To find the derivative of y = cos(sin(14x-13)), we will use the chain rule.
Let's start by defining two functions:
u = sin(14x-13)
v = cos(u)
We can now apply the chain rule:
dy/dx = dv/du * du/dx
First, let's find dv/du:
dv/du = -sin(u)
Next, let's find du/dx:
du/dx = 14*cos(14x-13)
Now we can put it all together:
dy/dx = dv/du * du/dx
dy/dx = -sin(u) * 14*cos(14x-13)
But we still need to substitute u = sin(14x-13) back in:
dy/dx = -sin(sin(14x-13)) * 14*cos(14x-13)
So the derivative of y = cos(sin(14x-13)) is:
dy/dx = -14*sin(sin(14x-13)) * cos(14x-13)
To find the derivative of the function y = cos(sin(14x - 13)), we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
Let u = sin(14x - 13), so y = cos(u). Now we find the derivatives:
1. dy/du = -sin(u)
2. du/dx = 14cos(14x - 13)
Now, using the chain rule, we get:
dy/dx = dy/du × du/dx
dy/dx = -sin(u) × 14cos(14x - 13)
Since u = sin(14x - 13), we can substitute back in:
dy/dx = -sin(sin(14x - 13)) × 14cos(14x - 13)
To learn more about derivative visit;
/brainly.com/question/30365299
#SPJ11
A soccer field (football pitch) has a length of 102. 9 m and a width of 66. 3 m. Find the total area of the field in square meters (m2) and convert this measurement to square yards (yd2). Use the fact that 1 yard = 0. 9144 m. Round your answer to the nearest whole number
The total area of the soccer field is approximately 8150 square yards.
We'll find the total area of the soccer field in square meters first, and then convert it to square yards using the conversion factor provided.
Find the area in square meters (m²):
Area = Length × Width
Area = 102.9 m × 66.3 m
Area ≈ 6816.47 m²
Convert the area to square yards (yd²):
Use the conversion factor: 1 yard = 0.9144 meters
1 m² = (1/0.9144)² yd²
1 m² ≈ 1.19599 yd²
Now, multiply the area in m² by the conversion factor to get the area in yd²:
Area ≈ 6816.47 m² × 1.19599 yd²/m²
Area ≈ 8150 yd² (rounded to the nearest whole number).
For similar question on area.
https://brainly.com/question/17335144
#SPJ11
What is the volume of this oblique cone?
well, according the Cavalieri's Principle, the volume of the oblique cone will be the same volume as the non-oblique cone, so
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=9\\ h=16 \end{cases}\implies V=\cfrac{\pi (9)^2(16)}{3}\implies V=432\pi ~cm^3[/tex]
A national grocery chain is considering expanding their selection of prepared meals available for purchase. They believe that nationwide, 67 percent of households purchase at least one prepared meal per week from the grocery store. The results of a survey given to a random sample of Maryland households found that 641 out of 1,035 households purchase at least one meal per week at the store
Based on the survey results from Maryland households, approximately 62 percent (641/1,035) of households in Maryland purchase at least one prepared meal per week from the grocery store.
To determine if the national grocery chain should expand their selection of prepared meals, we need to compare the nationwide percentage of households that purchase at least one prepared meal per week (67%) with the percentage of Maryland households that do the same.
Here's a step-by-step explanation:
1. Calculate the percentage of Maryland households that purchase at least one prepared meal per week by dividing the number of households that do (641) by the total number of households surveyed (1,035).
Percentage of Maryland households = (641 / 1,035) * 100= 62%
2. Compare the percentage of Maryland households with the nationwide percentage (67%).
Based on the survey results from Maryland households, approximately 62 percent (641/1,035) of households in Maryland purchase at least one prepared meal per week from the grocery store.
This is slightly lower than the national estimate of 67 percent. However, it is still a significant portion of households and suggests that expanding the selection of prepared meals could be a viable option for the national grocery chain in Maryland.
To know more about survey results refer here:
https://brainly.com/question/19618591
#SPJ11
Larry went to Home Depot and buck 32 ft.² of treated plywood for $50 and 40 ft.² a regular plywood for $64 how much more does the treated plywood cost in the regular plywood in dollars per foot 
If Larry went to Home Depot and buck 32 ft.² The amount the treated plywood cost in the regular plywood in dollars per foot is: -$1.80 per foot
What is the cost?Treated plywood cost per square foot:
50 / 32
= $1.5625 per square foot
Regular plywood cost per square foot:
64 / 40
= -$1.60 per square foot
Difference in cost per square foot
1.5625 - 1.60
= -$0.0375 per square foot
Difference in cost per foot is:
(-$0.0375 / 0.0208)
≈ $1.80 per foot
Therefore based on the above calculation it treated plywood costs $1.80 less per foot than the regular plywood.
Learn more about cost here:https://brainly.com/question/28147009
#SPJ1
Kaleb’s mom owns a confidence store. He is helping her replace the tile floor. The tile costs $2.00 per ft squared.
How much will the tile cost?
Answer:
425
Step-by-step explanation:
212,5*2=425
A cuboid has a volume of 1815 cm³. Each side of the cuboid is a whole number of centimetres and each side is longer than 1 cm. Find all the possible dimensions of the cuboid
There are 4 possible sets of dimensions for the cuboid with a volume of 1815 cm³.
How to solve for the dimensionsFirst, find the prime factors of 1815:
1815 = 3 × 5 × 11 × 11
Now, we need to find all possible combinations of these factors into three whole numbers. Each combination of three numbers, when multiplied, should give 1815. We can do this by finding the different ways the prime factors can be distributed among the three dimensions:
3 × 5 × (11 × 11) = 15 × 121 (height × width × length)
3 × 11 × (5 × 11) = 33 × 55
5 × 11 × (3 × 11) = 55 × 33
11 × 11 × (3 × 5) = 121 × 15
We have found 4 different sets of dimensions for the cuboid:
15 × 121 × 1
33 × 55 × 1
55 × 33 × 1
121 × 15 × 1
There are 4 possible sets of dimensions for the cuboid with a volume of 1815 cm³.
Read more on cuboid here:https://brainly.com/question/26403859
#SPJ4
I NEED HELP ON THIS ASAP! PLEASE IT'S DUE TODAY, I WILL GIVE BRAINLIEST!!
Answer:
Function A: f(x) = -8^x
Function B: f(x) = 2^x
Function A has a greater horizontal asymptote. As x approaches negative infinity, Function A approaches y = 0 faster than Function B.
PLS HELP____________
Answer:
the answer is the 1st one
2+2=4
3+1=4
4+0 = 4
Hey guys, i need your help!
a carnival game features a flip of a special coin and a roll of a number cube. the coin has a 3 on one side and a 7 on the other. the number cube contains the numbers 1-6. a player flips the coin then roll the number cube. determine each probability: (as a whole %)
please provide instructions; i am so lost, haha.
In this carnival game, a player flips a coin that has a 3 on one side and a 7 on the other, and then rolls a number cube that has numbers 1-6.
To determine the probabilities, we need to analyze each event separately and then use the multiplication rule of probability to find the probability of both events happening together.
The probability of getting a 3 on the coin is 50%, since there are only two possible outcomes. The probability of rolling each number on the cube is 16.67%, since the cube has six sides.
The probability of both events happening together depends on the individual probabilities and is found by multiplying them. Finally, we can use the addition rule of probability to find the probability of either event happening.
To know more about carnival game refer here
https://brainly.com/question/29155909#
#SPJ11
TEXT ANSWER
Use the multiplication rule to simplify:
b7 . b²
Tip: When writing math questions, the coefficient would go in front of variables: 7b*[tex]b^2[/tex]
Anyways, in this case, since we cannot mutiply 7 by b, the 7 will stay put
But.... we can mutiply b by b
[tex]b^2[/tex][tex]*b[/tex]=b^3
Tip: B's with no exponent has an exponent with one
Questions?
