The parametric vector represents a line, whose slope and intercept are 12 and - 35, respectively.
How to analyze and interpret parametric functions
Parametric functions are multi-dimensional functions in terms of a variable t that is a real number. In this problem we find a parametric function with coordinates, that is, a vector of the form (x, y) = (f(t), g(x)) and we are supossed to determine the rectangular form of such function, that is, a function of the form:
y = f(x)
The rectangular form of the function is a line if and only if the resulting expression is of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableFirst, write the components of the parametric functions:
x = 2 · t + 3
y = 24 · t + 1
Second, clear variable t in each parametric expression:
t = (x - 3) / 2
t = (y - 1) / 24
Third, eliminate parameter t by transitive property:
(x - 3) / 2 = (y - 1) / 24
Fourth, obtain the equation of the line:
24 · (x - 3) = 2 · (y - 1)
24 · x - 72 = 2 · y - 2
24 · x - 70 = 2 · y
y = 12 · x - 35
Fifth, determine the slope and intercept of the equation of the line:
m = 12, b = - 35
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A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism. 1-2 in. 5 in. T 2 in. T 3 in. I -2 in. 2 in. t 3 in. What is the surface area, in square inches, of the container?
A 19
B 30
C 38
D 62
The surface area of the container is 62 square inches.
The correct option is D.
What is prism?In three-dimensional space,
a prism is a polyhedron where two ends are similar.
Given:
A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism.
We have H = 2 inches
L = 5 inches
W = 3 inches
Surface area of the rectangular prism,
A = 2(W×L + H×L + H×W)
A = 2(3×5+2×5+2×3)
A = 2(15+10+6)
A = 2(31)
A = 62 square inches
Therefore, the surface area is 62 square inches.
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If a shipment has at least 5% defective light bulbs, it will be replaced. If a sample of 60 light bulbs has 2 that are which statement is true? defective,
A The shipment will be replaced.
B The shipment will not be replaced.
C The shipment has 12 defective light bulbs.
D The shipment has 30 defective light bulbs.
The sample has 3.33% of defective bulbs so, B. The shipment will not be replaced.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, If a shipment has at least 5% defective light bulbs, it will be replaced.
Now, A sample of 60 light bulbs has 2 that are defective.
Therefore, The percentage of defective bulbs is,
= (2/60)×100%.
= (1/30)×100%.
= 3.33%, So, the shipment will not be replaced.
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should you give any discount to people who order two dozen cookies? if every customer orders 2 dozen, will your capacity increase? if yes, you may want to offer discount to encourage customers to order 2 dozen. you may assume the company operates 24/7 here.
Yes, it is possible to offer a discount to customers who order two dozen cookies.
What is Discount ?
The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
1 dozen=12 pieces
Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to consider the cost of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.
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Yes, it is possible to offer a discount to customers who order two dozen cookies.
What is Discount ?
The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
1 dozen=12 pieces
Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to cocost nsider the of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.
So ,Yes it is possible to offer a discount to customers who order two dozen cookies.
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5. THOUGHT PROVOKING
To find the arithmetic mean of n numbers, divide
the sum of the numbers by n. To find the geometric
mean of n numbers a₁, a₂, a3,..., an, take the nth
root of the product of the numbers.
geometric mean =
a₁a₂ a3 •...• An
Compare the arithmetic mean to the geometric
mean of n numbers.
Arithmetic mean deals will middle number while geometric mean deals with typical value
How to compare the different types of meansFrom the question, we have
Arithmetic mean and Geometric mean
The arithmetic mean is the sum of a set of numbers divided by the number of items in the set, and is often used to find the "middle" value of a dataset.
On the other hand, the geometric mean is the nth root of the product of a set of numbers and is often used to find the "typical" value of a dataset when dealing with quantities that can increase or decrease exponentially.
The above definitions imply that the difference between the arithmetic mean and geometric mean can be significant when dealing with sets of numbers that have large variations in values.
In general, the geometric mean will be less than or equal to the arithmetic mean.
