The function represented by the data is f(1/4)x³ + 2x² - 24. The correct option is 2.
In the given table, we have the values of x and f(x) for x=0,1,2,3, and 4. We need to find a polynomial function that satisfies these data points.
Looking at the table, we can see that f(x) is negative for x=0,1,2 and positive for x=3,4. This suggests that the polynomial has a root or a zero between x=2 and x=3.
To find the degree of the polynomial, we count the number of data points given. Since we have 5 data points, we need a polynomial of degree 4.
We can use interpolation to find the coefficients of the polynomial. One way to do this is to set up a system of equations using the data points:
f(0) = -24 = a(0)⁴ + b(0)³ + c(0)² + d(0) + e
f(1) = -21.75 = a(1)⁴ + b(1)³ + c(1)² + d(1) + e
f(2) = -14 = a(2)⁴ + b(2)³ + c(2)² + d(2) + e
f(3) = 0.75 = a(3)⁴ + b(3)³ + c(3)² + d(3) + e
f(4) = 24 = a(4)⁴ + b(4)³ + c(4)² + d(4) + e
Solving this system of equations gives us the polynomial function:
f(x) = -0.25x⁴ + 2x³ - 2.75x² - 0.5x + 24
Therefore, the correct option is 2. f(x) = (1/4)x³ + 2x² - 24.
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What is the process of solving this?
The solution of the trigonometric equation
cos(2x) = cos(x) + 2
is x = 180°
How to solve the trigonometric equation?Here we want to solve the equation:
cos(2x) = cos(x) + 2
First, we know that:
cos(2x) = 2cos(x)² - 1
Then we can rewrite:
2cos(x)² - 1 = cos(x) + 2
We can define:
cos(x)= y
2y² - 1 = y + 2
Then we need to solve the quadratic:
2y² - 1 - y - 2 =0
2y² - y - 3 = 0
Using the quadratic formula we will get:
[tex]y = \frac{1 \pm \sqrt{(-1)^2 - 4*2*2*-3} }{2*2} \\\\y = \frac{1 \pm 5}{4}[/tex]
so the solutions are:
y = (1 + 5)/4 = 6/4
y = (1- 5)/4 = -1
And remember that y = cos(x), then y = 6/4 can be discarded.
Then the solution comes from:
cos(x) = -1
then x = pi = 180°
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A water sample shows 0.063 grams of some trace element for every cubic centimeter of water. Tariq uses a container in the shape of a right cylinder with a radius of 7.6 cm and a height of 17 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Tariq collected? Round your answer to the nearest tenth.
Therefore, Tariq has collected 201.09 g trace element.
We are given that Tariq uses a container that is in the shape of a cylinder. The radius of the cylinder is 7.6 cm and the height of the cylinder is 17 cm.
Firstly, we will find the volume of the cylinder by applying the formula
The volume of the cylinder = [tex]\pi r^{2} h[/tex]
As we know the values of r and h, we will substitute these values in the given formula
The volume of cylinder = 3.14 * 17.6 * 7.6 *7.6
The volume of cylinder = 55.264 * 57.76
Volume = 3192.04 [tex]cm^{3}[/tex]
We are given that the water sample shows 0.063 grams of some trace element for every cubic centimeter of water. Therefore, we will multiply the volume of the cylinder by 0.063 to calculate the number of trace elements collected.
= 3192.04 * 0.063
= 201.09
Therefore, a total of 201.09 g of trace elements was collected by Tariq.
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Find the reduction formula for the following integrals
In = ∫cot^n dx, then find I4
The reduction form is [tex]I_4 i= cot^3 x =ln |sin x| - 3 cot x + 3x + C[/tex].
To find the reduction formula for ∫cot^n x dx, we can use integration by parts. Let u = cot^(n-1) x and dv = cot x dx, then[tex]du = (n-1)cot^(n-2) x csc^2[/tex]x dx and v = ln |sin x|. By the formula for integration by parts, we have:
∫cot^n x dx = ∫u dv = uv - ∫v du
= [tex]cot^(n-1) x ln |sin x| - (n-1) ∫cot^(n-2) x csc^2 x ln |sin x| dx.[/tex]
This gives us the reduction formula:
[tex]I_n = ∫cot^n x dx = cot^(n-1) x ln |sin x| - (n-1) I_(n-2).[/tex]
Using this formula, we can find I_4 as follows:
[tex]I_4 = ∫cot^4 x dx = cot^3 x ln |sin x| - 3 I_2\\= cot^3 x ln |sin x| - 3 ∫cot^2 x dx\\= cot^3 x ln |sin x| - 3 (cot x - x) + C,\\[/tex]
where C is the constant of integration. Therefore, the solution for I_4 is [tex]cot^3 x ln |sin x| - 3 cot x + 3x + C.[/tex]
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help me find the fraction please
Answer: 9/64
Step-by-step explanation:
First, we find the probability of blue in one spin.
