Answer:
k = -3x
Step-by-step explanation:
To find the slope, use rise over run
I started from (0, 0)
To get to the next whole number point, you must go up (rise) 3 and go back (run) 1
Since we are going back, the slope is negative.
The rise over run is -3/1 which simplifies to -3
To find y-intercept, we look at the point when x = 0. When x = 0, y = 0 so the y-intercept is 0 (which means you don't have to include it into the equation
y = -3x or k if that's what you use
Best answer gets brainliest and 5 stars
Answer:
B
Step-by-step explanation:
5^2+12^2=25+144=169=13^2 which will form a right angle triangle
Consider the wave packet: ψ(x)=[ 2πa 2
1
] 1/2
exp[− 4a 2
(x−⟨x⟩) 2
+i ℏ
px
]. Calculate the uncertainties ⟨Δx 2
⟩=⟨( x
^
−⟨x⟩) 2
⟩ and ⟨Δp 2
⟩=⟨( p
^
−⟨p⟩) 2
⟩, where ⟨ A
^
⟩ denotes the expectation value ⟨ψ∣ A
^
∣ψ⟩ of the observable A
^
on the state ∣ψ>.
The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.
The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.
To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.
Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
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A box has the shape of a rectangular prism with height 30 cm. If the height is increased by 0.9 cm, by how much does the surface area of the box increase?
Find the perimeter. Simplify your answer.
Answer:
20v-6
Step-by-step explanation:
To find the perimeter we have to add up all of our sides
9v-6+9v-6+2v+6
Combine light terms
20v-6
Rectangular Coontinates Directions: Coasader the three points A−(−2,1) and B−(2,3), and C−(3,1). 1) Plot each point and form the triangle ABC 2) Verify that the triangle is a right triangle. Chapter 1.2 - Grephis of Faquations Directions: Show algobraically that the grapit below is symmetry to the x and y - axis and the origin. 3) y=x2−9−x3 Chapter 1.3 - Lincar Equations in Two Variahles 4) find an equation of the line passing through the pair of points. Sietch the line. (4,3) and (−4,−4)
1) The points A(-2,1), B(2,3), and C(3,1) form a triangle ABC when plotted on a coordinate plane.
2) To verify if the triangle is a right triangle, we can check if the square of the length of one side is equal to the sum of the squares of the other two sides.
3) The graph of the equation y = x^2 - 9 - x^3 exhibits symmetry with respect to the x-axis, y-axis, and the origin.
4) To find the equation of the line passing through the points (4,3) and (-4,-4), we can use the formula for the slope-intercept form of a linear equation.
1) Plotting the points A(-2,1), B(2,3), and C(3,1) on a coordinate plane will form a triangle ABC with these vertices.
2) To verify if the triangle is a right triangle, we can calculate the slopes of the sides AB, BC, and AC. If the product of any two slopes is -1, then the triangle is a right triangle. Alternatively, we can also check if the square of the length of one side is equal to the sum of the squares of the other two sides using the Pythagorean theorem.
3) The equation y = x^2 - 9 - x^3 represents a curve on a graph. By observing the equation, we can see that it is symmetric with respect to the x-axis, y-axis, and the origin. This means that if we reflect the graph across any of these axes or the origin, we obtain an identical graph.
4) To find the equation of the line passing through the points (4,3) and (-4,-4), we can use the formula for the slope-intercept form of a linear equation: y = mx + b. First, we can find the slope (m) using the formula (change in y)/(change in x). Then, substituting one of the points into the equation, we can solve for the y-intercept (b). Finally, we can write the equation of the line in the form y = mx + b.
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PLEASE HELP EMERGENCY have a great day
Answer:
d) 55°Step-by-step explanation:
CABD is half-circle as CD is diameter and cuts the circle in half
CABD = CA + AB + BD180° = x + 70° + x110° = 2x x = 110°/2x = 55°Correct choice is d)
What are the differences in km, km square, and square km?.
Answer:
km square is the area and square km is the same as km square
PLLLZZZZ I NEED HELP WITH THIS!
Answer:
8
Step-by-step explanation:
now, just draw a pic and it will make sense
PLS HELP ITS URGENT!!
Answer:
d) 10t +12;$52
Step-by-step explanation:
what would be the value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 6.89? a. 19.32 b. 15.32 c. 18.43 d. 31.89
The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 31.89
What is regression?Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).