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what’s the geometric mean of 6 and 1/2
Answer:
1.7320508075689
there exists an intewger that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers
there exists an integer that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers ∃x∈ℤ: x > 5 ∧ x² < 40
1. Start by writing down the equation: x² < 40
2. Take the square root of both sides of the equation to isolate the variable x: √x² < √40
3. Simplify both sides of the equation: x < √40
4. Check that the result makes sense: x < 6.3
5. Take the integer part of the result: x < 6
6. Since the requirement is that x is greater than 5, the answer is x = 6.
We start by writing the equation x² < 40 and then take the square root of both sides to get x < √40. We check that the result is reasonable and then take the integer part of the result to get x < 6. Since the requirement is that x is greater than 5, the answer is x = 6. To confirm, we can calculate that x² = 36 which is smaller than 40, and indeed, 6 is greater than 5. Therefore, the integer that is greater than 5 and whose square is smaller than 40 is 6. This can be expressed mathematically as ∃x∈ℤ: x > 5 ∧ x² < 40 which translates to: There exists an integer x such that x is greater than 5 and the square of x is smaller than 40.
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Find the equation of the line with slope = 7 and passing through (2,19)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{19}=\stackrel{m}{ 7}(x-\stackrel{x_1}{2}) \\\\\\ y-19=7x-14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]
A diet is being prepared for WTAMU dorms. The varied diet is to be made of three foods: A, B and C. Food A costs $2.25 per pound and contains 500 calories. Food B costs $ 2 per pound and contains 700 calories. Food C costs $ 3 per pound and contains 600 calories No more than 0.75 pounds of food C can be used per resident. No less than 2 pounds of food B should be used per resident. The objective is to feed the students at the least cost, but the diet must have at least 1800 calories.
If we define the decision variables as A: pounds of food A, B: pounds of food B, and C pounds of food C, the object function is to minimize Blank 1. In addition to non-negative constraints, other constraints are Blank 2,Blank 3, and Blank 4.
(1. No need to use multiplication sign. For example, just write 10A not 10*A. For greater(less) than sign, just write it as >= (<=).
2. Also please leave no space in equation. For example, write A<=100, not A <= 100.
3. Please write decimal number for example as 0.32 not .32 when applicable. )
This problem is designed to minimize the cost of feeding students in the dorms while providing a minimum of 1800 calories. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost and adding them together. The constraints of the problem are that A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75.
1. 2.25A + 2B + 3C
2. A >= 0
3. B >= 2
4. C <= 0.75
The objective of this problem is to minimize the cost of feeding students in the dorms, while the diet must contain a minimum of 1800 calories. To achieve this, three decision variables were defined: A, B, and C, which represent the pounds of food A, B, and C respectively. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost, and adding them together. There are three constraints in the problem: A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75. These constraints ensure that the diet contains the desired amount of each food and that the total calories meet the minimum requirements.
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G(-3,-2). What would be the reflection point G
The reflection of point G across the x-axis would be at (-3, 2).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The coordinates of point G in the question are (-3,-2)
When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate is changed.
Therefore, the reflection of point G, which is located at (-3, -2), across the x-axis would be at (-3, 2).
The x-coordinate is the same, but the y-coordinate has changed from negative to positive.
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The question seems incomplete, the completed question would be as:
The coordinates of point G are (-3,-2)
What would be the reflection point G across the x-axis?
At the start of a trip, you fill up your car's fuel tank with gas. After you drive for x hours, the amount y (in gallons) of gas remaining is given by the equation y = 18 - 2x.
a. Find the x-intercept and the y-intercept of the given equation's
graph. Use the intercepts to graph the equation.
b. Interpret What real-life quantities do the x- and y-intercepts
represent in this situation?
c. After how many hours of driving do you have only tank of gas left?
Use the intercepts to graph the equation y = 18-2x
What is meant by graph ?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.A graph that has any two vertices connected by a path is said to be connected. Any two vertices or nodes in a disconnected graph are those that are separated by a path.Graph that completes a cycle is called a cycle graph. Complete Graph: A graph is said to be complete when every pair of vertices is connected by an edge.A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges. The edges in the graph connect any two nodes, and the nodes themselves are also known as vertices.Interpret What real-life quantities do the x- and y-intercepts
represent in this situation:
when x = 0, y = 18, when y = 0 x = 9
The x intercept is 9, y intercept is 18.
After 9 hours the gas is run not .