One spin: 3/8
Next, we also know that the second spin will also have a probability of 3/8.
To combine these probabilities in both spins, we multiply. This will combine the two independent events. It can be similar to Permutation.
Probability of both spins: 3/8 x 3/8
=9/64
9/64 is the combined probability of both spins.
Read the following question:
Answer: 5 hours of service
Step-by-step explanation:
25 + x(15) = 20x
⇒ 25 = 20x - 15x
⇒ 25 = 5x
⇒ x = 5
(5, -8) reflected across the y axis and then reflected across the x axis
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
Q4. A. A triangle has vertices (-2, 3), (1, 1) and (-1,-2).
a. Find the length of the sides. (3mks)
b. Name this triangle. (Imks)
The length of the sides AB, BC and AC are √13, √13 and √26, hence the triangle is a isosceles triangle.
a. Points (-2, 3), (1, 1), (-1, 2) in the triangle are vertex. The distance formula for any two points is,
AB = √[(d-b)²+(c-a)²]
= √[(1 - (-2))² + (1 - 3)²]
= √[3² + (-2)²]
= √13
BC = √[(d-b)²+(c-a)²]
= √[(-1-1)²+(-2-1)²]
= √[(-2)² + (-3)²]
= √13
AC = √[(d-b)²+(c-a)²]
= √[(-1 - (-2))² + (-2 - 3)²]
= √[1² + (-5)²]
= √26
b. The triangle is an isosceles triangle because AB = BC.
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The kinetic energy of a moving object varies directly with the square of its velocity. A bowling ball traveling at 15 meters per second has about 1000 joules of energy.
Write the equation that relates the kinetic energy, E, to its velocity, v.
Round your answer to the nearest hundredth.
About how much energy will a bowling ball have if it is moving at 11 meters per second?
Use your answer from part one. Round your answer to the nearest hundredth
A bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.
The kinetic energy (E) of a moving object varies directly with the square of its velocity (v). To write the equation relating E to v, we can use the formula: E = k * v^2, where k is a constant of proportionality. Given a bowling ball traveling at 15 meters per second with 1000 joules of energy, we can find the value of k:
1000 = k * (15^2)
1000 = k * 225
k ≈ 4.44
So, the equation relating the kinetic energy and velocity is: E ≈ 4.44 * v^2.
Now, we want to find the energy of the bowling ball when it's moving at 11 meters per second. Using the derived equation:
E ≈ 4.44 * (11^2)
E ≈ 4.44 * 121
E ≈ 537.64
Therefore, a bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.
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Complete question:
The kinetic energy of a moving object varies directly with the square of its velocity. A bowling ball traveling at 15 meters per second has about 1000 joules of energy.
Write the equation that relates the kinetic energy, E, to its velocity, v.
Round your answer to the nearest hundredth.
About how much energy will a bowling ball have if it is moving at 11 meters per second?
Use your answer from part one. Round your answer to the nearest hundredth
Help with problem in photo
Check the picture below.
Answer:
250 degrees
Step-by-step explanation:
For any circle tangent to line FG at point F, as shown in the diagram, and for any point E on the circle, the relationship between the measure of angle GFE and the arclength of FE is given by [tex]m~\text{arc}~FE=2m \angle GFE[/tex].
So, the measure of the arc FE is 110 degrees. Since a circle is fully 360degrees, the missing arc represented by the question mark is given by the following equation:
? + 110 = 360
Solving for the ?
? = 250 degrees
Find the area of a parallelogram with the given vertices: p(3, 3), q(5, 3), r(7, 7), s(9, 7). a. 16 units2 b. 8 units2 c. 4 units2 d. none of these
The area of the parallelogram is 8 units², which is option (b).
To find the area of a parallelogram, we need to use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we can use the distance formula to find the base and height.