The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).
Linear regression determines the actual linear relationship between two variables based on a line of best fit. As a result, the slope of a straight line was used to depict linear regression indicating how altering one variable impacts modifying another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.
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Classify each pair of events as dependent or independent.
You select a number 1 through 6 by tossing a standard number cube. You select a second number by tossing the number cube again.
The pair of events, selecting a number 1 through 6 by tossing a standard number cube, and selecting a second number by tossing the number cube again, can be classified as independent events.
In probability theory, two events are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the occurrence of the other event. In this case, the outcome of the first toss has no influence on the outcome of the second toss.
Let's consider the sample space for each event:
Event A: Selecting a number 1 through 6 on the first toss of the number cube.
Event B: Selecting a number on the second toss of the number cube.
For Event A, the sample space is {1, 2, 3, 4, 5, 6}, as there are six possible outcomes.
For Event B, the sample space is also {1, 2, 3, 4, 5, 6}, as the outcome of the first toss does not affect the possible outcomes of the second toss.
Since the sample space for both events is the same, and the outcome of the first toss does not impact the outcome of the second toss, the pair of events can be classified as independent events.
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What is 9,150,000,000,000,000,000 expressed in scientific notation?9.15 × 10189.15E189.15E-189.15E-199.15 × 10199.15E199.15 × 10-199.15 × 10-18
To express a number in cientific notation (often refered to as scientific form), we take the first digit and then put a decimal right after it. Next we take a count of all other numbers after the first digit and that would determine the value of the index (exponent).
In this case, we hould have 9, followed by a decimal, and then followed by 18 numbers. Note that any number aside zero would be written down after the first digit. Any zero would be disregarded.
Hence;
\(\begin{gathered} 9,150,000,000,000,000,000 \\ In\text{ scientific notation becomes;} \\ 9.15\times10^{18} \end{gathered}\)find the values of x for which the series converges. (enter your answer using interval notation.) [infinity]
∑ (x − 3)^n / 2n n = 0
Values of x for which the series converges are in the interval (1, 5).
A more detailed explanation of the answer.To find the values of x for which the series converges, we will use the Ratio Test. The series is given by:
∑ (x − 3)ⁿ / 2n, n = 0 to ∞
1. First, let's find the ratio of the (n+1)th term to the nth term:
((x - 3)ⁿ⁺¹ / 2ⁿ⁺¹) / ((x - 3)ⁿ / 2ⁿ) = (x - 3)ⁿ⁺¹ * 2ⁿ / (2ⁿ⁺¹ * (x - 3)ⁿ)
2. Simplify the ratio:
((x - 3)ⁿ⁺¹ / (x - 3)ⁿ) * (2ⁿ / 2ⁿ⁺¹) = (x - 3) * (1/2)
3. Apply the Ratio Test, the series converges if the absolute value of the ratio is less than 1:
| (x - 3) * (1/2) | < 1
4. Isolate x:
-2 < x - 3 < 2
5. Add 3 to all parts of the inequality:
1 < x < 5
Series converging values are in the interval (1, 5).
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What is a random variable? Choose the correct answer below. O A. A variable is random when it has an uncountable number of possible outcomes. O B. A variable is random when it has a finite or countable number of possible outcomes that can be listed. O C. The outcome of a probability experiment is often a category or label. When this occurs, the outcome is called a random variable. O D. The outcome of a probability experiment is often a count or a measure. When this occurs, the outcome is called a random variable.
A random variable is a numerical quantity resulting from a probability experiment. It assigns a numerical value to each possible outcome of the experiment. The correct answer is D.
The outcome of a probability experiment is often a count or a measure. When this occurs, the outcome is called a random variable.
Random variables can be classified into two types: discrete and continuous.
Discrete random variables have finite or countable outcomes, while continuous random variables have uncountable outcomes, making it essential to consider the probability density function to determine the probabilities associated with various intervals.
Hence,the answer of the question is D.
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ACTIVITY (EXPERIMENTAL PROBABILITY) 50 trials
The dice i roll: 2, 3, 4, 4, 4, 4, 6, 5, 2, 4, 2
What is the probability of rolling a sum of even number?
What is the probability of rolling a sum of odd number?
What is the probability of rolling a sum of greater than 5?
