V = ∫2πx f(y) dy volume of the solid
a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:
∫ dz = z + C
b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:
∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'
where C' is the constant of integration.
c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.
If we rotate the region about the x-axis, we can use the formula:
V = ∫2πy f(x) dx
where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.
If we rotate the region about the y-axis, we can use the formula:
V = ∫2πx f(y) dy
where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.
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NEXT QUESTION >
Triangle HNR is shown where point K is the
centroid, KW = (2y — 8.9), KH
(2y 8.9), KH = (4.5w - 5.9),
KR = (0.5y + 3.2), KN = (5x – 5.2), KD = (9w
and KT = (7.1x – 11.8).
Z
W
H
K
Answer:
a b e
Step-by-step explanation:
A triangle has side lengths 6 cm, 7 cm, and √13 cm. Is this triangle a right triangle? Do these side lengths form a Pythagorean triple? Explain.
A triangle with side lengths 6 cm, 7 cm, and √13 cm is right triangle and the side lengths form a Pythagorean triple.
To determine if the triangle with side lengths 6 cm, 7 cm, and √13 cm is a right triangle and if these side lengths form a Pythagorean triple, we'll use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Identify the longest side. In this case, it's the side with length 7 cm.
Check if the Pythagorean theorem holds true for these side lengths:
(6 cm)² + (√13 cm)² = (7 cm)²
Calculate the squares of the side lengths:
(6 cm)² = 36 cm²
(√13 cm)² = 13 cm²
(7 cm)² = 49 cm²
Check if the sum of the squares of the two shorter sides equals the square of the longest side:
36 cm² + 13 cm² = 49 cm²
Compare the results:
49 cm² = 49 cm²
Since the equation holds true, the triangle is indeed a right triangle, and the side lengths 6 cm, 7 cm, and √13 cm form a Pythagorean triple.
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1. Sally wants to buy a pair of shoes for $12. 50 and a shirt for $23. 50. If 50 points the sales tax is 8. 25%, what will be the amount of the sales tax Sally's purchase?
To calculate the amount of the sales tax on Sally's purchase, we first need to add the prices of the shoes and the shirt together. So, $12.50 + $23.50 = $36. Then, we need to calculate 8.25% of $36, which is done by multiplying 36 by 0.0825. That gives us a sales tax of $2.97. So, the amount of the sales tax on Sally's purchase is $2.97.
In summary, Sally wants to buy shoes for $12.50 and a shirt for $23.50, and the sales tax is 8.25% on a purchase of 50 points. The amount of the sales tax on Sally's purchase is $2.97. In order to calculate the sales tax, we added the prices of the items together and then calculated 8.25% of that total.
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You invest ten thousand dollars in an account that pays eight percent APR compounded monthly. After how many years will the account have twenty thousand dollars.
As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.
what is percentage ?As a quarter of 100, a number can be expressed as a percentage. It is frequently used to describe distinctions or express changes in numbers. The symbol for percentages is %, and they are frequently utilized to describe ratios, rates, and certain other numerical connections. An 80 percent score on a test, for instance, indicates that the student correctly answered 80 of the 100 questions. Similar to this, if a retailer were offering a 20% discount on a $100 item, the sale price would be $80.
given
With P = 10000, r = 0.08 (8% stated as a decimal), n = 12 (compound monthly), and t to be found when A = 20000, the situation is as follows.
When these values are added to the formula, we obtain:
[tex]20000 = 10000(1 + 0.08/12)^(12t) (12t)[/tex]
By multiplying both sides by 1000, we obtain:
[tex]2 = (1 + 0.08/12)^(12t) (12t)[/tex]
When we take the natural logarithm of both sides, we obtain:
ln(2) = 12t ln(1 + 0.08/12)
When we multiply both sides by 12 ln(1 + 0.08/12), we obtain:
t = ln(2) / (12 ln(1 + 0.08/12))
Calculating the answer, we discover:
10.24 years is t.
As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.
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celine ordered a set of beads. she received 10,000 beads in all, 9,100 of the beads were brown. what percentage of the beads were brown?
