I assume the given plane has equation
x + 3y + 4z = d
for some constant d ≠ 0.
You want to maximize the function V(x, y, z) = xyz subject to the above constraint. The Lagrangian would be
L(x, y, z, λ) = xyz - λ (x + 3y + 4z - d)
Find its critical points:
∂L/∂x = yz - λ = 0
∂L/∂y = xz - 3λ = 0
∂L/∂z = xy - 4λ = 0
∂L/∂λ = x + 3y + 4z - d = 0
The first three equations tell you that λ = yz = xz/3 = xy/4. Then, for instance,
yz = xz/3 → 3yz - xz = z (3y - x) = 0 → z = 0 or 3y - x = 0
If z = 0, we get zero volume which is not useful. So 3y = x. Similarly, you would find x = 4z and 3y = 4z, so a critical point occurs when x = 3y = 4z.
In the fourth equation, we get upon substituting
x + 3y + 4z = 3x = d → x = d/3, y = d/9, z = d/12
Then the largest volume of this box would be
V(d/3, d/9, d/12) = d ³ / 324
SOMEONE PLEASE HELP NO LATE RESPONSES JUST PLEASE ASAP
Answer:
93.5
Step-by-step explanation:
Kent is 12 4/5 years old. Lane is 1 1/6
Years Older than kent and jane
is 1 1/3 year older than lane
How old is jane?
Answer:
[tex]Jane = 15\frac{3}{10}[/tex]
Step-by-step explanation:
Given
[tex]Kent = 12\frac{4}{5}[/tex]
[tex]Lane = 1\frac{1}{6} + Kent[/tex]
[tex]Jane = 1\frac{1}{3} + Lane[/tex]
Required
Determine Jane's age
Substitute [tex]Kent = 12\frac{4}{5}[/tex] in [tex]Lane = 1\frac{1}{6} + Kent[/tex]
[tex]Lane = 1\frac{1}{6} + 12\frac{4}{5}[/tex]
[tex]Lane = \frac{7}{6} + \frac{64}{5}[/tex]
Take LCM
[tex]Lane = \frac{45+384}{30}[/tex]
[tex]Lane = \frac{419}{30}[/tex]
Substitute [tex]Lane = \frac{419}{30}[/tex] in [tex]Jane = 1\frac{1}{3} + Lane[/tex]
[tex]Jane = 1\frac{1}{3} + \frac{419}{30}[/tex]
[tex]Jane = \frac{4}{3} + \frac{419}{30}[/tex]
Take LCM
[tex]Jane = \frac{40+419}{30}[/tex]
[tex]Jane = \frac{459}{30}[/tex]
[tex]Jane = 15\frac{3}{10}[/tex]
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error (in cm2) in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
Simplify 6(4x - 3) show work plz
Answer:
24x-18
Step-by-step explanation:
To simplify this we will need to use the distributive property
we can start with
6*4x=24x
then we can do
6*3=18
and since their is a negative sign in the middle that is what we do, so it will be
24x-18
Can I please have brainliest :)
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Simplify 6(4x - 3)}[/tex]
[tex]\large\text{DISTRIBUTE}\downarrow[/tex]
[tex]\large\text{6(4x - 3)}[/tex]
[tex]\large\text{6(4x) + 6(-3)}[/tex]
[tex]\large\text{6(4x) = 24x}[/tex]
[tex]\large\text{6(-3) = -18}[/tex]
[tex]\large\text{\bf = 24x - 18}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \bf \huge 24x - 18 }}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
True or False: To calculate the amount of change, you must find the
difference between the new and original values. *
Given the graphs of f(x) = 2x + 2 and g(x) = x - 2, find the solution to this system of equations:
Answer:
(-4,-6)
hope this helps !
what is the gratest common factor of 36 and 90
Answer:
I believe it is 18
Step-by-step explanation:
If you write out the count by's then the last number they both have in common is 18.
Hope this helps, have a wonderful day!
Danny reads for one half hour every day.
At the end of four weeks, how many hours has Danny read?
There are 7 days in a week.
1/2 hour x 7 days = 3 1/2 hours per week.
3 1/2 hours per week x 4 weeks = 14 hours
He read for a total of 14 hours
Answer:
14 hours
Step-by-step explanation:
half hour = 30 minutes
1 week = 7 days
30(minutes) x 7(days) = 210 minutes
210(minutes) x 4(weeks) = 840 minutes
Now we know how much time Danny has read (840 minutes), but we need to know what that is in hours.
840 minutes = how long Danny has read in minutes
60 minutes = hour
840(minutes) ÷ 60(minutes) = 14(hours)
The sum of a number times 8 and 23 is at most 26.
