Answer:
r = 42,32 ft
h = 84.8 ft
Step-by-step explanation:
We are going to apply Lagrange multipliers method
The greatest space means maximum volume
V(cage) = Vol. of the cylinder + volume of the hemisphere
V(cylinder ) = π*r²*h
V(sphere) = (4/3)*π*r² ⇒ V(hemisphere) = (2/3)*π*r³
V(cage) = π*r²*h + (2/3)*π*r³
Associated costs:
Costs = cost of cylinder + cost of hemisphere
Area of the cylinder = Lateral area ( no bottom no top)
Area of the cylinder = 2*π*r*h
Area of hemisphere = 2*π*r²
A(r,h) = 2*π*r*h + 2*π*r²
C(r , h ) = 10* 2*π*r*h + 20* 2*π*r² C(r , h ) = 20*π*r*h + 40*π*r²
4500 = 20*π*r*h + 40*π*r²
20*π*r*h + 40*π*r² - 4500 = 0 20*π*r*h + 40*π*r² - 4500 = g(r,h)
V(cage) = π*r²*h + (2/3)*π*r³
δV/δr = 2*r*π*h + 2*π*r² δg(r,h)/δr = 20*π*h + 80*π*r
δV/δh = π*r² δg(r,h)/δh = 20*π*r
δV/δr = λ* δg(r,h)/δr
2*r*π*h + 2*π*r² = λ* 20*π*h + 80*π*r
2*r*π* ( h + r ) = 20*π* λ* ( h + 4*r)
r* ( h + r ) = 10*λ* ( h + 4*r) (1)
δV/δh = λ* δg(r,h)/δh
π*r² = 20*λ*π*r r = 20*λ (2)
20*π*r*h + 40*π*r² - 4500 = 0 (3)
We need to sole the system of equation 1 ; 2 ; 3
r = 20*λ plugging that value in equation 1
20*λ ( h + 20*λ ) = 10*λ* ( h + 4*r)
2( h + 20*λ ) = ( h + 4*20*λ)
2*h + 40*λ = h + 80*λ
h = 40*λ
20*π*r*h + 40*π*r² - 4500 = 0
20*π*20*λ*40*λ + 40*π+400λ² - 4500 = 0
16000*π*λ² + 16000*π*λ² = 4500
32000*π*λ² = 4500
320*π*λ² = 4500
λ² = 4500/1004,8 λ² = 4.48 λ = 2.12
Then
r = 20* λ r = 42,32 ft
h = 40* λ h = 84.8 ft
i'll promise to give the brainliest ! so, can someone help me with this one please
Answer:
13inches
Step-by-step explanation:
hope it works boy
answer:
thanks for the points luv
Y=x^2-x what's the domaine and range
Answer:
y = 0 domain is all real numbers and range is 1 i believe
Step-by-step explanation:
hope this helps
please help me please help me please help me please help me please help me please help me please
Answer:
q5 is 4
q6 is 72
Step-by-step explanation:
yan na po ..sana maktulong sau
what is the x and y intercepts for y=3x-1 on a graph
Answer:
x = [tex]\frac{1}{3}[/tex] y = -1
Step-by-step explanation:
x = 0 to solve for y
[tex]y=3x-1[/tex]
[tex]y=3(0)-1[/tex]
[tex]y=-1[/tex]
y = 0 to solve for x
[tex]y=3x-1[/tex]
[tex]0=3x-1[/tex]
Add 1 to both sides
[tex]1=3x[/tex]
Divide by 3 to isolate x
[tex]\frac{1}{3} =x[/tex]
Chan drew the triangle below. Which two angles are congruent?
Answer:
Q and R
Step-by-step explanation:
So lets look at the triangle.
P seems very thin, wheareas Q and R seem wider.
Normally, if given the degrees of the angles, we can subtract them from 180, which is the degrees of a full triangle, to find if two or more angles are congruent.
In this case however, we just go off of looks.
We see that angle P points strait up. This would not be the case if either Q or R where not going at the same angle, for if they were not congruent, angle P would be tilted to either the left or rihgt side.
So in the end, the best answer is Q and R.
HOpe this helps!