Answer:
91%
Step-by-step explanation:
Aimie is looking for a golf ball that he hit into the air towards a fence surrounding the golf course. The fence has a height of 2 yards and is located at a distance of 120 yards from where Jaimie hit the ball. Jaimie wants to determine if his golf ball landed inside or outside of the fence.
The golf ball's height, h, in yards with respect to time, t, in seconds, can be modeled by the quadratic function h=−0. 6t2+3t. Jaimie's golf ball reached its maximum height at the fence.
What is the maximum height, in yards, the golf ball reached before landing back on the ground?
_____yards
The maximum height the golf ball reached before landing back on the ground is 3.75 yards.
To find the maximum height the golf ball reached before landing back on the ground, we need to find the vertex of the quadratic function[tex]h(t) = -0.6t^2 + 3t.[/tex] The vertex of a quadratic function in the form of[tex]f(x) = ax^2 + bx + c[/tex] is given by the formula x = -b/(2a).
In this case, a = -0.6 and b = 3. Plugging these values into the formula:
t = -3 / (2 * -0.6) = 3 / 1.2 = 2.5
Now that we have the time at which the ball reaches its maximum height, we can plug this value back into the height function to find the maximum height:
[tex]h(2.5) = -0.6(2.5)^2 + 3(2.5) = -0.6(6.25) + 7.5 = -3.75 + 7.5 = 3.75[/tex]
So, the maximum height the golf ball reached before landing back on the ground is 3.75 yards.
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The value of car depreciates by 15% every year. if its present value is rs.80000 what is its value after 3 years.
X is a discrete random variable. The table below defines a probability distribution for X.
What is the expected value of X?
The expected value of x is given as follows:
E(X) = 1.6.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
The distribution for this problem is given as follows:
P(X = -7) = 0.2.P(X = -3) = 0.1.P(X = 3) = 0.4.P(X = 7) = 0.3.Hence the expected value is given as follows:
E(X) = -7 x 0.2 - 3 x 0.1 + 3 x 0.4 + 7 x 0.3
E(X) = 1.6.
Missing InformationThe table is given by the image presented at the end of the answer.
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5 Work out the volume of this prism. Write your answer
a in cm³
b in mm³.
20cm
120cm
30cm
10 cm
Answer:
a_48000cm^3
b_48000000mm^3
Step-by-step explanation:
first of all, let's find the base area:
Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2
then, to find the volume, we need to multiplicate the base area to the height of the prism:
V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3
Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.
Vertex at (0,0); axis of symmetry the y-axis; containing the point (6,4).
What is the equation of the parabola? Find the two points that define the latus rectum.
The equation of the parabola is:
x = ay²The two points that define the latus rectum are (±9/64, 4).
How to find the equation of the parabola?The equation of the parabola with vertex at (0,0) and axis of symmetry the y-axis can be written in the form x = ay^2, where a is a constant. Since the parabola contains the point (6,4), we can substitute these values to solve for a:
6 = a(4²)
6 = 16a
a = 6/16 = 3/8
So the equation of the parabola is x = (3/8)y².
To find the two points that define the latus rectum, we need to determine the focal length, which is the distance from the vertex to the focus.
Since the axis of symmetry is the y-axis, the focus is located at (0, f), where f is the focal length. We can use the formula f = a/4 to find f:
f = a/4 = (3/8)/4 = 3/32
So the focus is located at (0, 3/32). The two points that define the latus rectum are the intersections of the directrix, which is a horizontal line located at a distance of f below the vertex, with the parabola. The directrix is located at y = -3/32.
To find the intersections, we can substitute y = ±(16/3)x^(1/2) into the equation of the directrix:
y = -3/32
±(16/3)[tex]x^(^1^/^2^)[/tex]= -3/32
x = 9/64
So the two points that define the latus rectum are (±9/64, 4).
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A two digit number is 11 times its units digit. The sum of the digits is 12. Find the number
According to the given condition the two-digit number is 66.