This is for statistics ok? Ty!U,,w,,U
The probability of rolling a sum greater than 5 is 13/18.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
a) The probability of rolling a sum of even number
Number of favorable outcomes = 9
Total number of outcomes = 36
Now, probability = 9/36
= 1/4
b) The probability of rolling a sum of odd numbers
Number of favorable outcomes = 9
Total number of outcomes = 36
Now, probability = 9/36
= 1/4
c) The probability of rolling a sum of greater than 5
Number of favorable outcomes = 26
Total number of outcomes = 36
Now, probability = 26/36
= 13/18
Therefore, the probability of rolling a sum greater than 5 is 13/18.
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NEED HELP can some explain how to do this THANKS :D
Using translation concepts, the translation rule is given by:
(x,y) -> (x + 13, y + 7).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Comparing v with v', and w with with w', we get that:
The x-coordinates differ by 13.The y-coordinates differ by 7.Hence the translation rule is given by:
(x,y) -> (x + 13, y + 7).
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Which option below demonstrates the correct notation for a continuous set of all numbers between 5 and 6, not including 5, but including 6?
Answer:
The set is (5, 6]
Step-by-step explanation:
Ok, let's see the different possibles notations to describe sets.
If we want to describe a discrete set, we use {}
Like in the set:
{1, 2, 3}
That set only contains the numbers 1, 2, and 3.
If we want to describe a continuous set that does not include the extremes, we use ()
For example:
(1, 3)
Contains all the numbers between 1 and 3, but does not include 1 and 3.
If we want to include the extremes, we need to use []
[1, 3]
This set is all the numbers between 1 and 3, including the values 1 and 3.
And we can mix these last two notations, so if we want a set that includes all the numbers between 5 and 6, not including 5 but including 6, we need to write:
(5, 6]
If anyone can help me with this problem!! I would greatly appreciate it.
AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.
What is triangle?
A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.
Since we have:
∠A ≅ ∠Y
∠B ≅ ∠X
∠C ≅ ∠Z
We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.
Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:
AB : YX = BC : XZ = AC : YZ
where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.
In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.
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Round 1.983 to the nearest hundredth
Answer:
1.98
Step-by-step explanation:
Find the number in the hundredth place 8 and look one place to the right for the rounding digit 3. Round up if this number is greater than or equal to 5 and round down if it is less than 5.
Cleveland, OH, where the maximum and minimum temperatures were 70
∘
F and 58
∘
F respectively, experienced a mean temperature of
∘
F (round up if necessary). a. 58 b. 60 c. 64 d. 66 11. The mean temperature derived from the maximum and minimum temperatures at Cleveland indicates degree days were accumulated. a. heating (HDD) b. cooling (CDD) 12. Therefore, Cleveland accumulated degree day(s) on 6-7 September 2022. a. 0 b. 1 c. 3 d. 7 13. Based on the plotted temperatures across the rest of Ohio, remaining stations HDD on 6-7 September 2022. a. accumulated b. did not accumulate You can observe and calculate HDD or CDD as we progress into the fall and through the winter. Wind Chill HDD and CDD values and their effect on homeowners' utility bills may stress tight budgets through the seasons. Since energy bills are dependent on the human who uses the energy, another factor for homeowners to consider when budgeting energy consumption is wind chill. The wind chill is an air temperature index that takes into account heat loss from exposed skin caused by the combined effect of wind and low air temperature. Outdoors, the cooling effect of wind along with the ambient temperature is reflected by using the wind chill equivalent temperature. Go to NWS Daily Weather Map for the most recent map. The pane to the left allows you to select any date back to 1 January 2003. Each day's map series includes the surface map, colorcoded maps of maximum and minimum temperatures, mid-tropospheric flow at the 500−mb level, and total precipitation. The surface and 500−mb maps are for 12Z(8a.m. EDT or 7a.m. EST, etc.) while the temperatures and precipitation maps are for the entire day. Clicking on the maps opens a more detailed map. Bring up the daily weather map set for 23 January 2022 . Scroll down and click on either the Maximum or Minimum Temperature map. 14. For 23 January 2022, on the North Dakota-Minnesota border, Fargo had a minimum temperature of −25
∘
F. With the minimum temperature there, assume Fargo was experiencing a wind speed of 10mph. With the NWS Wind Chill Chart in Figure 4A-5 from Investigation 4A, the wind chill for this combination of temperature and wind speed would have been
∘
F. a. −16 b. −20 c. −35 d. −41 e. −47
The mean temperature in Cleveland, OH, was 64°F. The accumulated degree days for Cleveland on 6-7 September 2022 were 1. The rest of Ohio accumulated degree days during the same period.