Base = distance between points P and Q
= √[(5-3)² + (3-3)²]
= √4
= 2 units
Height = distance between point P and the line containing points R and S. We can find the equation of this line by first finding its slope:
slope = (y2 - y1)/(x2 - x1)
= (7 - 7)/(9 - 7)
= 0
Since the slope is 0, the line is horizontal and has an equation of y = 7. Therefore, the height is the distance between point P and this line, which is:
Height = distance from point P to line y = 7
= |3 - 7|
= 4 units
Now we can plug in the values of b and h into the formula A = bh:
A = 2 x 4
= 8 units²
Therefore, the area of the parallelogram is 8 units², which is option (b).
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D Moon 17 The sun is composed primarily of A wat A one average star C. Three stars D. one alder dimmer star and one younger brighter star 19 The Planets that are closest to the sun, OR the A. Moon B. outer planets inner planets 20 The general formula of the main shell is- A. 2n Proto B. Proto 8. several stars spread across 21. All spin in the same direction except one. A. Mercury B. Venus 22. Which of the following is the inner planet in the solar system? 8. Jupiter C. Uranus D. Saturn 23. Rock like objects in the region of space b/r the orbits of mars and Jupiter are planets planets Asteroids D. Meteorites Asteroids A. Comets B. are rocky and are similar in
Therefore , the solution of the given problem of unitary method comes out to be space between Mars' and Jupiter's orbits contains rock-like objects.
An unitary method is defined as what?To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.
Here,
What makes up the majority of the sun?
hydrogen a
The names of the planets nearest to the sun are:
Inner planets, B
A. 2n² is the general formula for the main shell.
Except for one planet, all of them revolve in the same direction. What planet is that?
(1) Venus
Which of the following is the solar system's inner planet?
Mercury, a.
The region of space between Mars' and Jupiter's orbits contains rock-like objects, which are known as:
Asteroid C.
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you are planning a trip to australia. your hotel will cost you a$110 per night for seven nights. you expect to spend another a$3,400 for meals, tours, souvenirs, and so forth. how much will this trip cost you in u.s. dollars if $1
The total cost of the trip in U.S. dollars as per given rates and conversion is equal to approximately USD 3,232.58.
Total cost of the trip in U.S. dollars,
Convert the Australian dollars to U.S. dollars.
Using the exchange rate of 0.7752 USD per 1 AUD.
The cost of the hotel is,
7 nights × A$110/night = A$770
To convert this to U.S. dollars, multiply by the exchange rate,
A$770 × 0.7752 USD/AUD
= USD 596.904
Expected cost of meals, tours, souvenirs, etc. is,
A$3,400
Convert this to U.S. dollars, we again multiply by the exchange rate,
A$3,400 × 0.7752 USD/AUD
= USD 2,635.68
Total cost of the trip in U.S. dollars is the sum of these two amounts is,
USD 596.904 + USD 2,635.68 = USD 3,232.584
Rounding to two decimal places = approximately USD 3,232.58.
Therefore, the cost of the trip in the U.S. dollars is equal to approximately USD 3,232.58.
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The above question is incomplete, the complete question is:
You are planning a trip to Australia. your hotel will cost you a$110 per night for seven nights. you expect to spend another a$3,400 for meals, tours, souvenirs, and so forth. How much will this trip cost her in U.S. dollars if the USD equivalent is .7752?
22. Your choir is taking a trip. The trip has an initial cost of $500, plus $150 for
each student.
a. Estimate how many students must go on the trip for the average cost
per student to fall to $175.
b. What happens to the average cost as more students go on the trip?
a. There would be at least 20 students must go on the trip for the average cost per student to fall to $175.
b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases.
a. To find out how many students must go on the trip for the average cost per student to fall to $175, we can use the formula:
Total Cost = $500 + $150 x Number of Students
Average Cost per Student = Total Cost / Number of Students
Setting the average cost per student to $175 and solving for the number of students, we get:
$175 = ($500 + $150 x Number of Students) / Number of Students
Multiplying both sides by Number of Students, we get:
$175 x Number of Students = $500 + $150 x Number of Students
Simplifying, we get:
$25 x Number of Students = $500
Number of Students = $500 / $25 = 20
Therefore, at least 20 students must go on the trip for the average cost per student to fall to $175.
b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases. This is because the fixed cost of $500 is spread over more students, making the cost per student lower. So, as more students go on the trip, the average cost per student will continue to decrease.
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In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees
In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.
In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.
Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)
Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.
Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848
If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.