To find the two-digit number that is 11 times its units digit and has a sum of digits equal to 12, we can use the following steps:
1. Let's represent the two-digit number as XY, where X is the tens digit and Y is the units digit.
2. The number is 11 times its units digit, so we can write the equation: 10X + Y = 11Y.
3. The sum of the digits is 12, which means X + Y = 12.
4. Now, we have two equations with two variables:
- 10X + Y = 11Y
- X + Y = 12
5. We can solve for X from the second equation: X = 12 - Y.
6. Substitute the value of X in the first equation: 10(12 - Y) + Y = 11Y.
7. Simplify and solve for Y: 120 - 10Y + Y = 11Y.
8. Combine the Y terms: 120 - 9Y = 11Y.
9. Move all the Y terms to one side: 120 = 20Y.
10. Divide by 20 to get Y: Y = 6.
11. Now, substitute the value of Y back into the X equation: X = 12 - 6.
12. Solve for X: X = 6.
So, the two-digit number is 66.
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Which of the following combinations of side lengths would NOT form a triangle with vertices X, Y, and Z?
A.
XY = 7 mm , YZ = 14 mm , XZ = 25 mm
B.
XY = 11 mm , YZ = 18 mm , XZ = 21 mm
C.
XY = 11 mm , YZ = 14 mm , XZ = 21 mm
D.
XY = 7 mm , YZ = 14 mm , XZ = 17 mm
The combinations of side lengths that would NOT form a triangle with vertices X, Y, and Z is 7 mm , YZ = 14 mm , XZ = 25 mm.
option A.
What are the possible lengths of triangle?
The lengths of triangle are determined base a given set of rules;
let a, b, and c be the side lengths of a triangle;
Based on the rules of side lengths of triangles, the sum of length a and b must be greater than c, or the sum of a and c must be greater than b or the sum of b and c must be greater than a.
For option A;
7 mm + 14 mm < 25 mm (this cannot be)
For option B;
11 mm + 18 mm > 21 mm (this will work)
For option C;
11 mm + 14 mm > 21 mm (this will work)
For option D;
7 mm + 14 mm > 17 mm (this will work)
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If a photo measures 4 inches by 6 inches is places in a frame that measure 2 inches wide all around what percent of the fear is the photo itsel
The photo takes up 30% of the framed area.
To calculate the percentage of the frame that is taken up by the photo, we first need to calculate the dimensions of the framed photo. If the photo measures 4 inches by 6 inches, the dimensions of the framed photo will be 8 inches by 10 inches (adding 2 inches to each side).
To calculate the area of the frame, we need to subtract the area of the photo from the area of the framed photo. The area of the photo is 4 inches x 6 inches = 24 square inches. The area of the framed photo is 8 inches x 10 inches = 80 square inches. So, the area of the frame is 80 square inches - 24 square inches = 56 square inches.
To calculate the percentage of the frame that is taken up by the photo, we divide the area of the photo by the area of the framed photo and multiply by 100.
24 square inches / 80 square inches x 100 = 30%
Therefore, the photo takes up 30% of the framed area.
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What is the sum of the series?
Σ (2k2 – 4)
k=1
The sum of the series Σ (2k² - 4) from k = 1 to n can be found using the following formula:
Σ (2k² - 4) = [2(1²) - 4] + [2(2²) - 4] + [2(3²) - 4] + ... + [2(n²) - 4]
= 2(1² + 2² + 3² + ... + n²) - 4n
The sum of squares of the first n natural numbers can be calculated using the formula:
1² + 2² + 3² + ... + n² = [n(n + 1)(2n + 1)] / 6
Substituting this value in the above equation, we get:
Σ (2k² - 4) = 2[(n(n + 1)(2n + 1)) / 6] - 4n
= (n(n + 1)(2n + 1)) / 3 - 4n
Therefore, the sum of the series Σ (2k² - 4) from k = 1 to n is (n(n + 1)(2n + 1)) / 3 - 4n.
In right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (s)
In right triangle RST, the value of tan (s) is 12/5.
To find tan(s), we first need to determine which side is opposite angle S and which side is adjacent to angle S.