The graph of an exponential function passes through (2,−12) and (3,−24). Find the exponential function that describes the graph.
no fancy math here, just some reasoning with words. I just feel like it
for one step in x-direction the value of the function doubles, so the common factor is 2.
so let's trace it back
(1,-6)
(0, -3)
For an exponential function the y-intercept is the "initial value".
do let's write is as a function
[tex]y = - 3 \times {2}^{x} [/tex]
you could also use the points and plug their numbers into the general formula, but I felt this explanation could give you more understanding, since it's meant to be more intuitive.
hope it helps
PLEASE ANSWER ASAP
Select all equations for which -2 is a solution.
1) x^2=4
2) x^2=-4
3) x^3=8
4) x^3=-8
5) -x^2=4
6) (-x)^2=4
Answer:
1.
4.
6.
Mark me as brainlist ez
What is the answer to number question
Answer:
1.5
Step-by-step explanation:
5*.3
What’s the area ?????
Answer:
The answer is D. 22 square feet
Answer:
D
Step-by-step explanation:
3(2) + 8(2) = 22 sq ft
someone pls help ill give you a kiss and a cookie fi you help meee
for the point (6,8) find the csc theta and sec theta
Answer:
cscθ = 5/4, secθ = 5/3
Step-by-step explanation:
First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10
Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4
Similarly, cosθ = 6/10=3/5, and secθ = 5/3
Find the volume of a sphere with a radius of 9 inches. Use 3.14 for π
.
Round your answer to the nearest hundredth.
Answer:
The volume of the sphere is 3053. 63 inches.
Step-by-step explanation:
Formula for volume of a sphere is : V = 4 /3 · π · r³
V = 4/3 · π · 9³
V ≈ 3053. 63
The volume of the sphere is 3053. 63 inches.
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 47.3 miles per hour.Speed (miles per hour) 42-45 46-49 50-53 54-57 58-61Frequency 21 15 6 4 2The mean of the frequency distribution miles ______ per hour. (Round to the nearest tenth as needed.)Which of the following best describes the relationship between the computed mean and the actual mean?A. The computed mean is not close to the actual mean because the difference between the means is more than 5%.B. The computed mean is not close to the actual mean because the difference between the means is more than 5%.C. The computed mean is not close to the actual mean because the difference between the means is less than 5%.D. The computed mean is close to the actual mean because the difference between the means is less than 5%.
Answer:
47.4167
D. The computed mean is close to the actual mean because the difference between the means is less than 5%
Step-by-step explanation:
Given the distribution :
Speed(m/hr) ___ midpoint(x) ___ F ___fx
42 - 45 _______ 43.5 ________21 __ 913.5
46 - 49 _______47.5 _________15 __712.5
50 - 53 _______ 51.5 _________6 __ 309
54 - 57 _______ 55.5 ________ 4 ___ 222
58 - 61 ________59.5 ________ 2 ___ 119
The midpoint, x= sum of lower and upper boundary divided by 2
For instance, (42 + 45) / 2 = 43.5
The computed mean, Σfx / Σf = 2276 / 48 = 47.4167
Actual mean = 47.3 miles
(47.4167 - 47.3) / 47.3 * 100% = 0.24%
Charlie wants to order lunch for his friends. He'll order 6 sandwiches and a $3 kid's meal for his little brother. Charlie has $27. How much can he spend on each sandwich if they are all the same price?
i need equation and awnser plz :)
Answer:
Step-by-step explanation:
Charlie has $27
He spent $3 for kid's meal for his little brother
Remaining money=27-3=$24
Number of Sandwiches he wants to buy = 6
Money he needs to pay for each sandwich = 24/6 = $4
Answer:
a) Answer: $4 or less
b) Inequality: 6x + 3 ≤ 27
Step-by-step explanation: took the quiz and got it right!
Anyone can help me ?
9514 1404 393
Answer:
∠x = 80°∠y = 40°∠z = 60°Step-by-step explanation:
The angle marked x and the one marked 100° form a linear pair, so are supplementary. The measure of x is ...
x = 180° -100° = 80°
__
The angle marked 40° and the one marked y are "alternate interior angles" with respect to the parallel lines and the diagonal that crosses them. As such, they have the same measure:
y = 40°
__
The angle marked 100° and the sum of angles in the lower right corner are "corresponding" angles, so have the same measure. That is ...
100° = 40° +z
z = 100° -40° = 60°
Marisol's new tablet is 9 inches long and has a diagonal of 11 inches. What is the perimeter of
the tablet, in inches, to the nearest tenth of an inch? *Hint: Use the Pythagorean Theorem to
find the width of the tablet.
The perimeter is type your answer...
inches.