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I will mark you brainliysit help
WHAT IS 2X36 DIVED BY 3 PLUS 9 -4=
HEEELPPP
Answer:
Step-by-step explanation:
2 x 36 ÷ 3 + 9 - 4
= 72 ÷ 3 + 9 - 4 (perform multiplication first)
= 24 + 9 - 4 (perform division)
= 29 (perform addition and subtraction)
Therefore, 2x36 ÷ 3 + 9 - 4 = 29.
Answer:
29
Step-by-step explanation:
2×36=72
72/3=24
24+9=33
33-4=29
Write and solve an inequality to represent the scenario, then explain the solution.
Brianna has a $50 online gift certificate from a book store. The cost of each book is $9. There is also a shipping charge of $5 for her entire order. How many
books can Brianna buy without spending more than her gift certificate amount?
Enter the correct answers in the boxes.
Brianna can buy up to 5 books without spending more than her gift certificate amount.
We can set up the inequality: 9x + 5 <= 50. where x is the number of books Brianna can buy. To solve for x, we can start by subtracting 5 from both sides of the inequality: 9x <= 45
Divide both sides by 9: x <= 5. The inequality 9x + 5 <= 50 represents the fact that the total cost of Brianna's order (the cost of the books plus the shipping charge) should not exceed the amount of her gift certificate, which is $50.
We subtracted 5 from both sides to isolate the term 9x and then divided by 9 to solve for x, which represents the number of books she can buy. The solution, x <= 5, indicates that Brianna can buy up to 5 books without going over her gift certificate amount.
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A street light is mounted on a pole. the tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 42o. a woman standing on the opposite side of the pole has an angle of elevation from the tip of her shadow to her head of 50o. if the two people are 60 feet apart, how far is the street light from the head of each person?
the man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.
the man’s head is 41.2 ft away and the woman’s head is 39.5 ft away.
the man’s head is 1105.1ft away and the woman’s head is 1277.6 ft away.
the man’s head is 46.0 ft away and the woman’s head is 40.2 ft away.
The correct option is (a). The man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.
How to find the distance from the street light to each person's?To solve this problem, we can use trigonometry to find the distances from the street light to each person's head. Let x be the distance from the street light to the man's head and y be the distance from the street light to the woman's head. Then, we can set up two equations using the tangent function:
tan(42) = x / d and tan(50) = y / d
where d is the distance between the two people (60 ft). Solving for x and y, we get:
x = d * tan(42) = 78.3 ft
y = d * tan(50) = 89.6 ft
Therefore, the man’s head is 78.3 ft away from the street light and the woman’s head is 89.6 ft away from the street light.
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I need this problem solved.
The relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).
What is a 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.
You can compare various data sets using bar graphs.
In a line graph, the data is represented by tiny dots, and the line that connects them indicates what happens to the data.
So, we have the coordinates:
(-1, 3); (-2, 4); (1, 2); (2, 4)
Now, plot it on the graph as follows:
(Refer to the graph attached below.)
(-1, 3) and (-2, 4) are in the 2nd quadrant, and (1, 2) and (2, 4) are in the 1st quadrant.
Therefore, the relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).
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Correct question:
Express the relation (-1, 3); (-2, 4); (1, 2); (2, 4) on the graph.
A rectangular prism shaped fish tank is 2014 inches wide, 1012 inches long, and 1812 inches tall.
What is the volume of the fish tank in cubic inches?
Responses
49 1/4
212 5/8
3600 1/16
3933 9/16
The volume of the fish tank is approximately 3,693,142,608 cubic inches
How to solveTo find the volume of the rectangular prism-shaped fish tank, we need to multiply its width, length, and height.
Given the dimensions are 2014 inches wide, 1012 inches long, and 1812 inches tall, the calculation is as follows:
Volume = Width × Length × Height
Volume = 2014 in × 1012 in × 1812 in
Upon calculating the product, we get:
Volume ≈ 3,693,142,608 cubic inches
The volume of the fish tank is approximately 3,693,142,608 cubic inches
N.B: None of the answer choices has the correct answer.
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The expedition team decides to have another practice run. Two team members head due north at a pace of 4 km/h. The second pair decide to head 60° west of north travelling at the same pace. How far from the first pair is the second pair after 2 h?
After the duration of 2 hours the distance between the first pair and the second pair is 3.07 km, under the condition that the second pair decide to head 60° west of north travelling at the same pace.
In order to evaluate the distance between two points with given coordinates, we can apply the distance formula. The distance formula is
d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]
Here,
(x₁, y₁) and (x₂, y₂) = coordinates of the two points.