In this case, RT is the side opposite angle S, and ST is the side adjacent to angle S. Since tangent (x) or tan(x) is defined as the ratio of the length of the opposite side to the length of the adjacent side, we can write the formula for tan(s) as follows:
tan(s) = (opposite side) / (adjacent side)
Now we can plug in the given side lengths to calculate the value of tan(s):
tan(s) = RT / ST
tan(s) = 12 / 5
Thus, tan(s) = 12 / 5.
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What is the solution for 11\31×38\33
Answer:
38/93
Step-by-step explanation:
11/31 x 38/33
11 x 38 = 418
31 x 33 = 1023
= 418/1023
Simplifying
The simplified form of 418/1023 is 38/93.
38/93 is your final answer.
Please help... 100 points promised!
Answer:
Step-by-step explanation:
The probability of drawing 2 red cards from a standard 52-card deck can be calculated as follows:
There are 26 red cards in the deck, so the probability of drawing a red card on the first draw is 26/52.
After the first card is drawn, there are 25 red cards remaining in the deck out of 51 total cards, so the probability of drawing a red card on the second draw is 25/51.
To find the probability of both events happening together (drawing 2 red cards), we multiply the probabilities of each event:
(26/52) * (25/51) = 0.245 or approximately 24.5%
Therefore, the probability of drawing 2 red cards in a standard 52 card deck is approximately 24.5%.
The equation m = 1. 4p represents the mass, m, in grams, of
p polished stones.
We know that the total mass of 5 polished stones would be 7 grams according to this equation
Sure! The equation m = 1.4p represents the mass, m, in grams, of p polished stones.
This means that if you know the number of polished stones, p, you can use this equation to calculate their total mass, m, in grams. For example, if you have 5 polished stones, you can plug in p = 5 and solve for m: m = 1.4 x 5 = 7 grams.
So the total mass of 5 polished stones would be 7 grams according to this equation.
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Based on the equation, the number of grams which the mass increase for every 7 polished stones is: D. 9.8 g.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the mass in grams is given by;
y = mx + c
m = 1.4p
By substituting the given parameter (x = 7 polished stones), we have the following:
m = 1.4(7)
m = 9.8 g
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Manuel types at a rate of 34 words per minute. How many words does he type in 2 minutes?
Manuel can type 68 words in two minutes at a rate of 34 words per minute.
What is the number of words typed in the given time?Given that; Manuel types at a rate of 34 words per minute.
To determine how many words Manuel can type in two minutes, we simply need to multiply his typing rate by the number of minutes he is typing.
Since Manuel is typing for two minutes
Hence;
Number of words = Typing rate × Time
Plugging in the values we have from the problem.
Number of words = 34 words/minute × 2 minutes
Simplifying
Number of words = 34 words × 2
Number of words = 68 words
Therefore, he can type 68 words in two minutes.
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Una carretera recta forma un angulo de 22° con la horizontal dde cierto punto Q en ella el angulo de elevacion del avion en el punto A 57 en el mismo instante dde otro punto Q a 100 m adelante del primero el angulo de elevacion 63 los puntos P Q A quedan en el plano vertical calcule la distancia de P al avion
The distance from P to the airplane is y = x + 100 ≈ 628.38 m.
What is the triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
From a certain point Q on a straight road, which forms an angle of 22° with the horizontal, the angle of elevation of an airplane at point A is 57°. At the same instant from another point Q, 100 meters ahead of the first point, the angle of elevation of the airplane is 63°. The points P, Q, and A are in the same vertical plane. Find the distance from P to the airplane.
To solve the problem, we can use the concept of similar triangles. Let's call H the height of the airplane and x the distance from Q to the airplane. Then, the distance from P to the airplane is given by y = x + 100.
From triangle QA1H, we have:
tan(57°) = H / x
From triangle QA2H, we have:
tan(63°) = H / (x + 100)
Dividing these two equations, we get:
tan(57°) / tan(63°) = x / (x + 100)
Solving for x, we get:
x = 100 * tan(63°) / (tan(63°) - tan(57°)) ≈ 528.38 m
Therefore, the distance from P to the airplane is:
y = x + 100 ≈ 628.38 m.