Based on the given information, the maximum temperature in Cleveland was 70°F and the minimum temperature was 58°F. To find the mean temperature, we add the maximum and minimum temperatures and divide by 2: (70°F + 58°F) / 2 = 128°F / 2 = 64°F.
Degree days are a measure of heating or cooling requirements. In this case, since the mean temperature in Cleveland was lower than a certain base temperature, degree days were accumulated. The base temperature is typically set at 65°F for cooling and 55°F for heating. Since the mean temperature in Cleveland was below the base temperature, the accumulated degree days are heating degree days (HDD).
For the specific date of 6-7 September 2022, Cleveland accumulated 1 heating degree day (HDD). This means that the average temperature for that period was 1 degree below the base temperature of 55°F.
The remaining stations in Ohio also accumulated heating degree days (HDD) on 6-7 September 2022. This indicates that the temperatures across the rest of Ohio were below the base temperature during that period.
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(5/2) (×) = 1 ×=? 2/5 4/10 5/2 10/4 5 2
Answer:
3.1666667
Step-by-step explanation:
The answer is 3.1666667
Stacy uses 4 cups of milk to make a batch of rice pudding. How many batches of rice pudding
can she make with 3 gallons of milk?
Hint: There are 16 cups in 1 gallon.
Answer:
12
Step-by-step explanation:
There are
16 cups = 1 gallon
3 gallons = 48 cups
48 divided by 4 = 12 batches of rice pudding
Answer
12
Step-by-step explanation:
4 cup of milk = 1 batch of rice pudding
1 gallon of milk= 16 cups of milk
3 gallon of milk = 3x 16
=48 answer
then, 48 cup of milk = 48 ÷ 4
= 12 answer
Hence, stacy can make 12 batch of pudding with 3 gallon of milk.
Unit: Module 1. Ratios and unit rates Ratio tables Hanna is recovering hundreds of treasure chests from an ancient shipwreck. She is able to recover 8 chests every 4 hours Complete the table using equivalent ratios. Treasure chests Hours 1 6 Stuck? Watch a video or use a hint.
She can cover 8 chests every 4 hours
The ratio is
\(\frac{8}{4}\)We need to find how many chests she can cover in 6 hours
We will use the equivalent ratio to solve it
\(\frac{8}{4}=\frac{x}{6}\)Where x is the number of chests
Use the cross multiplication
\(\begin{gathered} 4\times x=8\times6 \\ 4x=48 \end{gathered}\)Divide
1. four of the interior angels of a hexagon measure 92, 100, 94, and 140 degrees the remaining two angles each measure (x-32) degrees. what is the value of x
2. given right triangle abc with right angle b and cos(3x+30) = sin (12x) if angle a is (3x+10) what is the value of angle a
1. The value of x is 179.
2. The value of angle A is 22 degrees.
1. In a hexagon, the sum of all interior angles is equal to 720 degrees. We are given the measurements of four interior angles: 92, 100, 94, and 140 degrees. Let's calculate the sum of these four angles:
Sum of the four given angles = 92 + 100 + 94 + 140 = 426 degrees
To find the remaining two angles, we subtract the sum of the four given angles from the sum of all interior angles:
Sum of remaining two angles = 720 - 426 = 294 degrees
Since the two remaining angles are equal in measure, we divide the sum by 2 to find the measure of each angle:
Measure of each remaining angle = 294 / 2 = 147 degrees
We are given that each remaining angle measures (x - 32) degrees, so we can set up the equation:
x - 32 = 147
Solving for x:
x = 147 + 32 = 179
Therefore, the value of x is 179.
2. In right triangle ABC, we are given that cos(3x + 30) = sin(12x), and angle A is represented as (3x + 10). We need to find the value of angle A.
Since cosine is equal to the sine of the complementary angle, we can write:
cos(3x + 30) = cos(90 - 12x)
By comparing the angles inside the parentheses, we set up the equation:
3x + 30 = 90 - 12x
Solving for x:
15x = 60
x = 4
Now that we have the value of x, we can find the measure of angle A:
Angle A = 3x + 10 = 3(4) + 10 = 22
Therefore, the value of angle A is 22 degrees.
