P(10.88 ≤ x ≤ 15.3) is 61.38%
d. P(4.72 ≤ x ≤ 12.46) is 99.45%
Probability is the measure of the likelihood of an event occurring. It is a way of quantifying uncertainty and predicting the likelihood of an outcome. In this question, we will use the normal distribution to calculate probabilities.
The mean is the center of the distribution, and the standard deviation measures the spread of the distribution.
a. P(x ≥ 12.5):
Using a standard normal distribution table, we find that the area to the right of 12.5 is 0.0668. This means that the probability of x being greater than or equal to 12.5 is 0.0668 or 6.68%.
b. P(x ≤ 9):
Using a standard normal distribution table, we find that the area to the left of 9 is 0.0228. This means that the probability of x being less than or equal to 9 is 0.0228 or 2.28%.
c. P(10.88 ≤ x ≤ 15.3):
Using a standard normal distribution table, we find that the area to the left of 15.3 is 0.9987 and the area to the left of 10.88 is 0.3849. Therefore, the area between 10.88 and 15.3 is
=> 0.9987 - 0.3849 = 0.6138.
This means that the probability of x being between 10.88 and 15.3 is 0.6138 or 61.38%.
d. P(4.72 ≤ x ≤ 12.46):
Using a standard normal distribution table, we find that the area to the left of 12.46 is 0.9946 and the area to the left of 4.72 is 0.0001. Therefore, the area between 4.72 and 12.46 is
=> 0.9946 - 0.0001 = 0.9945.
This the probability of x being between 4.72 and 12.46 is 0.9945 or 99.45%.
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What are the Variable, coefficients, and constant terms for 4x+15x, 6n+25+7n+4, 3a+4a+17+a+1 ?
In the expression, 4x+15x, variable: x; coeficient: 4, 15; constant: 0
In the expression 6n+25+7n+4, variable: n, coeficient: 6, 7; constant: 25, 4
In the expression 3a+4a+17+a+1, variable: a, coeficient: 3, 4, 1; constant: 17, 1
What are the parts of an algebraic expression?Generally, in an algebraic expression terms, variables, coefficients, and constants are seen. The parts of an expression that are added by either an addition or a subtraction notation are called the terms. The letter of a term is called a variable, the numerical value written along the variable of a term is called a coefficient, and the term contains only the numerical value called a constant.
Take the expression 4x+15x. The terms are 4x and 15x.
Clearly, the variables of the terms are x, the coefficients of the terms are 4 and 15, and the constant is 0. So, the required answers are obtained.
Take the expression 6n+25+7n+4. The terms are 6n, 25, 7n, and 4.
Clearly, the variables of the terms are n, the coefficients of the terms are 6 and 7, and the constants are 25 and 4. So, the required answers are obtained.
Take the expression 3a+4a+17+a+1. The terms are 3a, 4a, 17, a, and 1.
Clearly, the variables of the terms are a, the coefficients of the terms are 3, 4, and 1, and the constants are 17 and 1. So, the required answers are obtained.
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Which problem situation could be solved using the open sentence below?
24 - k = ?
A.Mrs. Garcia took 24 science papers home to grade. She graded k science papers before dinner. How many science papers did she have to grade after dinner?
B.Mrs. Garcia took 24 science papers and k reading papers home to grade. How many papers did she have to grade?
C.Mrs. Garcia had k science papers to grade. She now has 22 left to grade. How many papers did she grade already?
D. Mrs. Garcia has 22 science papers and 22 reading papers to grade. If she has k papers to grade in all, how many papers does she have to grade?
stuck on this question plsss helpp
Answer:
2 vases of lilacs
3 vases of irises
Step-by-step explanation:
7( lilacs ) × 2( vases) = 14 flowers
5( irises ) × 3( vases) = 15 flowers
14 + 15 = 29 flowers
-gress:
The movement of the progress bar may be uneven because questions can be worth more or less (including z
Multiply: 4.000329 × 1000
O 400.0329
O 4,000.329
O40.00329
O 4.329
The product of 4.000329 × 1000 is the second option 4,000.329.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have to find the product of 4.000329 × 1000.
When a number is being multiplied by (10)ⁿ, 'n' number of zeroes will be added to the right of the number.
If the number is decimal number, decimal point is being shifted n digits to the right.
The question here is 4.000329 × 1000.
4.000329 × 1000 = 4.000329 × (10)³
Decimal point is shifted three digits to the right.
4.000329 × (10)³ = 4,000.329
Hence the correct option is B. 4,000.329.
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Evaluate 4y ÷ x if x = 2 and y =5
This figure was created by using two semi-circles and one rectangle. Find the area of the figure in square inches.
The area of the figure is 596.625 in².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
We will consider the figure to have a rectangle and a circle.
Rectangle:
Length = 28 in
Breadth = 15 in
Area = 28 x 15 = 420 in²
Semicircle:
Diameter = 15 in
Radius = 7.5 in
Area = 1/2 πr²
= 1/2 x 3.14 x 7.5²
Area = 176.625/2
Area = 88.3125
There are two semicircles so,
= 2 x 88.3125
= 176.625 in²
Now,
Area of the figure.
= 420 + 176.625
= 596.625 in²
Thus,
596.625 in² is the area of the figure.
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A radio station broadcasts a signal over an area with a 45-mile radius. What is the area of the region that receives the radio signal to the nearest tenth?
Rounded to the nearest tenth, the area of the region that receives the radio signal is approximately 6,366.2 square miles.