So,7 will stay put and b and b^2 will simply to b^3
[tex]7b^3[/tex]=Answer
En un viaje en mula hacia el pico duarte el jinete observa en un poste 1, 290 m sobre el nivel del mar , luego de 5 horas de camino presta atencion a otro poste que indica , 2, 480 m sobre el nivel de mar. ¿ cual ha sido su desplazamiento en direccion vertical?
The vertical displacement of the mule comes out to be the difference between the final and the initial position which is 1190 m.
The displacement refers to the distance between the final and the initial position of an object. It is the shortest distance between these points is the displacement of the object. It is a vector quantity.
Vector quantity refers to the measurement in which both magnitude and direction are considered.
Starting point = 1290 m
Final point = 2480 m
Displacement = 2480 - 1920
= 1190 m
1190 m is the vertical displacement of the mule when traveling from one post to another.
Learn more about Displacement:
https://brainly.com/question/28370322
#SPJ4
The question is in Spanish and when translated to English, it is:
On a mule trip to Duarte Peak, the rider observes a post 1,290 m above sea level, after 5 hours of walking he pays attention to another post that indicates 2,480 m above sea level. What has been its displacement in the vertical direction?
Find the Surface Area of the triangular Prism below:
Answer:
≈ 12,78 m^2
Step-by-step explanation:
The surface area is equal to the sum of the areas of all the sides
This figure has sides of 2 triangles (bases) and 3 rectangles (lateral surface)
h (triangle) = 1m
We can find the base of the triangle by using the Pythagorean theorem (multiply by 2, because the triangle's base contains two of these identicals sides)
[tex](( {1.5})^{2} - {1}^{2} ) \times 2=( 2.25 - 1 ) \times 2= 1.25 \times 2 = 2.5> 0[/tex]
The triangle's base is equal to:
[tex] \sqrt{2.5} = \frac{ \sqrt{10} }{2} [/tex]
First, let's find the area of 2 bases (triangles):
[tex]a(bases) = 2 \times \frac{1}{2} \times 1 \times \frac{ \sqrt{10} }{2} = \frac{ \sqrt{10} }{2} [/tex]
Now, we can find the whole surface area by adding the areas of the rectangles to the bases' areas:
[tex]a(surface) = \frac{ \sqrt{10} }{2} + 2.4 \times 2 + 1.5 \times 2 + 1.7 \times 2 = \frac{ \sqrt{10} }{2} + \frac{56}{5} ≈12.78[/tex]
Use the function f(t) = -16t^2 + 60t + 16 to answer parts A, B, and C.
(Look at the image!)
1) Note that t is either 4 or -0.25 by virtue of the quadratic function.
2) the vertex and line of summer try are t = 1.875. See the attached graph.
How did we arrive at the above conclusion?
First, identify the values of a, b, and c in the equation...
a = -16
b = 60
c = 16
substitute these values into the quadratic formula
t = (-b ± √(b² - 4ac)) / 2a
t = (-60 ± √(60² - 4(-16)(16))) / 2(-16)
t = (-60 ± √(3600 + 1024)) / (-32)
t = (-60 ± √(4624)) / (-32)
t = (-60 ± 68) / (-32)
So, t can be:
t = (-60 + 68) / (-32) = -1/4
or
t = (-60 - 68) / (-32) = 4
2) To find the line of symmetry, we used t = -b/2a
-60/2(-16)
t = 1.875
Learn more about line of symmetry:
https://brainly.com/question/30963765
#SPJ1
In a survey of 175 females ages 16 to 24 who have completed
high school during the past 12 months, 72% were enrolled in college. In
survey of 160 males ages 16 to 24 who have completed high school during the
past 12 months, 65% were enrolled in college. At a = 0. 01, can you reject
the claim that there is no difference in the proportion of college enrollees
between the two groups?
There is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.
To determine if the difference in proportions is statistically significant or if it could be due to chance.
