To solve this problem let us say that,
h = height of the can
r = radius of the can
We try to minimize the amount of metal used which is the surface area (SA), and the equation for a cylinder is:
SA = 2πrh + πr^2
To get the minima, we take the derivative of this function and set it equal to 0. But first, the function is in two variables so we must eliminate one of them. We use the extra information given in the problem which is volume:
V = 8π = πr^2 h
Therefore,
h = 8/r^2
Plug this into the SA function to have it in terms of one variable only:
SA = 2πrh + πr^2
SA = 2πr(8/r^2) + πr^2
SA = 16π/r + πr^2
Taking the 1st derivative of the function:
0 = −16π r^−2 + 2πr
0 = −16π/r^2 + 2πr
16π/r^2 = 2πr
r^3 = 8
r = 2 in
By obtaining r, we calculate for h:
h = 8/r^2
h = 8/(2)^2
h = 8 / 4
h = 2 in (ANSWER)
Pedro has created the function f(x)= 4x-3/2 to represent the number of assingments he has completed where x represents the number of weeks in the course Person discovers that using the inverse function to solve for x=30, he can predict when he will have 30 assignments completed explain to Pedro how to accomplish this using complete sentences
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
Answer:
An expression can be used to find the value of y when x is 2 is,
y=8x ; Value of y = 16 when x = 2
Step-by-step explanation:
Direct variation states:
If y varies directly as x
⇒[tex]y \propto x[/tex]
then the equation is in the form of:
[tex]y = kx[/tex] where, k is the constant of variation.
As per the statement:
If y varies directly as x, and y is 48 when x is 6.
⇒[tex]y = kx[/tex]
y = 48 when x = 6
Substitute the given values in [1] and solve for k we have;
[tex]48= 6k[/tex]
Divide both sides by 6 we have;
8 = k
or
k = 8
Then, an equation we have;
y =8x ....[2]
We have to find value of y when x is 2.
Substitute the value of x = 2 in [2] we have;
[tex]y = 8(2) = 16[/tex]
Therefore, an expression can be used to find the value of y when x is 2 is,
y=8x and Value of y = 16 when x = 2
Three different circles and one line intersect each other.What is the largest possible number of intersection points
The largest possible number of intersection points between three different circles and one line is 12. This is calculated by considering that a line can intersect each circle at two points and each pair of circles can intersect at two points.
Calculating the Maximum Number of Intersection Points
To determine the largest possible number of intersection points between three different circles and one line, we can analyze the intersections one circle can have with a line and with another circle. A line can intersect a circle at most at two points - where it enters and exits the circle. Therefore, one line can intersect three circles at a maximum of 2 points per circle, totaling 6 points for the line intersections.
As for circle to circle intersections, each pair of circles can intersect at most at two points. With three circles, we can form three distinct pairs (Circle 1 with Circle 2, Circle 1 with Circle 3, and Circle 2 with Circle 3). Each pair can contribute up to 2 points of intersection, which gives us 6 points for the circle intersections.
Combining both types of intersections, we have a total possible number of intersections of 6 (from the line) + 6 (from the circles) = 12. Therefore, the maximum number of intersection points is 12.
What is the sum of the measures of the exterior angles in a heptagon? Explain
Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
Angle c and angle d are supplementary, the measure of angle d is eight times the measure of angle
c. find measure of angle c and measure of angle d
Answer:
160
Step-by-step explanation:
The point P(12, 16) is on the terminal side of θ. Evaluate tan θ.
Answer:
tan(θ)=4/3
Step-by-step explanation:
Since opposite leg of the reference triangle equals 16 and the adjacent leg equals 12, tan(θ)=16/12 simplified to tan(θ)=4/3.
In attachment, help please 1 QUESTION, BRAINLIEST GETS 20 PTS
Answer:
Above is the right answer he got here first so give him brainiest
In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Because C is the centroid, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40
A bus averages 60 mi/h traveling to its destination in the first half of its trip through an expressway and 72 mi/h in the second half traveling through a motorway. What is the bus's average speed for the entire trip rounded to the nearest tenth?
A) 64.2 mi/h
B) 63.0 mi/h
C) 65.5 mi/h
D) 66.0 mi/h
Answer:
The correct answer is 65.5 mi/h
Hope this helps :)
Anita and Joelle bowled together and their combined total score for one game was 425 points. Anita’s score was 40 less than twice Joelle’s. What were their scores? Write a system of equations to model the problem if x represents Joelle’s score and y represents Anita’s score.
Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.
Answer: f(x) = -1/4x² -x + 4
y varies inversely with x
k = 0.6
What is the value of x when y is 0.6?
to find X when K is known
divide K by Y
0.6/0.6 = 1
X = 1
At what value of x does the graph of the function f(x) have a vertical asymptote?
F(x) = 5X/ 2X-6
Iodine-123 is a radioactive substance used in medicine. It has a half-life of 13 hours. A nurse received a solution that initially contained 48 grams of iodine-123. Now only 12 grams of the iodine-123 remain. How many hours have passed since the nurse received the solution?
PLS HELP ILL GIVE BRAINLIEST TO WHO EVER ATTEMPTS THIS: The function H(t) = −16t2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 4 through 7 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
a randomly generated list of numbers from 0 to 4 is being used to simulate an event with numbers 3 and 4 representing a success. what is the estimated probability of a success
A. 75%
B. 60%
C. 25%
D. 40%
Answer: 40% appex
Step-by-step explanation:
The probability of success, where success is defined as generating a 3 or 4 in a random list of numbers from 0 to 4, is 40%.
To calculate the probability of success in a random number generation scenario. The numbers 0 to 4 are possible outcomes, with 3 and 4 being defined as success. There are 5 equally likely outcomes in total, and 2 of these (3 and 4) represent success. Hence, the probability of success (P(success)) is calculated as the number of successful outcomes divided by the total number of possible outcomes.
P(success) = Number of successful outcomes / Total number of outcomes
P(success) = 2/5
This fraction simplifies equals 0.4, which, when converted into a percentage, results in a 40% chance of success. Therefore, the correct answer is D. 40%.
Let log p/n=6 and log m/n=8 what is the relationship between p and m?
Given the logarithmic equations, it can be deduced that m is 100 times greater than p, assuming n>0 which is not zero to avoid division by zero and it is positive as logarithm is undefined for negative numbers.
Explanation:The question asks to find the relationship between p and m given two log equations. Using the rule of logarithms The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers (also known as the quotient rule), we can work out the relationship.
Given that log p/n = 6, it can be rearranged in exponential form: p = 106*n. And log m/n = 8 can be rewritten as m = 108*n.
Therefore, the relationship between p and m is that m is 100 times p, assuming n>0.
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Solve :
3x − 6 = 2x − 1
Prove that a set with n elements has 2n subsets.
The number of electrons in the shell equals 2n² and in each subshell is 2(2l + 1), derived from the quantum mechanical principles and the Pauli exclusion principle governing electron arrangement in atoms.
Explanation:To prove that the number of electrons in the shell equals 2n² and that the number in each subshell is 2(2l + 1), we need to use the quantum mechanical principles that govern the arrangement of electrons in an atom. According to the quantum model, each electron in an atom is described by four quantum numbers: n, l, mi, and ms. The principal quantum number n represents the shell level, the angular momentum quantum number l describes the subshell (with values ranging from 0 to n-1), the magnetic quantum number mi describes the orientation of the subshell (ranging from -l to +l), and the spin quantum number ms indicates the electron's spin (which can be +1/2 or -1/2).
Each shell level n can have subshell values from 0 to n-1. For each value of l, there are 2l+1 possible values for mi, and for each mi, there can be two electrons (one with spin up and one with spin down, according to the Pauli exclusion principle). Therefore, the maximum number of electrons in any subshell is 2(2l+1). Summing over all values of l will give the total number of electrons in a shell, which is 2n². This follows from considering all possible orientations and spin states for each value of l within a shell. For the n=2 shell as an example, there are l=0 and l=1 subshells. The s subshell (l=0) can hold 2 electrons, and the p subshell (l=1) can hold 6 electrons, for a total of 2(2^2) = 8 electrons in the n=2 shell. Using similar calculations for other values of n will confirm the general formula.
The application of the Pauli exclusion principle ensures that no two electrons can have the same set of all four quantum numbers, which fundamentally limits the number of possible electrons in a subshell and a shell.
Are the functions f(x) = (x^2-1)/(x-1) and g(x)= x+1 equal for all x?
A mother has 3 kids. Kid A is half the mother's current age. Kid B is 4 years younger than Kid A. In 3 years, Kid C will be 1/5 of his mother's age (not her current age). The sum of all their current ages is the mother's current age.