The amount of gas in a car when it is not running
18 × 1/4 = 4.5
4.5 = 18-2x
x= 6.75 hours
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Several college students conduct a survey at their local community college. They find that 67% of the students live with their parents in the house they grew up in. Of the students who live with their parents 23% live within walking distance to campus. Of the students who do not live with their parents only
6% live within walking distance to campus. a) What is the probability of a student living within walking distance to campus? ( 1 point) b) What is the probability given a student lives within walking distance to campus they live with their parents? (1 point) c) Are living with parents and living within walking distance independent events? (2 points)
a) The probability of a student living within walking distance of campus is 0.1521.
To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:
P(A and B) = P(A) * P(B|A).
For this situation, An is "living within walking distance to campus" and B is "living with parents."
Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.
Hence, the probability of a student living within walking distance of campus is 0.1521.
b) The probability given a student living within walking distance of campus they experience with their parents is 0.67.
To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:
P(A|B) = P(A and B)/P(B).
In this situation, A is "living with parents" and B is "living within walking distance to campus."
Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.
Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.
c) Living with parents and living within walking distance are independent events.
To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).
On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.
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49, 34, and 48 students are selected from the sophomore, junior, and senior classes with 496, 348, and 481 students respectively.
The sampling used in this situation is Stratified sampling
In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.
We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.
This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.
Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes.
This is, therefore, a stratified sampling.
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Q: 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?
Can someone help me please
Answer: 3 + y = 24
Step-by-step explanation: Hello!
If she rode 3 miles one day and y miles the other 6 days of the week, and in total that adds up to 24 miles, that means the equation should be addition.
3 miles + y miles = 24 miles
Monday, other 6 days, total seven days
The equation should be:
3 + y = 24
Analyze the diagram below and complete the instructions that follow.
C
A
B
Given that
A. 10
B. 10.5
C. 11
D. 11.5
6
CB
CA
DE
DF'
find BA.
D
4
E
7
F
Save and Exit
Next
Submit
Analyze the diagram of the trapezoid gives BA = 10.5 units
How to find the side BA of the trapezoid the analyzing the diagram?A trapezoid (also known as a trapezium) is a four-sided geometric shape that has two parallel sides (the bases) and two non-parallel sides (the legs). The bases of a trapezoid can have different lengths, but the legs must be congruent and parallel to each other.
Let's analyze the diagram below and complete the instructions:
Since CB / CA = DE / DF
where CB = 6, DE = 4, EF = 7
We can say:
DF = DE + EF = 4 + 7 = 11
CA = CB + BA = 6 + BA
CB / CA = DE / DF
6/(6 + BA) = 4/11
6 × 11 = 4(6 + BA)
66 = 24 + 4BA
24 + 4BA = 66
4BA = 66 - 24
4BA = 42
BA = 42/4
BA = 10.5 units
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a bicycle has wheels 32 inches in diameter. a tachometer determines the weheels are rotating at 150 rpm(revolutions per minute). Find the speed the bicycle is traveling down the road.
The speed of the bicycle is 381 meters per minutes
we know that,
revolutions per minute = speed in meters per minute / circumference in meters.
Diameter = 32 inches
Circumference of the wheel = 2πr
r = Diameter/2 = 32/2 = 16
Circumference = 2 × π × 16
= 100.5714 inches
Approximately = 100 inches
we know that,
1 inch = 0.0254 meter
100 inches = x
x = 100 × 0.0254 meters
x = 2.54 meters
Hence:
Revolutions per minute = Speed in meters per minute / circumference in meters.
Speed = Revolutions per minute × circumference in meters.
Speed = 150 RPM × 2.54 meters
Speed = 381 meters per minutes
so, the speed of the bicycle is 381 meters per minutes.
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Mike is buying dinner for his family. He buys 5 lemonades that each cost $1.50, and 5 hamburgers that each cost $8.25. If
the prices include tax, and he also leaves a $6 tip, how much does he spend in all? Write equations to show your work.
Write an equation for the cost of the lemonades. Select the correct choice below, and fill in the answer box to complete
your choice.
(Do not include the $ symbol in your answer.)
OA. 5x1.50 +6=
ETTE
OB. 1.50+5=
OC. 5x1.50 =
OD. 1.50+5+6=
The linear equation for the cost of lemonades is 1.50*x+6 where x=5 i.e. A and he spends $54.75 in total.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Cost of lemonade=$1.5, number of lemonades=5
Cost of hamburger=$8.25, number of hamburgers=5
Tip=$6
Hence,
Total cost=5*1.5+5*8.25+6
Total cost =$54.75
Cost of lemonades only = 5*1.5+6
In type of linear equation 1.50*x+6 where x=5
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1 The equation, A = P(1 + 0.037t), represents the amount of money earned on a savings account with 3.7% annual simple interest. If the amount after 5 years is equal to $1,422, what is the amount of the principal investment? $1,200 $1,422 $274.25 $294.86
The amount of the principal investment is, $1200. So option A is correct
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
A = P(1 + RT)
Given that,
A = $1422
R = 3.7%
T = 5 year
P = ?
After 5 year total amount
1422 = P ( 1 + 0.037 × 5)
P = 1422/( 1 + 0.037 × 5)
= 1422/1.185
P = 1200
Hence, the principal amount is $1200
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help on 4 and 6 please!!
The measures of the angles are Z = 146 degrees, X and W = 34 degrees and B = 119 degrees
How to determine the measure of the anglesQuestion 4
From the question, we have
<Y = 146 degrees
Because the lines XY and WZ are equal, it means that
<Z = 146
So, we have
X = W = (180 - 146)
Evaluate
X = W = 34
Question 6
Here, we have
Sum of the angles = 180 degrees
This gives
9x + 2 + 5x - 4 = 180
Evaluate the like terms
14x = 182
Divide by 14
x = 13
So, we have
B = 9 * 13 + 2
B = 119 degrees
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Find the image of A(4, 2) after the following transformations
a. (1,4) ∘ (−) (4, 2)
b. (−) ∘ (1,4) (4, 2)
HELP PLEASE
∠FGK and ∠KGH form a linear pair. Find m∠KGH.
Applying the linear pair definition, m<KGH = 60°.
What is a Linear Pair?In geometry, a linear pair is a pair of adjacent angles that are supplementary, meaning that their measures add up to 180 degrees. The two angles must be adjacent, meaning that they share a common side or vertex, and they must be linear, meaning that they are formed by two intersecting lines.
Therefore:
m<FGK + m<KGH = 180
Substitute
120 + m<KGH = 180
m<KGH = 180 - 120
m<KGH = 60°
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Find an angle whose supplement is 30 degrees greater than 4 times the supplement.
Explanation needed
The angle whose supplement is 30 degrees greater than 4 times the supplement is 30°
What are supplementary angles?Two angles are called supplementary when their measures add up to 180 degrees.
For example:- 120° and 60°, 110° and 70°, 140° and 40°, 90° and 90°, 20° and 160°, 135° and 45° are some example of supplementary angles.
Given that, an angle whose supplement is 30 degrees greater than 4 times the supplement.
Let the angle asked be x,
Therefore, the supplement of x, will be = 180°-x
According to the question, Its supplement is 30 degrees greater than 4 times the supplement.
Therefore, establishing the equation,
So, for solving for x, we have,
180°-x = 30°+4x
4x+x = 180°- 30°
5x = 150°
5x/5 = 150°/5
x = 30°
As, we considered the angle asked be x,
Hence, the angle whose supplement is 30 degrees greater than 4 times the supplement is 30°
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What is the value of 3h(2) + 4g(1)
The value of 3h(2) + 4g(1) is 39
How to evaluate a given mathematical expression with variables if values of the variables are known?You can simply replace those variables in function with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.
Given;
h(x)= 3x x<2
= 4x+1 x>2
g(x)= x^2+2 x<3
= x^3 x>3
Now, substituting the values;
3h(2)= 3*(4*2+1)
=3*9
=27
4g(1)= 4(1^2 + 2)
=4(3)
=12
3h(2)+4g(1)=27+12
=39
Therefore, the answer of the function will be 39
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25. There were 13 gummies in a packet. Mrs. Sooklal bought a few packets of gummies. After giving 3 sweets to each of her 27 students, she has 10 gummies remaining, how many packets of gummies did she purchase?
5x - y = -5
3x - 6y = 24
Solve using substitution
Answer:
x = -2
y = -5
Step-by-step explanation:
5x - y = -5
3x - 6y = 24
First, multiply the first equation by -6
-30x + 6y = 30
3x - 6y = 24
-27x = 54
x = -2
Now, put in -2 for x and solve for y
5(-2) - y = -5
-10 - y = -5
-y = 5
y = -5
Let's Check
5(-2) -(-5) = -5
-10 + 5 = -5
-5 = -5
So, x = -2 y = -5 is the correct answer.
shatter cones are key features that uniquely characterize impact structures (i.e., their presence provides evidence that an impact occurred). shatter cone surfaces exhibit a texture with a series of intersecting ridges that produce its conical geometry. based on the labeled version below, what is the general direction in which the shatter cone ridges converge (or point)? choose one: a. s b. e c. w d. n
As per the cone surface, the general direction in which the shatter cone ridges converge is south.