Answer:
30.64 inches
Step-by-step explanation:
use Pythagoras theoryum to find the width:
11²=121
121-9²=40
√40=6.32
perimeter is all sides added together so:
6.32+6.32+9+9=30.64
The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet. Cameron determines the area of the wall to be 1423.125 square feet. Which best explains the reasonableness of Cameron’s solution?
Cameron’s solution is reasonable because there are four decimal places in the factors and four decimal places in the product.
Cameron’s solution is reasonable because there are three decimal places in the factors and three decimal places in the product.
Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.
Cameron’s solution is unreasonable because 10 times 10 is 100, and 100 is not close to his product
Answer:
Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.
Step-by-step explanation:
Area of a rectangle:
The area of a rectangle, of length l and height h, is given by:
[tex]A = lh[/tex]
The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet.
This means that [tex]l = 16.5, h = 8.625[/tex]
Estimate of the area:
To use an "easy" multiplication, lets consider [tex]l = 17, h = 9[/tex]. So
[tex]A = lh = 17(9) = 153[/tex]
Cameron determines the area of the wall to be 1423.125 square feet.
Very far from the area of 153, which means that he made a confusion with the decimal places. Thus, the correct answer is:
Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.
Help mew with this please
Step-by-step explanation:
There are many ways
-1 - 1 = - 2
-5 + 3 = -2
Answer:
(-3+1) and 1,000,000+(-1,000,002)
What is the measure of A?
Answer:
60
Step-by-step explanation:
Since the sides are equal, the angles have to be equal
The angles of a triangle add to 180
180/3 = 60
Angle A = 60
Answer:
60
Step-by-step explanation:
Because each side is equal the angles are as well, therefore the angles must add up to 180
180/3=60
HELP ASAP Which expression is equivalent to this polynomial expression?
(2x^2 - 3y^2)(4x^4 + 6x^2y^2 + 9y^4)
choices in picture
Answer:
B, if you have any questions how I did anything, or questions in general, let me know.
Step-by-step explanation:
First you want to make sure you understand distributing. Just using variables I will show how to districute a similar expression.
(a - b)(c + d - e)
There are several ways to think of it. you could treat (a-b) as one term and distribute it into c + d - e like this. pretend (a- b) = x
x(c + d - e) = cx + dx - ex = c(a-b) + d(a-b) - e(a-b)
Then just do a bit more distributing, then combine like terms.
You could instead make (c + d - e) a single term and distribute that into (a-b)
I prefer doing it all in one step, similar to FOIL-ing. Take the first term of one of the expression in parenthesis and distribute it, then move on to the second and so on.
so with (a - b)(c + d - e) I would start with a and distribute that into (c + d - e) and get ac + ad - ae then do the same to -b and get -bc - bd + be then you add the two parts together. ac + ad - ae + -bc - bd + be = ac + ad - ae -bc - bd + be. Then you would combine like terms. Let me know if you need help with that.
Anyway, now for your problem. Keep in mind you can use any of the methods.
(2x^2 - 3y^2)(4x^4 + 6x^2y^2 + 9y^4)
First distribute 2x^2 into (4x^4 + 6x^2y^2 + 9y^4)
8x^6 + 12x^4y^2 + 18x^2y^4
Next distribute -3y^2 into (4x^4 + 6x^2y^2 + 9y^4)
-12x^4y^2 - 18x^2y^4 - 27y^6
Now add the two together.
8x^6 + 12x^4y^2 + 18x^2y^4 + -12x^4y^2 - 18x^2y^4 - 27y^6 = 8x^6 + 12x^4y^2 + 18x^2y^4 - 12x^4y^2 - 18x^2y^4 - 27y^6
Finally combine like terms.
12x^4y^2 - 12x^4y^2 = 0
18x^2y^4 - 18x^2y^4 = 0
So that leaves us with 8x^6 - 27y^6
B is the only answer that works, none of the other 3 can be simplified or adjusted to make them equal what we need, so B is the only right answer.
If you have any questions though let me know.
PLEASE HELP
What is the following product?
It is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 1616 students in the class, what is the probability that the first 22 presentations will be by Drake and Todd, in that order
Answer:
[tex]\frac{1}{240} = 0.0042[/tex] = 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, since the order in which the students are chosen is important, the permutations formula is used to solve it.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Desired outcomes:
Drake then Todd, so only one outcome, which means that [tex]D = 1[/tex]
Total outcomes:
Two students from a set of 16, so:
[tex]T = P_{16,2} = \frac{16!}{14!} = 16*15 = 240[/tex]
What is the probability that the first 2 presentations will be by Drake and Todd, in that order?