We will conduct a hypothesis test. Our null hypothesis (H₀) is that there is no difference in the proportion of college enrollees between females and males. Our alternative hypothesis (H₁) is that there is a difference in the proportion of college enrollees between females and males.
We can use a two-sample z-test to test this hypothesis. The formula for the test statistic is:
z = (p₁ - p₂) / √(p'* (1 - p') * ((1 / n₁) + (1 / n₂)))
where p₁ and p₂ are the sample proportions, p' is the pooled proportion, n₁ and n₂ are the sample sizes.
Given, p₁ = 0.72, p₂ = 0.65, n₁ = 175, n₂ = 160
p' = (x₁ + x₂) / (n₁ + n₂)
x₁ = 126 (0.72 * 175) and x₂ = 104 (0.65 * 160).
p' = (126 + 104) / (175 + 160) = 0.684
By applying the above values we get,
z = (0.72 - 0.65) / √(0.684 * (1 - 0.684) * ((1 / 175) + (1 / 160))) ≈ 2.11
The critical value for a two-tailed test with alpha = 0.01 is approximately ±2.58. Since our calculated z-value (2.11) is less than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant difference in the proportion of college enrollees between females and males.
Therefore, there is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.
To know more about Proportion here
https://brainly.com/question/31319397
#SPJ4
Please help me with this page I’m so confused
Answer:
f(0) = 1
g(-2) = 3
f(-7)= und
g(4) x f(3) = -2 x 0 = 0
g(-4) = 2
g(x) = 0 --> x = 6, 0.5
f(x) = -1 --> x = -3, 5
f(g(3)) = f(-3) = -1
g(f(-2) = g(0) = -3
f(g(1)) = f(-3) = -1
f(g(5)) = f(-1) = 1
g(f(-4)) = g(-2) = 2
g(g(-6)) = g(4) = -2
g(f(0)) = g(1) = -3
g(f(-6)) = und
Step-by-step explanation:
In order to find the first group, such as f(0), you want to look at the f graph and find 0 on the x-axis. Wherever the y coordinate is will be the correct answer.
To find one such as f(g(3)), you want to dissect it like it is 2 problems. First, we want to find g(3) which is -3. Then we will find -3 on the f graph and find the answer with that y-coordinate.
(1 point) Consider the power series 00 Σ (-4)" -(x + 6)". n=1 Vn Find the radius of convergence R. If it is infinite, type "infinity" or "inf", Answer: R= What is the interval of convergence? Answer
The radius of convergence R is 1/4 and the interval of convergence is (-6.25, -5.75) for the power series
∑((-4[tex])^n[/tex]) * (-(x + 6[tex])^n[/tex]) / sqrt(n)
To find the radius of convergence (R) and interval of convergence for the power series ∑((-4[tex])^n[/tex]) * (-(x + 6[tex])^n[/tex]) / sqrt(n)
where n starts from 1 to infinity,
We can use the Ratio Test.
Step 1: Apply the Ratio Test
We want to find the limit as n approaches infinity of the absolute value of the (n+1)th term divided by the nth term:
lim (n→∞) |((-4[tex])^{(n+1)[/tex] * (-(x + 6)^(n+1)) / sqrt(n+1)) / ([tex](-4)^n[/tex] * (-(x + 6[tex])^n[/tex]) / sqrt(n))|
Step 2: Simplify the expression
The limit simplifies to:
lim (n→∞) |((-4)(x + 6))/sqrt((n+1)/n)|
Step 3: Find when the limit is less than 1
For the series to converge, the limit must be less than 1:
|(-4)(x + 6)| / sqrt((n+1)/n) < 1
As n approaches infinity, (n+1)/n approaches 1, so the expression simplifies to:
|-4(x + 6)| < 1
Step 4: Determine the radius of convergence (R)
Divide both sides by 4:
|-(x + 6)| < 1/4
The radius of convergence, R, is 1/4.
Step 5: Determine the interval of convergence
To find the interval of convergence, solve for x:
-1/4 < (x + 6) < 1/4
-1/4 - 6 < x < 1/4 - 6
-6.25 < x < -5.75
Thus, the interval of convergence is (-6.25, -5.75).
In summary, the radius of convergence R is 1/4 and the interval of convergence is (-6.25, -5.75).
To know more about Power series:
https://brainly.com/question/29888415
#SPJ11
Use this information for Ms. Yamagata is going to tile the floor of her rectangular bathroom that is 9 feet long and 73 feet wide. The cost per 6-inch tile is $0. 50. The cost per 18-inch tile is $2. 75. 4. If Ms. Yamagata uses 6-inch tiles, what are the least number of tiles that she needs to buy to cover the floor? оâ
Ms. Yamagata needs to buy at least 2628 6-inch tiles to cover the floor of her rectangular bathroom.
To determine the least number of 6-inch tiles Ms. Yamagata needs to buy to cover her 9 feet long and 73 feet wide bathroom floor, follow these steps:
1. Convert the dimensions of the bathroom to inches, as the tiles are measured in inches:
9 feet * 12 inches/foot = 108 inches long
73 feet * 12 inches/foot = 876 inches wide
2. Determine the total area of the bathroom in square inches:
Area = length * width = 108 inches * 876 inches = 94,608 square inches
3. Calculate the area of a single 6-inch tile:
Area = length * width = 6 inches * 6 inches = 36 square inches
4. Divide the total area of the bathroom by the area of a single tile to find the least number of tiles needed:
Number of tiles = total area / tile area = 94,608 square inches / 36 square inches ≈ 2,628.56
Since Ms. Yamagata cannot buy a fraction of a tile, she needs to buy at least 2,629 6-inch tiles to cover her bathroom floor.
learn more about "Area" :- https://brainly.com/question/25292087
#SPJ11
A pet store owner has huge aquarium tanks of the same size, A and B.
Tank A has 2 feet of water and is filled at a rate of 2. 2 inches per minute.
Tank B has 8 feet of water and is filled at a rate of 5 inches per minute.
Tank B fills faster than Tank A, taking approximately 1.75 minutes to fill while Tank A takes approximately 1.14 minutes.
How long will it take for each tank to completely drain?The problem presents two aquarium tanks, A and B, which are of the same size but have different water levels and fill rates. Tank A has 2 feet of water and is being filled at a rate of 2.2 inches per minute, while Tank B has 8 feet of water and is being filled at a faster rate of 5 inches per minute. The goal is to determine how long it will take to fill each tank.
To solve this problem, we need to use the formula: Time = Volume / Rate. We know that the volume of each tank is the same, so we can set up two equations:
For Tank A: Time = (2 feet * 12 inches/foot) / 2.2 inches/minute = 10.91 minutes or approximately 1.14 minutes.
For Tank B: Time = (8 feet * 12 inches/foot) / 5 inches/minute = 19.2 minutes or approximately 1.75 minutes.
Therefore, Tank A will take approximately 1.14 minutes to fill, while Tank B will take approximately 1.75 minutes to fill. It is important to note that Tank B is being filled at a faster rate than Tank A, despite having a greater volume of water.
Learn more about aquarium tanks
brainly.com/question/18597048
#SPJ11
Geometry!! will mark brainliest if correct!!!
Sierra is constructing an inscribed square. Keaton is constructing an inscribed regular hexagon. In your own words, describe one difference between Sierra's construction steps and Keaton's construction steps
The main difference is that Sierra needs to create two equal arcs, while Keaton needs to create six equal arcs to form the vertices of their respective shapes.
For Sierra's inscribed square:
1. Draw a circle with a compass.
2. Mark a point on the circle as one vertex of the square.
3. Draw a diameter passing through the marked point.
4. Use the compass to create two equal arcs, one on each end of the diameter, intersecting the circle.
5. Connect the intersection points to create the square.
For Keaton's inscribed regular hexagon:
1. Draw a circle with a compass.
2. Mark a point on the circle as one vertex of the hexagon.
3. Use the compass to create six equal arcs around the circle, each arc intersecting the end of the previous arc.
4. Connect the intersection points to create the hexagon.
The main difference is that Sierra needs to create two equal arcs, while Keaton needs to create six equal arcs to form the vertices of their respective shapes.
Learn more about "intersection points":-https://brainly.com/question/11337174
#SPJ11
Simplify −2r(−16r + 3r − 18). −26r2 − 36r 26r2 + 36 26r2 + 36r −26r2 + 36r
Answer:
26r^2 + 36r.
Step-by-step explanation:
In the following equation, what is the value of c?
8^c = (8^-4)^5
Consider the function f(x,y,z) = 1 + 2xyz, the point P(-1,-1,-1), and the unit vector u = (1/√3, -1/√3, -1/√3)
a. Compute the gradient off and evaluate it at P. b. Find the unit vector in the direction of maximum increase off at P.
The unit vector in the direction of maximum increase of f(x,y,z) at P is:
v = (∇f(-1,-1,-1)) / ||∇f(-1,-1,-1)|| = (2/2√3, 2/2√3, 2/2√3) = (√3/3, √3/3, √3/3)
a. The gradient of f(x,y,z) is given by the vector ∇f(x,y,z) = (∂f/∂x, ∂f/∂y, ∂f/∂z). Using the partial derivative rules, we have:
∂f/∂x = 2yz
∂f/∂y = 2xz
∂f/∂z = 2xy
Therefore, the gradient of f(x,y,z) is:
∇f(x,y,z) = (2yz, 2xz, 2xy)
Evaluating this at P(-1,-1,-1), we get:
∇f(-1,-1,-1) = (2(-1)(-1), 2(-1)(-1), 2(-1)(-1)) = (2,2,2)
b. The unit vector in the direction of maximum increase of f(x,y,z) at P is given by the unit vector in the direction of ∇f(-1,-1,-1). Since ∇f(-1,-1,-1) = (2,2,2), the unit vector in the direction of ∇f(-1,-1,-1) is:
v = (∇f(-1,-1,-1)) / ||∇f(-1,-1,-1)||
where ||∇f(-1,-1,-1)|| is the magnitude of the gradient vector, which is:
||∇f(-1,-1,-1)|| = sqrt((2)^2 + (2)^2 + (2)^2) = 2√3
Therefore, the unit vector in the direction of maximum increase of f(x,y,z) at P is:
v = (∇f(-1,-1,-1)) / ||∇f(-1,-1,-1)|| = (2/2√3, 2/2√3, 2/2√3) = (√3/3, √3/3, √3/3)
To learn more about unit vector visit: https://brainly.com/question/30279109
#SPJ11
Randomly meeting a -child family with either exactly one or exactly two children
Considering the function f(x) = x(x-4), if the point (2+c, y) is on the graph of f(x), then the following point will also be on the graph of f(x): (2-c, y). Explanation: Since f(x) is symmetric with respect to the vertical line x = 2 (due to the fact that f(x) = x(x-4) = (x-2+2)(x-2) = (x-2)^2 - 2^2), if the point (2+c, y) is on the graph, then its symmetric counterpart, (2-c, y), will also be on the graph.
About functionThe definition of a function in mathematics can also be interpreted as a relation that connects each member of x in a set called the domain with a single value f(x) from a second set called the codomain.
Learn more about Function at https://brainly.com/question/29162580
#SPJ11
whats the area for the figure below??
Answer:
68in
Step-by-step explanation:
square: 3x3=9
9+9= 18
trapezoid (centre area) : 7x3x5=25
25x2=50
50+18=68
not entirely sure abt this
HELP!!
What will most likely happen in the absence of a vacuole?
Photosynthesis will not take place.
Genetic information will not be transmitted by the cell.
Energy will not be released during cellular respiration.
The cell will not store food, water, nutrients, and waste.
Answer:
if vacuole are absent in plant cell then there is no storage of food and ions in the process of and permeability of cell may be distorted
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
The dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
Let's start by finding the formula for the cost of the container in terms of its dimensions.
The volume of the cylinder is given as 600 cubic centimeters, so we have:
πr^2h = 600
where r is the radius of the cylinder and h is its height. Solving for h, we get:
h = 600 / (πr^2)
The surface area of the cylinder is given by:
A = 2πrh + 2πr^2
Substituting h in terms of r, we get:
A = 2πr(600/(πr^2)) + 2πr^2
= 1200/r + 2πr^2
The cost of the container is the sum of the cost of the styrofoam sides and bottom and the cost of the paper top. Let's call the radius of the paper top R, and assume that the height of the cylinder is greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Then the cost of the container is:
C = 0.04(2πrh + πr^2) + 0.05(πR^2)
Substituting h in terms of r, we get:
C = 0.08πr(600/(πr^2)) + 0.04πr^2 + 0.05πR^2
= 4.8/r + 0.04πr^2 + 0.05πR^2
To minimize the cost, we need to find the values of r and R that minimize the cost function C. To do this, we take the partial derivatives of C with respect to r and R, and set them equal to zero:
dC/dr = -4.8/r^2 + 0.08πr = 0
dC/dR = 0.1πR = 0
Solving for r and R, we get:
r = ∛(60/π) ≈ 2.78 cm
R = 2.5 cm
We can check that these values give us a minimum by checking the second derivatives:
d^2C/dr^2 = 9.6/r^3 + 0.08π > 0 (minimum)
d^2C/dR^2 = 0.1π > 0 (minimum)
Therefore, the dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
To learn more about second derivatives visit: https://brainly.com/question/29090070
#SPJ11
00 13. Suppse that an is a convergent series with known sum L. Let S = ax be then the partiul sum for this series. a) (a) Find lim S. +00 (b) Find limo 0. (e) Find lim S. d) Find lim 100T 0
Partial sums are:
a) limx→∞ S = L
b) The limit does not exist.
c) limx→∞ S = L
d) The limit does not exist.
We need to use the formulas for partial sums and limits of sequences.
First, recall that the nth partial sum of a series is given by:
Sn = a1 + a2 + ... + an
And the limit of a sequence (if it exists) is given by:
limn→∞ an
Now, let's use these formulas to answer the parts of the question:
a) Find lim S as n approaches infinity:
We have:
S = ax = a1 + a2 + a3 + ... + ax
Taking the limit as x approaches infinity, we get:
limx→∞ S = limx→∞ (a1 + a2 + a3 + ... + ax) = limn→∞ Sn
But we know that the series is convergent, so the limit of the partial sums exists and is equal to the sum of the series:
limn→∞ Sn = L
Therefore:
limx→∞ S = L
b) Find lim as x approaches 0:
We have:
S = ax = a1 + a2 + a3 + ... + ax
Taking the limit as x approaches 0, we get:
limx→0 S = limx→0 (a1 + a2 + a3 + ... + ax)
But as x approaches 0, the number of terms in the sum approaches infinity, so this limit does not exist.
c) Find lim S as x approaches infinity:
We have:
S = ax = a1 + a2 + a3 + ... + ax
Taking the limit as x approaches infinity, we get:
limx→∞ S = limx→∞ (a1 + a2 + a3 + ... + ax) = limn→∞ Sn
Again, we know that the limit of the partial sums exists and is equal to the sum of the series:
limn→∞ Sn = L
Therefore:
limx→∞ S = L
d) Find lim as x approaches 100:
We have:
S = ax = a1 + a2 + a3 + ... + ax
Taking the limit as x approaches 100, we get:
limx→100 S = limx→100 (a1 + a2 + a3 + ... + ax)
But as x approaches 100, the number of terms in the sum approaches infinity, so this limit does not exist.
Learn more about convergent series.
brainly.com/question/15415793
#SPJ11
Dan's small business earned about $85,000 this year. Based on data from similar businesses, Dan expects his annual earnings to increase by 12% each year. Write an exponential equation in the form y=a(b)x that can model Dan's annual earnings, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = _____ To the nearest hundred dollars, how much is Dan's small business predicted to earn in 5 years?
The equation would be written as: y = $85,000(1 + 0.12/1)^5
Then the predicted earning would be y = $132,559
How to solve for the earningy=a(b)x
where y = income
a = $85,000
b = (1 + r = percent increase)
then x = time period = 5 years
When we put in the values we would have y = $85,000(1 + 0.12/1) ^5
The exponential function of the form y = a(b)^x is: y = $85,000(1 + 0.12/1) ^5
When we solve the above, we would have the income = y = $132,559
Therefore the predicted earnings that Dans small business would have in a period of five years is equal to $132,559
Read more on exponential equation here:https://brainly.com/question/2456547
#SPJ1
a
particle moves along a path in the xy-plane. the path is given by
the parametric equations x(t)=sin(3t) and y(t)=cos(3t), help with
steps A-E
a. Find the velocity b. Find the acceleration. c. Find the speed and simplify your answer completely. d. Find any times at which the particle stops. Thoroughly explain your answer. e. Use calculus to
The given set of questions are solved under the condition of parametric equations x(t)=sin(3t) and y(t)=cos(3t) .
Hence, the length of the curve from t= 0 to t= π is 3π.
Now,
A. To evaluate the velocity, we need to perform the derivative of x(t) and y(t) concerning t.
x'(t) = 3cos(3t)
y'(t) = -3sin(3t)
Therefore, the velocity vector is
v(t) = <3cos(3t), -3sin(3t)>
B. To define the acceleration, we need to evaluate the derivative of v(t) concerning t.
a(t) = v'(t) = <-9sin(3t), -9cos(3t)>
C. To describe the speed, we need to calculate the magnitude of the velocity vector.
|v(t)| = √((3cos(3t))² + (-3sin(3t))²)
= 3
D. In order to find the number of times at which the particle stops, to find when the speed is equal to zero.
|v(t)| = 0 when cos(3t) = 0
sin(3t) = 0.
Therefore,
cos(3t) = 0 when t = (π/6) + (nπ/3),
here n = integer.
sin(3t) = 0 when t = (nπ/3),
here n = integer.
E. To calculate the length of the curve from t=0 to t=π by performing calculus
L = ∫[a,b] √((dx/dt)² + (dy/dt)²) dt
Therefore, a=0 and b=π.
L = ∫[0,π] √((3cos(3t))² + (-3sin(3t))²) dt
= ∫[0,π] 3 dt
= 3π
The given set of questions are solved under the condition of parametric equations x(t)=sin(3t) and y(t)=cos(3t) .
Hence, the length of the curve from t=0 to t=π is 3π.
To learn more about parametric equations,
https://brainly.com/question/30451972
#SPJ4
The complete question is
A particle moves along a path in the xy-plane. the path is given by
the parametric equations x(t)=sin(3t) and y(t)=cos(3t), help with
steps A-E
a. Find the velocity
b. Find the acceleration.
c. Find the speed and simplify your answer completely.
d. Find any times at which the particle stops. Thoroughly explain your answer.
e. Use calculus to find the length of the curve from t=0 to t = π , show your work.
This coordinate plane represents an area on a golf course. A sand hazard is located at (4, 6) and a water hazard is located at (7, 2).
Plot a point at each of the two locations. Plot only two points.
Answer:
See attached
Step-by-step explanation:
You want a graph with points plotted at (4, 6) and (7, 2), representing a sand trap and a water hazard, respectively.
CoordinatesThe ordered pair (4, 6) represents the coordinates (x, y). The x-coordinate is the number of units right of the point x=0, and the y-coordinate is the number of units up from y=0.
Both points have positive coordinates for both x and y, so will be located up and right from the origin. The plot is shown in the attachment.
<951414049393>