The term cone in math is defined as a three-dimensional shape in geometry that narrows smoothly from a flat base to a point called the apex or vertex.
Here we have given that Shatter cones are key features that uniquely characterize impact structures
In this one their presence provides evidence that an impact occurred. Here we also know that the Shatter cone surfaces exhibit a texture with a series of intersecting ridges that produce its conical geometry.
Based on the definition of cone surface we have identified that the the correct option is (a) that is the south.
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The circle graph shows the results of a national survey on the most popular afternoon activities of seventh graders. What percent of those students surveyed said that their favorite afternoon activity is playing video games?
Answer:
it is easy to add all the numbers up then you will get 77 then tell me how many number should you add to get to 100 it is easy trust me
Step-by-step explanation:
1.) Leila wants to sell her homemade candles at the Linwood Street Craft Fair. She decides to
sell her candles for $12 apiece. The materials for one candle cost Leila $2. If she also pays
$40 to rent the booth for the day, how many candles must Leila sell to cover all of her
expenses? How much will her sales and expenses be at that point?
The total cost of materials for one candle is $2 and she pays $40 for the booth for the day.
Therefore, the total cost for making and selling one candle is $2 + $12 + $40 = $54
To cover all her expenses, Leila must sell enough candles to make $54 from each candle.
She must sell 54/$12 = 4.5 candles
Therefore, Leila needs to sell at least 5 candles to cover all her expenses.
At that point, her sales and expenses will be 5 candles x $12/candle = $60
Therefore, Leila's sales and expenses will be $60 at that point.
use the definition of continuity and limits to find values of the constants a and b so that the piece-wise cubic function
The constants a and b can be found by ensuring the function is continuous and that the limits at each point match. This can be done by setting the values of a and b so that the function and its derivative are equal at each point.
To find the constants a and b for the given piece-wise cubic function, we must consider the definition of continuity and limits. Firstly, for the function to be continuous, the function and its derivative must be equal at each point. Thus, we need to set the values of a and b so that the function and its derivative are equal at the points x=1, x=2 and x=3. We can use this to create a system of equations to solve for a and b. Once we have determined the values of a and b, we can then check that the limits at each point match. This can be done by computing the left and right hand limits at each point, and ensuring they are equal. If the limits are equal, then the function is continuous and the constants a and b are correct.
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Find the value of x PLEASE I NEED HELPP :(
Answer: [tex]2\sqrt{13}-\sqrt{697}[/tex]
Step-by-step explanation:
Since ABD is a right triangle, 14^2 = 12^2 + BD^2
196 = 144 + BD^2
52 = BD^2
BD = [tex]\sqrt{52} = 2\sqrt{13}[/tex]
ADC is also a right triangle, so 29^2 = 12^2 + DC^2
841 = 144 + DC^2
DC^2 = 697
DC = [tex]\sqrt{697}[/tex]
Since x = BD + DC,
x = [tex]2\sqrt{13} +\sqrt{697}[/tex] :>
inspect a sketch of typical solution curves to determine the points for which the initial value problem has a unique solution.
We have to find solutions for the given differential equation when
y = 0, y = 1/(k-x) and y(a) = b using ordinary differential equations.
We have dy / dx = y^2
a. let's define the given y = 1/(k-x)
derive the above equation with respect to x :
dy / dx = y' = 1/(k-x)^2
So this is the general solution.
b) We would want a singular solution that is not included in the general form. Here we could use y = 0
dy / dx = 0 = 0^2
so,this is a trivial singular solution.
c) If we have y(a) = b,
then, y = 1(k-a) = b
To find the value of k we use the other condition: y'(^2) = 4 x y(2)
1/(k-a)^2 = 4 x 1/(k-a)
k - 2 = 1/4
therefore, k = 9/4
hence we got, y = 1/(9/4 - a) = b
So the points (a, b) are of the form: (a, 1/(9/4 - a))
Learn more about differential equations here :
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The complete question is :
Find a general solution of the differential equation dy/dx=y2
b. Find a singular solution that is not included in the general solution.
c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b