[tex]p = \frac{D}{T} = \frac{1}{240} = 0.0042[/tex]
[tex]\frac{1}{240} = 0.0042[/tex] = 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.
Select the correct answer.
What is the solution to the equation?
A.
-2 and -7
B.
2 and 7
C.
-2
D.
7
Answer:
D
Step-by-step explanation:
7 is it because it is positive
a number added to 3 is equal to negative 5, find the number
Answer:
-8
Step-by-step explanation:
An equation at represents this situation is:
-5 = 3 + x
Find x by;
-5 - 3 = -8
So x is -8:
-5 = 3 + -8 (TRUE)
Hope this helps
[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Sum of the two numbers = [tex]-5[/tex]
One of the number = [tex]3[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The other number.
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
The other number is [tex]\sf\blue{-8}[/tex].
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
Let the other number be [tex]x[/tex].
As per the question, we have
[tex]Sum \: \: of \: \: the \: \: two \: \: numbers = -5 [/tex]
[tex]➺ \: 3 + x = - 5[/tex]
[tex]➺ \: x = - 5 - 3[/tex]
[tex]➺ \: x = - 8[/tex]
[tex]\sf\purple{Therefore,\:the\:other\:number\:is\:-8.}[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex] ➪ \: 3 + ( - 8) = - 5[/tex]
[tex] ➪ \: 3 - 8 = - 5[/tex]
[tex] ➪ \: - 5 = - 5[/tex]
➪ L. H. S. = R. H. S.
[tex]\sf\orange{Hence\:verified.}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35\:ヅ}}}}}[/tex]
−12 as a ratio of two integers.
Answer:
-12 can be written as the ratio of -24 and 2, for example.
Step-by-step explanation:
Ratio of a to b:
The ratio of a to b is given by the division of a by b, that is:
[tex]r = \frac{a}{b}[/tex]
−12 as a ratio of two integers.
Here, we want any division in which the result is -12. One example is:
[tex]-12 = \frac{-24}{2}[/tex]
-12 can be written as the ratio of -24 and 2, for example.
The points A(-3, -4) and B(5, 0) form a line segment. Find the coordinates of the point P that partitions segment AB in a 2:3 ratio.
Answer:
Step-by-step explanation:
let the coordinates of P be (x,y)
[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\x=\frac{2(5)+3(-3)}{2+3} \\x=\frac{10-9}{5} =\frac{1}{5} =0.2\\y=\frac{2(0)+3(-4)}{2+3} \\y=\frac{0-12}{5} =\frac{-12}{5} =-2.4\\[/tex]
so coordinates of P are (0.2,-2.4)
Graph the image of Kite BCDE after a translation 5 units down.
Answer:
Step-by-step explanation:
Can someone help me simplify it more?
Answer:
8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz
Step-by-step explanation:
After sales tax, a $90 lamp costs
$95.40. What is the sales tax
percentage?
Answer:
the sales tax percentage is 6%
Step-by-step explanation:
To solve this you want to first find what percent $95.40 is of $90. Then we can subtract 100% to find the extra percent (the sales tax).
95.40 is what percent of 90?
95.40 = X · 90
Divide by 90 on both sides.
1.06 = X
So now we know that 95.40 is 106% of 90. We subtract 100% from 106% to get 6%. Therefore the sales tax percentage is 6%.
according to a salad recipe each serving requires 4 teaspoons of vegetable oil and 12 teaspoons of vinegar. if 14 teaspoons of vegetable oil were used how many teaspoons of vinegar should be used
Answer:
42 teaspoons of vinegar should be used
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
4 teaspoons of vegetable oil and 12 teaspoons of vinegar. 14 teaspoons of vegetable oil were used
So
4 teaspoons of vegetable oil - 12 teaspoons of vinegar
14 teaspoons of vegetable oil - x teaspoons of vinegar
So
[tex]4x = 12*14[/tex]
Dividing both sides by 4:
[tex]x = 3*14 = 42[/tex]
42 teaspoons of vinegar should be used
2. How to find the variance and standard deviation of a discrete
random variable?
Answer:
To find the variance just take the second moment and subtract that from the first moment squared
To find the standard deviation just take the square root of the variance
Step-by-step explanation: