f(x) = 5 sin(x) + 5 cos(x), 0 ≤ x ≤ 2π (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answers
f(x) is increasing on the interval [3π/4, 7π/4] and decreasing on the intervals [0, 3π/4) and (7π/4, 2π]. The local minimum value of f(x) is -5√2 and the local maximum value of f(x) is 5√2. The inflection points are (π/4, 0) and (5π/4, 0). f(x) is concave up on the intervals [3π/4, π) and (7π/4, 2π) and concave down on the intervals (0, 3π/4) and (π, 7π/4).
(a) To find the intervals on which f(x) is increasing and decreasing, we need to find the derivative of f(x) and determine where it is positive and negative:
f(x) = 5 sin(x) + 5 cos(x)
f'(x) = 5 cos(x) - 5 sin(x)
Setting f'(x) equal to zero, we get:
5 cos(x) - 5 sin(x) = 0
cos(x) = sin(x)
tan(x) = 1
x = π/4, 5π/4
These are the critical points of f(x). Now, we can use the first derivative test to determine the intervals on which f(x) is increasing and decreasing:
For x in [0, π/4), f'(x) is negative, so f(x) is decreasing.
For x in (π/4, 5π/4), f'(x) is positive, so f(x) is increasing.
For x in (5π/4, 2π], f'(x) is negative, so f(x) is decreasing.
Therefore, f(x) is increasing on the interval (π/4, 5π/4), and decreasing on the intervals [0, π/4) and (5π/4, 2π].
(b) To find the local minimum and maximum values of f(x), we need to examine the critical points and the endpoints of the interval [0, 2π]:
f(0) = 5 sin(0) + 5 cos(0) = 5
f(π/4) = 5 sin(π/4) + 5 cos(π/4) = 5√2
f(5π/4) = 5 sin(5π/4) + 5 cos(5π/4) = -5√2
f(2π) = 5 sin(2π) + 5 cos(2π) = 5
Therefore, the local minimum value of f(x) is -5√2 at x = 5π/4, and the local maximum value of f(x) is 5√2 at x = π/4.
(c) To find the inflection points of f(x), we need to find the second derivative of f(x) and determine where it changes sign:
f(x) = 5 sin(x) + 5 cos(x)
f''(x) = -5 sin(x) - 5 cos(x)
Setting f''(x) equal to zero, we get:
-5 sin(x) - 5 cos(x) = 0
sin(x) + cos(x) = 0
tan(x) = -1
x = 3π/4, 7π/4
These are the inflection points of f(x). Now, we can use the second derivative test to determine the intervals on which f(x) is concave up and concave down:
For x in [0, 3π/4), f''(x) is negative, so f(x) is concave down.
For x in (3π/4, π), f''(x) is positive, so f(x) is concave up.
For x in (π, 7π/4), f''(x) is negative, so f(x) is concave down.
For x in (7π/4, 2π], f''(x) is positive, so f(x) is concave up.
Therefore, f(x) is concave up on the intervals (3π/4, π) and (7π/4, 2π) and concave down on the intervals (0, 3π/4) and (π, 7π/4).
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Related Questions
we want to find a 95% confidence interval for the standard deviation of a large dataset, given a sample. can the bootstrap method be used? group of answer choices
Answers
The Bootstrap Method is straightforward and straightforward to comprehend. First, it chooses randomly from the original sample to produce bootstrap samples from our initial sample.
After that, it uses summary statistics like variation, standard deviation, mean, and so on to get replicates, which is how we can calculate a confidence interval from that sample.
Thus, the answer is "Yes."
The bootstrap method is a resampling method that uses replacement sampling to estimate population statistics. It can be used to estimate standard deviation and mean summaries.
Which scenarios call for the use of bootstrapping?Remember that bootstrapping isn't only valuable for computing standard blunders, it can likewise be utilized to build certainty spans and perform speculation testing. When working with data that doesn't seem to lend itself to conventional methods, always remember bootstrapping techniques.
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Full Question = We want to find a 95% confidence interval for the standard deviation of a large dataset, given a sample.
Can the bootstrap method be used?
Group of answer choices
yes
no
Recall that convex functions satisfy ƒ(0x1₁ + (1 − 0)x2) ≤ 0 ƒ (x1) + (1 − 0) ƒ (x₂) for any [0, 1] and any x₁, x2 in the domain of f. (a) Suppose f(x) is a convex function with x E Rn. Prove that all local minima are global minima. I.e., if there is a point xo such that f(x) ≥ f(xo) for all x in a neighbourhood of xo, then f(x) ≥ ƒ(x) for all x € R". (b) Draw a graph of a (non-convex) function for which the statement in part (a) is not true, and indicate why on the graph.
Answers
(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.
(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.
(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.
(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.
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I need help with those 2 the rest I know. I just don’t know what that means.
Answers
Answer:
What are the problems?
Step-by-step explanation:
AVALIAÇÃO DIAGNÓSTICA
Resolva os problemas abaixo
1) O quilo do feijão que custava R$ 3,90 teve um aumento de 70% Oual é o novo preço do quilo do
feijão?
2) O aluguel de uma casa teve um reajuste e passou de R$ 500,00 para R$ 925,00. Qual foi o percentual
de aumento do aluguel dessa casa
Answers
Answer:
hhhsyeuru isuegrjro ehgeurov didyrhy
jeremy owns 4 pairs of pants, 3 shirts, 3 ties, and 2 jackets. how many different outfits can he wear to school if he must wear one of each item?
Answers
The average Jeremy can create 24 different outfits for school by combining 1 pair of pants, 1 shirt, 1 tie, and 1 jacket.
Jeremy can mix and match his items to create different outfits for school. Since he owns 4 pairs of pants, 3 shirts, 3 ties, and 2 jackets, he can create 24 different outfit combinations. For each outfit, he must wear 1 pair of pants, 1 shirt, 1 tie, and 1 jacket. He can mix and match any of the items he owns to create a variety of looks. For example, he could wear a blue shirt, grey pants, and a striped tie with a black jacket. Or, he could wear a white shirt, black pants, a polka-dotted tie, and a brown jacket. By combining his items in different ways, he can create 24 different outfits for school.
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express 6160 as a product of their prime factor
Answers
→ The process of finding the Prime Factors of 6160 is called Prime Factorization of 6160.
→ To get the Prime Factors of 6160, you divide 6160 by the smallest prime number .
→ Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with..;-
• Prime Factorization process creates what we call the Prime Factor Tree of 6160:... see the above attachment ↑ ...• All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 6160... See here:
6160 ÷ 2 = 30803080 ÷ 2 = 15401540 ÷ 2 = 770770 ÷ 2 = 385385 ÷ 5 = 7777 ÷ 7 = 1111 ÷ 11 = 1All the prime numbers you used to divide above are the Prime Factors of 6160. Thus, the Prime Factors of 6160 are:
2, 2, 2, 2, 5, 7, 11.Hope this helps you :) ...
#Carry on learning# :)...
What is the value of f(3)=15[(2*15)+5)
Answers
Answer:
f(3) = 525
Step-by-step explanation:
f(3) = 15[(2*15)+5)
f(3) = 15[30+5)
f(3) = 15[35)
f(3) = 525
Find the sum of (8.6 x 106) and (3.7 x 105). Write the final answer in scientific notation.
8.97 x 105
8.97 x 106
1.23 x 1010
12.3 x 1011
Answers
Answer:
8.97 x \(10^{6}\)
Step-by-step explanation:
To add in scientific notation, the exponents need to be the same for the bases of 10. You can either make them both to the exponent of 6 or 5. It does not matter. I made them both to the power of 5
(8.6 x \(10^{6}\)) + (3.7 x \(10^{5}\))
(86 x \(10^{5}\)) + (3.7x\(10^{5}\))
(86 x 3.7) x \(10^{5}\)
89.7 x\(10^{5}\) Rewrite in scientific notation
8.97 x \(10^{6}\)
a measurable part of a line that consists of two points, called endpoints, and all of the points between them are
Answers
A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.
Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.