What is the region's signed area?Consider a plane region described by a xy-plane graph. The signed area of the region is defined as the area of the graph on or above the x-axis. The negative area of the graph is defined as the area below the x-axis.
The formula A = πr² gives the area of a circle with radius r. In this case, the radio station broadcasts over a 45-mile radius, so the region that receives the radio signal is:
A = π(45)²
A ≈ 6,366.2 square miles
The area of the region that receives the radio signal is approximately 6,366.2 square miles when rounded to the nearest tenth.
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suppose [tex]\frac{x^{2} }{25} +\frac{y^{2} }{64} =1[/tex] and y(3)=6.40000. find y^(derivative sign) (3) by implicit differentiation.
Answer:
To find y'(3), we need to use implicit differentiation to differentiate both sides of the equation with respect to x and then solve for y'.
Differentiating both sides with respect to x, we get:
(2x/25) + (2y/64) * (dy/dx) = 0
Now we can solve for dy/dx:
(2y/64) * (dy/dx) = -(2x/25)
dy/dx = -(2x/25) / (2y/64)
dy/dx = -32x/25y
To find y'(3), we need to substitute x=3 and y=6.4 into the expression for dy/dx:
y'(3) = -32(3)/(25)(6.4)
y'(3) = -0.3
Therefore, the value of y'(3) is -0.3
The value of y'(3) in (2x/25) + (2y/64) = 1, is - 0.3
What is implicit differentiation?Finding the derivative of an implicit function is the process of implicit differentiation.
In other words, this method is utilized to discover the implicit derivative.
To find y'(3), After differentiating both sides of the equation with respect to x using implicit differentiation, we must next solve for y'.
Differentiating both sides with respect to x we get,
(2x/25) + (2y/64)×(dy/dx) = 0
Solving for dy/dx
(2y/64)×(dy/dx) = -(2x/25)
dy/dx = -(2x/25) / (2y/64)
dy/dx = -32x/25y
To find y'(3), Replacing x=3 and y=6.4 into the expression for dy/dx:
y'(3) = -32(3)/(25)(6.4)
y'(3) = -0.3
Therefore, the value of y'(3) is - 0.3
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1) A system of equations is shown. What is the solution to the system of equations? Show all work. (3 points) 2 + 2 = 17 {4 − = 25
The value of x for the system of equations will be x=6.7.
What is a system of equations?
A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.
Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.
Multiply the second equation by 2 and subtract from the first equation,
2x+2y=17.
8x-2y=50.
10x=67.
x= 67/10
x = 6.7.
Therefore, the value of x for the system of equations will be x=6.7.
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Sandpiper Company has 25,000 shares of cumulative preferred 2% stock, $150 par and 50,000 shares of $15 par common stock. The following amounts were
distributed as dividends:
20Y1
2012
2013
$150,000
30,000
225,000
Determine the dividends per share for preferred and common stock for each year. Round all answers to two decimal places. If an answer is zero, enter "0".
Preferred Stock
(dividends per share)
2011
2012
2013
Feedback
X
Common Stock
(dividends per share)
Check My Work
X
Check My Work
Determine what amount of current dividends that preferred stock should receive per year.
< ✰ ✰ O
Keep in mind that the question is asking for a dividend per share for each year and class of stock, rather than the total amount to be distributed to
each class of stock.
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a) The determination of the dividends per share for the cumulative preferred and common stock for each year is as follows:
Preferred StockDividends per share
2011 $3.00
2012 $1.20
2013 $4.80
Common StockDividends per share
2011 $1.50
2012 $0
2013 $2.10
b) The determination of the amount of current dividends that preferred stock should receive per year is $75,000.
What is cumulative preferred stock?Cumulative preferred stock is a special class of preferred stock that enjoys cumulative dividends.
Cumulative dividends imply that any year when sufficient dividends are not declared, the arrears are carried forward to subsequent years.
It is the opposite of non-cumulative preferred stock.
On the other hand, the common stockholders can only receive dividends after the preferred stockholders have been paid, including their cumulative dividends.
Cumulative Preferred Stock:Number of shares = 25,000
Dividend rate = 2%
Par value = $150
Total cumulative preferred stock = $3,750,000 (25,000 x $150)
Annual dividend = $75,000 ($3,750,000 x 2%)
Common Stock:Number of shares = 50,000
Par value = $15
Total common stock = $750,000 (50,000 x $15)
Preferred StockDividends Due (Dividends per share)
2011 $75,000 $3 ($75,000/25,000)
2012 $30,000 $1.2 ($30,000/25,000)
2013 $120,000 $4.8 ($120,000/25,000)
Common StockDividends Available (Dividends per share)
2011 $75,000 ($150,000 - $75,000) $1.50 ($75,000/50,000)
2012 $0 ($30,000 - $30,000) $0
2013 $105,000 ($225,000 - 120,000) $2.10 ($105,000/50,000)
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C
Flagpole a and flagpole c are both casting a shadow that ends at point s.
The distance (x) between the flagpoles is 12 ft.
The distance (y) from flagpole c to point s is 10 ft.
The height of flagpole a is 13.2 ft.
What is the height of flagpole c?
Show all your work.
The height of flagpole c is given as follows:
66 ft.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.For each flagpole, the parameters are given as follow:
Flagpole a: Distance of 12 - 10 = 2 ft, height of 13.2 ft.Flagpole c: Distance of 10 ft, height of h ft.The triangles are similar, hence the proportional relationship to obtain the height of flagpole's c is given as follows:
2/10 = 13.2/h
Applying cross multiplication, the height is obtained as follows:
2h = 10 x 13.2.
h = 132/2
h = 66 ft.
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