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Frankie says that it
costs $12.50 to make a
wreath.
The table below shows the cost to
make a wreath. How much does it
Sost to make one wreath?
3
5
WREATH, w
COST, a
7
$87.50
9
$112.50
$37.50
$62.50
Fiona says that it costs
$13.50 to make a
wreath.
Answer:
Frainkie is correct it takes $12.50
Step-by-step explanation:
37.50 divided by 3 to find out one wreath's cost which is 12.50
hope this helps
plz mark me brainliest.
Suppose we estimate the following regression: yt = β1 + β2x2t +
β3x3t + ut. Suppose the variance of ut is related to a known
variable zt as follows: Var(ut) = σ^2(zt). How would you transform
the
To transform the regression equation, you would divide both sides of the equation by the square root of Var(ut), which is σ√(zt). This transformation helps in obtaining the transformed regression coefficients and standard errors that account for the heteroscedasticity in the error term.
When the variance of the error term (ut) is related to a known variable (zt), it implies the presence of heteroscedasticity in the regression model. Heteroscedasticity means that the variability of the error term is not constant across different levels of the independent variables.
To address this issue, we can transform the regression equation by dividing both sides by the square root of the variance of the error term, which is σ√(zt). This transformation is known as the weighted least squares (WLS) estimation.
By dividing both sides of the equation, we can obtain the transformed regression equation with the error term divided by its standard deviation. This transformation accounts for the heteroscedasticity by giving different weights to the observations based on the variability of the error term. It allows for a more appropriate estimation of the regression coefficients and standard errors, as it gives more weight to observations with smaller error variances and less weight to observations with larger error variances.
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Antonio gets £6 a week for his allowance. He saved 1/2 of it last week and 1/3 of it this week. How much money does he save in those 2 weeks?
Answer:
Antonio a économisé un total de 5 £ pendant ces deux semaines.
Step-by-step explanation:
La semaine dernière, Antonio a économisé la moitié de son allocation, soit:
1/2 * 6 £ = 3 £
Cette semaine, il a économisé un tiers de son allocation, soit:
1/3 * 6 £ = 2 £
Le montant total d'argent économisé pendant ces deux semaines est la somme des économies des deux semaines :
3 £ + 2 £ = 5 £
Ainsi, Antonio a économisé un total de 5 £ pendant ces deux semaines.
Answer:
Antonio saved £5 in two weeks.
Step-by-step explanation:
First week: 6(1/2) = 6/2 = 3
Second Week: 6(1/3) = 6/3 = 2
3 + 2 = £5
Hope this helps.
what kind of transformation converts the graph of f(x)=-|x|+1 imto the graph of g(x)=-8|x|+8
The transformation is a vertical stretch
How to determine the type of transformation?From the question, we have
f(x) = -|x| + 1
g(x) = -8|x| + 8
The transformation from the graph of f(x) = -|x| + 1 to the graph of g(x) = -8|x| + 8 is a vertical stretching by a factor of 8.
The transformation results in the graph of g(x) being 8 times taller than the graph of f(x).
Mathmatically, this is
g(x) = 8f(x)
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How do you graph a rational function example?
To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).
Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.
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EMERGENCY HELP PLS: The state decided that the angle a wheelchair ramp
makes with the ground should be no more than 4.3º.
a) What is the maximum height of a 25-foot ramp? Round to the nearest tenth of a foot.
b) What distance along the ground would this ramp
cover? Round to the nearest tenth of a foot.
Maximum height = ? ft.
Distance along the ground ? ft.
Answer:
1.9 feets (nearest tenth) ;
24.9 feets
Step-by-step explanation:
Given that :
Angle, θ = 4.3°
Length of ramp = 25
Maximum Height, h ;
sinθ = opposite / hypotenus
Sin 4.3 = h / 25
0.0749787 * 25 = h
1.874 feet = h
1.9 feets (nearest tenth)
Distance along the ground the ramp could cover :
Cos θ = Adjacent / hypotenus
Cos 4.3 = x / 25
0.9971851 = x / 25
0.9971851 * 25 = x
x = 24.929
x = 24.9 (nearest tenth)