\( \bar{AB}\)
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solve this by elimination method
a+2b=5
3a-b=1
(plz show the whole process)
Answers
Answer:
a=1 b=2
Step-by-step explanation:
a+2b=5
3a-b=1
Multiply the second equation by 2
6a-2b=2
Add the two equations together
a+2b=5
6a-2b=2
-------------------
7a = 7
Divide by 7
7a/7 = 7/7
a=1
Now find b
3a-b =1
3(1) -b =1
3-b=1
Subtract 3 from each side
3-b-3=1-3
-b = -2
Multiply by -1
b=2
Answer:
please mark me brainliest
Step-by-step explanation:
a+2b=5...equ 1
3a-b=1...equ 2
3a+6b=15...equ 3
3a-b=1...equ 4
elimination method
3a has been cancelled
so 6b+b=7b
15-1=14
7b=14
b=14/7
b=2
substitute 2 for b in equ 2
3a-b=1
3a-2=1
3a=1+2
3a=3
a=3/3
a=1
a=1,b=2
Work out the size of angle x
Answers
Answer:
angle X will be 180-47=133---------------------------------------------
Your answer would be 133.
The blueprint for Zahra's new office measures 4 cm
long and 2 cm wide. The scale for the blueprint is 6 cm to 15 ft.
1.1 What is the length and width of her actual office?
Answers
Using proportions, it is found that:
The length of her actual office is of 10 ft.The width of her actual office is of 5 ft.-----------------------
Scale problems are solved using proportions, by a rule of three.The scale is of 6 cm to 15 ft, which means that each 6 cm in the drawing represents 15 ft of real dimensions.In the drawing, the length is of 4 cm, thus:
4 cm - x ft
6 cm - 15 ft
Applying cross multiplication:
\(6x = 60\)
\(x = \frac{60}{6}\)
\(x = 10\)
The length of her actual office is of 10 ft.
The width is of 2 cm, thus:
2 cm - x ft
6 cm - 15 ft
Applying cross multiplication:
\(6x = 30\)
\(x = \frac{30}{6}\)
\(x = 5\)
The width of her actual office is of 5 ft.
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At the candy shop, Ameenah sells chocolate covered raisins, c, for $1.50 per pound, and peanuts, p, for $1.20 per pound. Ameenah wants to make 20 pounds of a mixture of raisins and peanuts that sells for $1.35 a pound. How many pounds of each should she use?
Thanks! :)
Answers
Answer:
10 pounds of raisins and 10 pounds of peanuts.
Step-by-step explanation:
Let c represent the pounds of chocolate covered raisins.
Let p represent the pounds of peanuts.
We know that the raisins cost $1.50 per pound and the peanuts cost $1.20 per pound.
Ameenah wants to make 20 pounds of a mixture of the raisins and peanuts that sells for 1.35 a pound. So, we can write the following expression:
\(1.5c+1.2p\)
This represents the cost given c pounds of raisins and p pounds of peanuts.
Ameenah wants to combine c and p to make them 1.35 per pound. In other words, the expression must equal:
\(1.5c+1.2p=1.35(c+p)\)
We also know that she wants to make 20 pounds. So, c plus p must total 20. Therefore:
\(c+p=20\)
We now have the system of equations:
\(\left\{ \begin{array}{ll} 1.5c+1.2p=1.35(c+p) \\ c+p=20\end{array}\)
First, since we know that c+p is 20, we can substitute that into the first equation.
Second, let's subtract p from both side for the second equation to isolate a variable. So:
\(c=20-p\)
Let's now substitute this into the first equation:
\(1.5(20-p)+1.2p=1.35(20)\)
Distribute:
\(30-1.5p+1.2p=27\)
Combine like terms:
\(-0.3p+30=27\)
Subtract 30 from both sides:
\(-0.3p=-3\)
Divide both sides by -0.3. So, the amount of peanuts needed is:
\(p=10\)
10 pounds of peanuts is needed.
This means that 20-10 or 10 pounds of raisins is needed.
Answer:
10 pounds of both raisins and peanuts.
Step-by-step explanation:
25.4,340/26= what is the answer to this
Answers
Answer:
0.978230769231
Step-by-step explanation:
Step 1:
25.4340 ÷ 26 = 0.978230769231
Answer:
0.978230769231
Hope This Helps :)
HELP ME A square pyramid is shown:
A square pyramid is shown. The sides of the square base are labeled 0.6 foot. The height of one of the triangular sides is labeled 7 feet.
What is the surface area of the pyramid? (1 point)
a
2.46 square feet
b
8.76 square feet
c
5.16 square feet
d
1.56 square feet
Answers
Answer:
B. 8.76 square feet------------------------
Each triangle face has height of 7 ft and base of 0.6 ft and the base of the pyramid is the square with side of 0.6 ft.