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Which choice correctly compares two decimals?
A 2.17 > 2.0172.17 > 2.017
B 2.018 > 2.172.018 > 2.17
C 2.16 < 2.0172.16 < 2.017
D 2.17 = 2.017
Answer:
A
Step-by-step explanation:
2.17 > 2.017
because
2.017 = 2 + 17/1000
while
2.17 = 2 + 17/100 = 2 + 170/1000
170/1000 is larger than 17/1000.
for that reason D is wrong, of course.
2.17 is NOT equal to 2.017. 17/1000 is NOT equal to 170/1000.
2.018 = 2 + 18/1000
2.17 = 2 + 17/100 = 2 + 170/1000
also 18/1000 is NOT larger than 170/1000.
2.16 = 2 + 16/100 = 2 + 160/1000
2.017 = 2 + 17/1000
17/1000 are NOT larger than 160/1000.
A garden bed is 4’ by 3’ and a 6’ layer of soil will be spread over the garden. A bag of soil contains 2ft3 of soil how many bags r needed
36 bags of soil are required to spread a 6 feet layer over a garden bed that is 4 feet by 3 feet.
How many bags of soil are required to spread a 4 feet layer over the garden bed?Given information:
The garden bed has a length of 4 feet.
The garden bed has a width of 3 feet.
The layer of soil to be spread over the garden bed is 6 feet.
One bag of soil contains 2 cubic feet of soil.
To find the number of bags of soil required to spread a 6 feet layer over the garden bed, we need to calculate the volume of soil needed and then divide it by the volume of each bag of soil.
The volume of soil needed can be calculated by multiplying the length, width, and height (depth) of the soil:
Volume = length x width x depth
Volume = 4 feet x 3 feet x 6 feet
Volume = 72 cubic feet
This means we need a total of 72 cubic feet of soil to spread a 6 feet layer over the garden bed.
Next, we need to determine the number of bags of soil required. Since each bag contains 2 cubic feet of soil, we can divide the total volume of soil needed by the volume of each bag to get the number of bags required:
Number of bags = Volume of soil needed / Volume of each bag
Number of bags = 72 cubic feet / 2 cubic feet per bag
Number of bags = 36 bags
Therefore, 36 bags of soil are required to spread a 6 feet layer over a garden bed that is 4 feet by 3 feet.
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Find the measure of each arc of ⊙ p, where rt is a diameter.
When rt is a diameter of circle p, it divides the circle into two equal halves. Since the sum of angles in a circle is 360 degrees, each half of circle p measures 180 degrees.
Thus, each arc of circle p that is intersected by diameter rt measures half of the circle or 90 degrees.
Therefore, each arc of circle p measures 90 degrees when rt is a diameter.
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Scott has a rectangular garage that has a length of 234 inches. The width is 1. 5 times shorter than the length. What is the area of his garage?
The area of garage is 36,504 square inches.
The width of Scott's garage is 156 inches (since it is 1.5 times shorter than the length of 234 inches).
so width = 234/1.5
=> 156
To find the area, we multiply the length by the width:
=> 234 inches x 156 inches
=> 36,504 square inches.
To explain, the formula for finding the area of a rectangle is length x width. In this problem, we are given the length of the garage as 234 inches and are told that the width is 1.5 times shorter than the length.
To find the width, we can multiply the length by 1.5 to get 351 inches (which is longer than the length, so we know it must be incorrect). Instead, we need to divide the length by 1.5 to find the width, which gives us 156 inches. Then, we can multiply the length by the width to find the area of the garage, which is 36,504 square inches.
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Ralph has a cylindrical container of parmesan cheese. The diameter of the base of the container is 2. 75 inches, and the height is 6 inches. What is the area of a horizontal cross section of the cylinder to the nearest tenth of a square inch? Use 3. 14 for π
The area of a horizontal cross-section of the cylinder whose diameter is 2.75 inches and height is 6 inches is 5.9 inch².