How old is the mother currently?
How old is each of her kids?
Final answer:
The mother is currently 40 years old. Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Explanation:
Let's denote the mother's current age as M. Kid A's age is A = M/2. Kid B is 4 years younger than Kid A, so B = A - 4 = M/2 - 4. Kid C will be 1/5 of his mother's age in 3 years, so if we denote Kid C's current age as C, we have C + 3 = 1/5(M + 3). The sum of all their current ages is the mother's current age, so M = A + B + C. With these equations, we can solve for M, A, B, and C.
We substitute A and B into the mother's age equation: M = M/2 + M/2 - 4 + C. Rearranging terms, we get M - 4 = C. Now we have two expressions for C: M - 4 and 1/5(M + 3) - 3. Setting them equal to each other, we get M - 4 = 1/5(M + 3) - 3. Solving for M, we find that M = 40 years old.
Now we can find Kid A, B, and C's ages using the mother's age. Kid A is half the mother's age, A = M/2 = 20 years old. Kid B is 4 years younger than Kid A, B = A - 4 = 16 years old. Kid C's age can be found by the substitution, C = M - 4 = 36 years old. So the mother is 40 years old, Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
1) What kind of figure is formed by the cross section below?
square
rectangle
circle
ellipse that is not a circle
Find all the real square roots of 0.0004.
A. 0.00632 and -0.00632
B. 0.06325 and -0.06325
C. 0.0002 and -0.0002
D. 0.02 and -0.02
An increase in the money supply that causes money to lose its purchasing power and prices to rise is known as______________
Answer: An increase in the money supply that causes money to lose its purchasing power and prices to rise is known as Inflation.
Inflation means an increase in the money supply that causes money to lose its purchasing power and prices to rise.
As in case of inflation situation, prices get rise because of increase in the money supply to reduce the purchasing power of the individual or firms.
Measures to rectify the inflation :
1) Fiscal expenditure
2) Revenue expenditure
3) Reduction in deficit financing
Hence, Inflation is the correct answer.
The length of a rectangle is 11 ft less than three times the width, and the area of the rectangle is 70 ft2 . find the dimensions of the rectangle.
The width and length of the rectangle is 7ft and 10 feet respectively.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, The length of a rectangle is 11 ft less than three times the width has an area of 70ft².
Assuming the width of the rectangle to be x ft, therefore the length of the rectangle is (3x - 11) ft.
We know the Area of a rectangle (A) = length×width.
∴ x.(3x - 11) = 70.
3x² - 11x = 70.
3x² - 11x - 70 = 0.
3x² - 21x + 10x - 70 = 0.
3x(x - 7) + 10(x - 7) = 0.
(x - 7)(3x + 10) = 0.
x - 7 = 0 Or 3x + 10 = 0.
x = 7 Or x = - 10/3.
A negative value of x is inadmissible here as length cannot be negative.
So, the width of the rectangle is 7 ft and the length of the rectangle is
10 ft.
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I already answered this but I just want to make sure if I did it right
an article with a net weight of 10 lb (pounds) is packaged in a box that weighs 1/2 lb. If 20 of these boxed articles are put into a freight container 15 lb, what is the gross weight?
Final answer:
The gross weight of the freight container with 20 boxed articles inside is 225 lb, calculated by adding the total weight of all the boxed articles (210 lb) to the weight of the container (15 lb).
Explanation:
To calculate the gross weight of the freight container with the packaged articles inside, we need to add the weight of the articles, the boxes, and the container itself.
First, we calculate the weight of one boxed article. Since the net weight of the article is 10 lb and the box weighs 0.5 lb, the total weight for one boxed article is 10 lb + 0.5 lb = 10.5 lb.
Next, we multiply the weight of one boxed article by the number of articles to find the total weight of all the boxed articles. For 20 articles, this is 20 imes 10.5 lb = 210 lb.
Finally, we add the weight of the freight container. The container weighs 15 lb, so the gross weight of the container with the articles is 210 lb + 15 lb = 225 lb.
Therefore, the gross weight of the freight container with 20 boxed articles inside is 225 lb.
Which of the following is equivalent to 36^1/2?
A) –18
B) –6
C) 1/18
D) 1/6
given the polynomail function below, find f(-5) f(x)=x^2-2x-7