Total surface area includes a square base and four triangular faces and the measure of it is:
S = 0.6² + 4*(1/2)*0.6*7 = 0.36 + 8.4 = 8.76 ft²The matching choice is B.
A process flowchart uses which of the following symbols to represent a decision point in a flow diagram? A. Rectangle B. Arrow C. Inverted triangle. D. Diamond
Answers
Decision points
are represented in the flowchart using a diamond symbol. Answer: D. Diamond.
A
flowchart
is a kind of diagram that is used to represent an algorithm, workflow, or process. A flowchart comprises different shapes, which represent distinct steps or activities in a procedure. Flowcharts are used in different fields, such as education,
engineering
, programming, and business, to demonstrate decision making, problem-solving, process control, and project management.
Flowcharts are used to:
Visualize
processes and workflows that need to be organized or improved
Communicate a sequence of steps that are essential to complete a project
Identify the root cause of a problem
Illustrate the steps of a procedure to new employees or staff members
A decision point in a flowchart is a point where the sequence of flowchart changes its direction based on the
outcomes
of the preceding steps. Decision points are represented in the flowchart using a diamond symbol.
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A group of friends were working on a student film. They spent $546 on props, which was 39% of their total budget. What was the total budget for their student film?
Answers
Answer:
Step-by-step explanation:
Spent=$546
Budget=100%
=39/100*546
Alejandra is packing a bag for a flight. The airline has a baggage weight limit, and Alejandra has already packed her bag with some essentials. All she has left is her outfits and shoes, which must weigh less than 30 pounds total.
If Alejandra estimates that one outfit welghs two pounds and one pair of shoes weighs three pounds, which graph represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit?
Answers
there are no pictures of a graph BUT i can give you the intercepts.
x=2
y=12
OR
x=4
y=8
OR (sorry i cant see the graph options its one of the three)
x=8
y=3
its a solid line
x are the shoes
y are the outfits
The region below the line 2x + 3y = 30 is considered and the graph is drawn.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Alejandra is preparing her suitcase for takeoff. Alejandra has already stuffed her luggage with the necessities because the airline has a weight restriction on checked bags. She only has her clothes and shoes remaining, which together must weigh no more than 30 pounds.
If Alejandra determines that one pair of shoes weighs three pounds and one dress weighs two pounds.
Let 'x' be the number of outfits and 'y' be the number of shoes. Then the inequality is formulated as,
2x + 3y < 30
The region below the line 2x + 3y = 30 is considered and the graph is drawn.
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The Toucan has a long, narrow beak that allows it to reach fruit that is hard to reach for other birds.
Plants, like the Monstera Plant, in HELP IM ON A TIME LIMIT!!!!
the rainforest have long, grooved leaves to drop water to the forest
floor. The excessive water that falls in the rainforest could lead to mold, so the leaves adapted to
have “drip tips” that allow the water to run off of the leaves.
What type of adaptations are these? Compare and contrast the adaptations of the Toucan and
Monstera Plants of the rainforest. Your answer should be 3–4 sentences long.
Answers
Answer:
They have large leaves with holes in them that the Toucan can use to reach the fruit inside. The Toucan's beak is also used to break open hard-shelled fruits, such as coconuts. The Toucan's beak is also used for defence against predators, as it can be used to peck and jab at them. The adaptations of the rainforest plants are examples of convergent evolution. Both the Toucan and Monstera Plants have adapted to their environment in order to survive. The Toucan has a large beak that helps it to reach fruit in the canopy, while the Monstera Plant has long, grooved leaves with drip tips that allow water to run off and prevent mould. Both adaptations are beneficial for the survival of the species in the rainforest.
Step-by-step explanation:
What is the answer to 2937682+28373938
Answers
Answer: 31311620
Step-by-step explanation: Calculator
Find 20 rational numbers between -3/7 and 2/3
Answers
The 20 rational numbers between -3/7 and 2/3 are: -0.42857, -0.14286, 0.14286, 0.42857, 0.71429, -0.28571, -0.07143, 0.07143, 0.28571, 0.57143, -0.61538, -0.38462, -0.15385, 0.15385, 0.38462, 0.61538, -0.5, -0.25, 0.25, 0.5.
Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not equal to zero. In other words, any number that can be written in the form of a fraction a/b, where a and b are integers and b is not equal to zero, is a rational number.
To find 20 rational numbers between -3/7 and 2/3, we need to find the difference between 2/3 and -3/7, which is 65/21. Then we divide 65/21 by 21 to get the increment value of 3/7. Starting with -3/7, we add 3/7 to it 20 times to get the 20 rational numbers between -3/7 and 2/3.
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A ________ is a set of points that extends infinitely in both directions.
Answers
Answer:
line
Step-by-step explanation:
A line is a set of points that extends infinitely in both directions.
how
do i solve
If \( t \) is the distance from \( (1,0) \) to \( (-0.9454,0,3258) \) along the circumference of the unit circle, find csc \( t \), sec \( t \), and cot \( t \).
Answers
To find the values of csc \( t \), sec \( t \), and cot \( t \) given the distance \( t \) along the circumference of the unit circle, we need to calculate the corresponding trigonometric ratios using the coordinates of the points on the unit circle.
We are given the coordinates of two points: \( (1, 0) \) and \( (-0.9454, 0.3258) \). The first point represents the initial position on the unit circle, and the second point represents the final position after traveling a distance \( t \) along the circumference.
To calculate the values of csc \( t \), sec \( t \), and cot \( t \), we can use the following definitions:
1. csc \( t \) (cosec \( t \)) is the reciprocal of the sine of \( t \). We can find the sine of \( t \) by using the \( y \)-coordinate of the final point. Thus, csc \( t = \frac{1}{\sin t} = \frac{1}{0.3258}\).
2. sec \( t \) is the reciprocal of the cosine of \( t \). We can find the cosine of \( t \) by using the \( x \)-coordinate of the final point. Thus, sec \( t = \frac{1}{\cos t} = \frac{1}{-0.9454}\).
3. cot \( t \) is the reciprocal of the tangent of \( t \). We can find the tangent of \( t \) by using the ratio of the \( y \)-coordinate to the \( x \)-coordinate of the final point. Thus, cot \( t = \frac{1}{\tan t} = \frac{1}{\frac{0.3258}{-0.9454}}\).
Therefore, csc \( t \), sec \( t \), and cot \( t \) have the values of approximately 3.070, -1.058, and -2.951 respectively.
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If \( t \) is the distance from \( (1,0) \) to \( (-0.9454,0,3258) \) along the circumference of the unit circle of csc \( t \), sec \( t \), and cot \( t \) have the values of approximately 3.070, -1.058, and -2.951 respectively.
We are given the coordinates of two points: \( (1, 0) \) and \( (-0.9454, 0.3258) \). The first point represents the initial position on the unit circle, and the second point represents the final position after traveling a distance \( t \) along the circumference.
To calculate the values of csc \( t \), sec \( t \), and cot \( t \), we can use the following definitions:
1. csc \( t \) (cosec \( t \)) is the reciprocal of the sine of \( t \). We can find the sine of \( t \) by using the \( y \)-coordinate of the final point. Thus, csc \( t = \frac{1}{\sin t} = \frac{1}{0.3258}\).
2. sec \( t \) is the reciprocal of the cosine of \( t \). We can find the cosine of \( t \) by using the \( x \)-coordinate of the final point. Thus, sec \( t = \frac{1}{\cos t} = \frac{1}{-0.9454}\).
3. cot \( t \) is the reciprocal of the tangent of \( t \). We can find the tangent of \( t \) by using the ratio of the \( y \)-coordinate to the \( x \)-coordinate of the final point. Thus, cot \( t = \frac{1}{\tan t} = \frac{1}{\frac{0.3258}{-0.9454}}\).
Therefore, csc \( t \), sec \( t \), and cot \( t \) have the values of approximately 3.070, -1.058, and -2.951 respectively.
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what is 400 divided by 48.18 and round to nearest tenths?
Answers
Answer:
8.3
Step-by-step explanation:
The original answer was 8.30220008
Let's start at the end, 8 rounded up is 10, so 1, 1 is rounded to 0 so 0, 0 is rounded to 0, so 0, 0 is rounded up to 0 so 2, 2 rounded is 0 so 2, 2 rounded is to 0 so 0, 0 so rounded to 3 so 3.