For the given case, we can consider that the first pair of team members start at the origin (0, 0) and cover the distance towards north for 2 hours at a pace of 4 km/h.
Hence, their final position is (0, 8).
The second pair of team members take the origin (0, 0) and travel 60° west of north for 2 hours at a pace of 4 km/h.
Now to evaluate their final position, we have to find their coordinates. Let us consider their final position (x, y).
We can apply trigonometry to find x and y.
The angle between their direction of travel and the y-axis is 60°.
sin(60°) = y / d
cos(60°) = x / d
Here,
d = distance travelled by the second pair of team members.
It is given that they travelled for 2 hours at a pace of 4 km/h.
d = 2 hours × 4 km/h
= 8 km
Staging this value into the above equations
y = d × sin(60°) = 8 km × sin(60°)
≈ 6.93 km
x = d × cos(60°) = 8 km × cos(60°)
≈ 4 km
Hence, the final position regarding the second pair of team members is approximately (4 km, 6.93 km).
Now we can apply the distance formula to evaluate the distance between the two pairs of team members
d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]
d = √ [ (4 − 0)² + (6.93 − 8)² ]
d ≈ 3.07 km
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Helppp translation and reflection
The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.
How to compute the image of a point by translation
In this problem we find must determine the image of two points by translation, whose formula is introduced below:
T(x, y) = P'(x, y) - P(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.First, determine the translation vector:
T(x, y) = (1, 4) - (0, 0)
T(x, y) = (1, 4)
Second, determine the images of points B and C:
B'(x, y) = (- 3, 2) + (1, 4)
B'(x, y) = (- 2, 6)
C'(x, y) = (- 2, 3) + (1, 4)
C'(x, y) = (- 1, 7)
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Carla, the baker, worked for 5 hours to make cookies..
She ended with 380 cookies altogether. Write an
equation to express how many cookies Carla made
each hour.
Answer:
5x=380
x = 76
Carla made 76 cookies each hours
Step-by-step explanation:
Just make an equation, so the total number of cookies is 380 and she works for 5 hours, so it is just 380/5.
On a certain plaats moon the acceleration due to gravity is 2.9 m/sec^2 if a rock dropped into a chivaste, how fast it will be going just before it hits the bottom 31 secs later?
the rock will be going 89.9 m/s just before it hits the bottom of the chaste on a certain plaats moon.
To answer your question, we need to use the formula for the acceleration due to gravity, which is:
a = g
where a is the acceleration, and g is the gravitational constant. In this case, we know that the acceleration due to gravity on the moon is 2.9 m/sec^2, so we can substitute that into the formula:
a = 2.9 m/sec^2
Now we need to use the formula for calculating the speed of an object that is falling under the influence of gravity, which is:
v = gt
where v is the speed, g is the gravitational constant, and t is the time. We know that the rock takes 31 seconds to hit the bottom of the chivaste, so we can substitute that into the formula:
t = 31 s
Now we can calculate the speed of the rock just before it hits the bottom:
v = gt
v = 2.9 m/sec^2 x 31 s
v = 89.9 m/s
So the rock will be going 89.9 m/s just before it hits the bottom of the chivaste on the certain plaats moon.
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Consider the following function f(x)=x^2+5
part a write a function in vertex form that shifts f(x) right 3 units
part b write a function in vertex form that shifts f(x) left 10 unites
Part a: f(x) = (x-3)^2 + 5
Part b: f(x) = (x+10)^2 + 5
Part a: To shift the function f(x) = x^2 + 5 right 3 units, we need to subtract 3 from the x-coordinate of the vertex. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Thus, the function in vertex form that shifts f(x) right 3 units is:
f(x) = (x-3)^2 + 5
Part b: To shift the function f(x) = x^2 + 5 left 10 units, we need to add 10 to the x-coordinate of the vertex. Using the same vertex form as before, the function in vertex form that shifts f(x) left 10 units is:
f(x) = (x+10)^2 + 5
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consider h(x)= 11x² - 6x calculate H (x) Fx 6.Xr1 유 11 6 3 (22.-6) 3 6 In(3) 11 A) 2 +1 (221 - 6)31 B) - (11r? - br)3*** In(3) 2 (3***") - 6 In(3) (221 - 63#* - (1142 – 63)3 (3***")" 2 +1 4 (221 - 63 - (1122 – 6x)3 In(3) i 1 D)
The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.
To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.
The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:
∫ (22x - 3x² - 6/x) dx = ∫ 22x dx - ∫ 3x² dx - ∫ 6/x dx= 11x² - x³ - 6ln|x| + Cwhere C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.
Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:
31 = 11(6)² - (6)³ - 6ln|6| + CSimplifying, we get:
31 = 132 - 216 - 6ln(6) + CC = 221/3 - 6ln(6)Therefore, the antiderivative of h(x) is:
H(x) = 11x² - x³ - 6ln|x| + 221/3 - 6ln(6)We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:
H(x) = 11x² - x³ - 6ln(3) - 6ln(x) + 2ln(3) + Cwhere C is the constant of integration. Thus, the final answer is:
B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.To learn more about integration, here
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What is an equation of the line that passes through the points ( 8 , 6 ) and ( − 3 , 6 )
The equation of line passing through the points (8, 6) and (-3, 6) is y = 6. Since the y-coordinate is the same for both points, the line is a horizontal line at y = 6.
To find the equation of the line passing through the points (8, 6) and (-3, 6), we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope, which is given by
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (8, 6) and (x2, y2) = (-3, 6)
m = (6 - 6) / (-3 - 8)
m = 0 / -11
m = 0
Since the slope is zero, the line is a horizontal line. We can see from the given points that the line passes through y = 6. Therefore, the equation of the line is
y = 6
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In A shown below radius AB is perpendicular to chord XY at point C If XY=30cm and AC=8m what is the measure of XC
pls help
Therefore, the measure of line segment XC is 3.75 cm.
What is perpendicular?In geometry, two lines or planes are said to be perpendicular if they intersect each other at a right angle (90 degrees). The term "perpendicular" is also commonly used to describe the relationship between a line and a surface, where the line is at a right angle to the surface at the point of intersection. In general, the concept of perpendicularity is fundamental to many mathematical and scientific fields, such as trigonometry, physics, and engineering. It is also a commonly used term in everyday language to describe objects or structures that intersect at right angles, such as the corners of a square or the legs of a chair.
Here,
In the given diagram, let O be the center of the circle and let XC = a.
Since AB is perpendicular to XY at C, we have AC = BC = 8 m (using Pythagoras theorem). Also, since AB is a radius of the circle, we have AB = r, where r is the radius of the circle.
By the power of a point theorem, we have:
AC × XC = BC × XY
Substituting the given values, we get:
8 m × a = 8 m × 30 cm
Simplifying and converting units, we get:
a = 3.75 cm
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A small printing company launched an online ordering system to expand its business. The equation с. 400-(1. 03)" represents the number of customers c it has in terms of the number of months m since it launched the ordering system. 1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value.
2. If y is the time in years write an equation for the numbers of costumers c as a function of the numbers of years y after the introduction of the ordering system.
1. The growth factor for the number of customers over a year is approximately 1.4266.
2. the growth factor in customers over a decade period is approximately 5.927.
Factors that affect how many consumers there are in a year are
c(12)/c(0) = (400 x (1.03)¹²) / (400 x (1.03)⁰)
= (1.03)¹²
= 1.4266....
Therefore, the growth factor for the number of customers over a year is approximately 1.4266.
2. To write an equation for the number of customers c as a function of the number of years y, we can substitute m = 12y into the original equation
[tex]c(y) = 400 x (1.03)^{12y}[/tex]
one decade = 10 years
= 120 months
We must calculate the value of the equation at m=120 and divide it by the equation's value at m=0.
c(120) / c(0) = [400 x (1.03)¹²⁰] / [400 x (1.03)⁰]
= (1.03)¹²⁰
= 5.927...
Therefore, the growth factor in customers over a ten-year period is approximately 5.927.
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Given Question is incomplete, complete question is given below:
A small printing company launched an online ordering system to expand its business. The equation [tex]c=400(1. 03)^m[/tex] represents the number of customers c it has in terms of the number of months m since it launched the ordering system.
1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value
2. If y is time in years, write an equation for the number of customers c as a function of the number of years y after the introduction of the ordering system. If this model continues to apply for a decade, by what factor will the number of customers grow in one decade?
what is the answer to 8 units away from zero.
Answer:
Step-by-step explanation:
How can I figure this out?
Answer:
Blue = 4
Red = 24
Green = 4
All = 32
Step-by-step explanation:
Area of a triangle: 1/2 * base * height, so for both blue and green:
1/2 * 2 * 4
1 * 4
4
Area of an object with 4 sides: length * width, so for red:
6 * 4
24
Area of everything: blue + red + green, so for all:
4 + 4 + 24
8 + 24
32