Diameter of the base of the container = 2.75 inch
Height of the cylinder = 6 inch
Area of a horizontal cross-section of the cylinder = πr²
Here, r = radius of the container
Radius = Diameter/2
Radius = 2.75/2
Radius = 1.375
Area of the horizontal cross-section of the cylinder = 3.14 × 1.375 × 1.375
Area = 5.9365625
Area of the horizontal cross- section of the cylinder to the nearest tenth is 5.9
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If a ball is dropped on the ground from a height of h m, then the ball reaches the ground with the
velocity V=4.43√h m/sec. Find the velocity with which a ball reaches the ground when it is dropped
from a height of 64 m.
The velocity with which a ball reaches the ground when it is dropped
from a height of 64 m is 35.44m/sec
How to determine the valueFrom the information given, we have that the equation representing the velocity of the ball is expressed as;
V = 4.43√h
Given that the parameters of the formula are;
V is the velocity of the ball from he ground.h is the height of the ball.Since the height of the ball from the ground is 64m, we have to substitute the value, we have;
V = 4.43√64
Find the square root of the value
V= 4.43(8)
Now, multiply both the values to determine the velocity, we get;
V = 35.44m/sec
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If a, b and c are distinct real numbers, prove that the equation(x−a)(x−b)+(x−b)(x−c)+(x−c)(x−a=0has real and distinct roots.
Answer:
Step-by-step explanation:
skating Dinero broke 1p revision yahoo d10
PLEASE HELP ( I CAN GIVE BRAINLIEST)
Answer:
x = √(6^2 + 18^2) = √(36 + 324) = √360
= 6√10
Answer:
[tex]x = 6\sqrt{10}[/tex]
Step-by-step explanation:
You can find the height using [tex]c^2 = a^2 + b^2[/tex] formula.
[tex](6\sqrt{2})^2 = 6^2 + b^2.[/tex]
[tex]b^2 = 72-36=36.[/tex]
[tex]b=6.[/tex]
You can find x using the same formula.
[tex]x^2 = 6^2 + 18^2 = 360.[/tex]
[tex]x = 6\sqrt{10}[/tex]
Find the critical point and determine if the function is increasing or decreasing on the given intervals. y = x2 - 4x?, x>0 (Use decimal notation. Give your answer to three decimal places.) critical point c= _____
The critical point is c = 2, the function is decreasing on the interval 0 < x < 2, and increasing on the interval x > 2.
To find the critical point of the function y = x^2 - 4x, we first need to find its derivative, which represents the slope of the tangent line at any point on the curve.
The derivative of y with respect to x is:
y' = 2x - 4
Now, we need to find the critical points, which occur where the derivative is zero or undefined. In this case, the derivative is a polynomial, so it is never undefined. To find where it equals zero, we set y' equal to zero:
0 = 2x - 4
Solving for x, we get:
x = 4/2 = 2
So, the critical point is c = 2.
Now, we need to determine if the function is increasing or decreasing on the interval x > 0. To do this, we can analyze the sign of the derivative. If y' > 0, the function is increasing; if y' < 0, the function is decreasing.
For x > 2 (to the right of the critical point), the derivative y' = 2x - 4 is positive (since 2x > 4 when x > 2). Therefore, the function is increasing on the interval x > 2.
For x < 2 (to the left of the critical point), the derivative y' = 2x - 4 is negative (since 2x < 4 when x < 2). Therefore, the function is decreasing on the interval 0 < x < 2.
In summary, the critical point is c = 2, the function is decreasing on the interval 0 < x < 2, and increasing on the interval x > 2.
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A telephone calling card company allows for $0.25 per minute plus a one-time service charge of $0.75. If the total cost of the card is $5.00, find the number of minutes you can use the card.
The number of minutes you can use the card is 9 minutes
Finding the number of minutes you can use the card.From the question, we have the following parameters that can be used in our computation:
Allows for $0.25 per minute One-time service charge of $0.75.Using the above as a guide, we have the following:
f(x) = 0.25x + 0.75
If the total cost of the card is $5.00, the number of minutes you is
0.25x + 0.75 = 5
So, we have
0.25x = 4.25
Divide by 0.25
x = 9
Hence, the number of minutes is 9
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