Rounded up is 8.3
What is the slope-intercept equation go the line below?
Answers
Answer:
b
Step-by-step explanation:
f(x)=y
this question tell us that f(0)=1 and f(4)=3
try b, b option matches those given.
if q is the point x, 4 3 − x , find the slope of the secant line pq (correct to six decimal places) for the following values of x.
Answers
You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:
For x = 2:
slope = -1 / (3 - 2(2))
slope = -1 / (3 - 4)
slope = -1 / (-1)
slope = 1
To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:
slope = (3 - 4) / (3 - x - x)
slope = -1 / (3 - 2x)
To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.
For example, if x = 1, the slope of the secant line PQ is:
slope = -1 / (3 - 2(1))
slope = -1 / (3 - 2)
slope = -1 / 1
slope = -1
Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:
For x = 2:
slope = -1 / (3 - 2(2))
slope = -1 / (3 - 4)
slope = -1 / (-1)
slope = 1
And so on, you can calculate the slope of the secant line for different values of x.
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The image below showcases a right triangle .
My questions:
What is a c, what does that represent
What is this problem asking for me
How do I solve this problem? Are there any formulas in place?
Answers
The perimeter of triangle is 66.24 units.
What is triangle?
In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane
Main body:
according to question :
c = 28
let the vertices be A,B,C
∠A= 30°
by using trigonometric ratios,
BC/ AB = sin30°
AB = C = 28
BC/28 = sin30°
BC = 28*sin30°
BC= 28*(1/2)
BC = 14
similarly
AB /CA = cos 30°
28/CA = √3/2
CA = 28*√3/2
CA = 14/√3
CA = 24.24
Hence , perimeter = AB +BC +CA = 28+14+24.24
=66.24 units
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Any population, P, for which we can ignore immigration, satisfies dP/dt = Birth rate - Death rate. For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the form dP/dt = aP^2 - bP with a, b > 0. This problem investigates the solutions to such an equation. Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative. dP/dt < 0 when P is in dP/dt > 0 when P is in
Answers
As a result, on a graph of dP/dt vs P, the curve would be concave down for P b/a and concave up for P > b/a. The curve would reach its maximum when P = b/a, with dP/dt equal to zero.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
The equation dP/dt = aP² - bP represents the rate of change of the population P over time t.
When dP/dt is positive, the population is increasing. When dP/dt is negative, the population is decreasing.
To find when dP/dt is positive and negative, we need to find the critical points where dP/dt = 0.
Solving the equation dP/dt = aP² - bP = 0, we get:
aP² - bP = 0
aP(P - b/a) = 0
This equation has two solutions: P = 0 and P = b/a.
For P < b/a, dP/dt is negative (the population is decreasing). For P > b/a, dP/dt is positive (the population is increasing).
So, on a graph of dP/dt against P, the curve would be concave down for P < b/a and concave up for P > b/a. At P = b/a, the curve would have a maximum and dP/dt = 0.
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The temperature is 45°F The temperature will decrease by 2°F each hour. Let
h be the number of hours.
When will the temperature be below 32°F?
Write an inequality for this problem.
A. 45 + 25 = 32
B. 45 - 2.32
C. 45 + 25 32
D. 45 - 253
Answers
The equation for line q is 3x + 5y 10, Line r is parallel to line q and passes through the
point (5,-4).
Write the equation for line r in slope-intercept form.
Answers
The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.
What is the equation for line r in slope-intercept form?The slope-intercept form is expressed as;
y = mx + b
The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line q : 3x + 5y = 10Point: (5,-4)Equation line r = ?First, determine the slope of the line q using the slope intercept-form.
y = mx + b
3x + 5y = 10
5y = -3x + 10
y = (-3/5)x + 10/5
y = (-3/5)x + 2
Hence;
Slope of line q m = -3/5
Since, line r is parallel to line q, they both have the same slope.
Therefore, slope of line r will be m = -3/5
Now, plug the point (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.
y - y₁ = m( x - x₁ )
y - (-4) = (-3/5)( x - 5 )
y + 4 = (-3/5)x + 3
y = (-3/5)x + 3 - 4
y = (-3/5)x - 1
Therefore, the equation of line r is y = (-3/5)x - 1.
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