Use the variable b for the unknown number
Answer:
b ≤ 3/8
Step-by-step explanation:
Let the unknown number be b.
Translating the word problem into an algebraic expression, we have;
8b + 23 ≤ 26
Rearranging the equation, we have;
8b ≤ 26 - 23
8b ≤ 3
Dividing both sides by 8, we have;
b ≤ 3/8
Simplify.
(5+squartrt3)2
25 + sqrtrt10
10 + 28sqrtrt3
28 + 10sqrtrt3
Answer:
Step-by-step explanation:
If the 2 is an exponent, it needs to be written as ^2.
(5+√3)² = 5² + 10√3 + 3 = 28 + 10√3
Pls answer all the questions
Answer:
A) 108 degrees
B) 90 degrees
C) 270 degrees
Using Postulates and/or Theorems learned in Unit 1, determine whether PRQ MRN.
Show all your work and explain why the triangles are similar or why they are not
Please help and give a good explanation
Answer:
RM / RP = 10/18 = 5/9
RN/RQ = 7/21 = 1/3
Since the two ratios are not the same, triangle PRQ is not similar to triangle MRN.
Step-by-step explanation:
The triangles PRQ and MRN are not similar.
Similar triangles:Triangles are similar if their corresponding angles are congruent and the corresponding sides are in proportion.
This means the ratio of there corresponding sides must be equal. The corresponding angles must be the same . Therefore, the following rules must apply:
∠R = ∠R
∠Q = ∠N
∠P = ∠M
The following proportion rule must apply below:
PR / MR = RQ / RN = PQ / MN
18 / 10 = 21 / 7
9 : 5 ≠ 3 : 1
Therefore, the triangles are not similar
learn more on similar triangles here: https://brainly.com/question/10810713
A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.
Exercise (a)
How much work W is done in pulling the rope to the top of the building?
Exercise (b)
How much work W is done in pulling half the rope to the top of the building?
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
divide 90kg into the ration 2:3:7
the answer would have to be 465
Answer:
Weight of a pile of sand = 90 Kg
Ratio of weight of sand in three bags =
2 : 3 : 7
Let the weights be 2x kg, 3x kg and 7x kg respectively
A.T.Q.
=> 2x + 3x + 7x = 90
=> 12x = 90
=> x = 90/12
=> x = 7.5 Kg
___________________________
Weight of sand in small bag =
=> 2 × 7.5
=> 15 Kg ANS
Weight of sand in medium bag =
=> 3 × 7.5
=> 22.5 Kg ANS
Weight of sand in large bag =
=> 7 × 7.5
=> 52.5 Kg ANS
Why are family traditions important? (Please write this essay for me)
Answer:
talk ab
- Generations
- culture
What cube is a unit cube
find the value of x. round to the nearest degree.
Answer:
What you should do in this case is to use the following trinonometric relationship:
senx = C.O / h
Where
C.O: Opposite leg.
h: hypotenuse.
Substituting:
senx = (7) / (9)
Clearing x:
x = ASIN ((7) / (9))
x = 51.05755873
Answer:
The value of x is
x = 51 degrees.
Step-by-step explanation:
3. Classify the triangle with the given side lengths as acute, right, obtuse, 10 points
or not a triangle: 11, 13, 25
Not a triangle
Acute
Right
Obtuse
4. Classify the triangle with the given side lengths as acute, right, obtuse, 10 points
or not a triangle. 21, 28, 35
Not a triangle
Acute
Right
Obtuse
Answer:
3) Obtuse
4) Right
Step-by-step explanation:
3)
11 + 13 > 25 It is a triangle
11² + 13² = 25²
121 + 169 = 625
290 ≠ 625
Since hypotenuse is larger, the triangle is obtuse
4)
21 + 28 > 35 It is a triangle
21² + 28² = 35²
441 + 784 = 1225
1225 = 1225
Since the hypotenuse is equal to the legs, it's a Right triangle
Marie necklace is 30 inches long. She decided to make it 6 inches shorter. How many feet long is the neck less now?
Answer:
24 inches
Step-by-step explanation:
Answer:
2 feet long
Step-by-step explanation:
12 inches in a foot
30-6=24
24 inches=2 feet
Solve for x.
X -8 = -11
With step by step explanation or with ur work.
Answer:
The value is X im not sure
Write the equation of a line that
passes through the point (0, 3)
with a slope of -3
.
Answer:
y = -3x + 3
Step-by-step explanation:
use the formula y - y1 = m ( x - x1)
y - 3 = -3 ( x - 0)
y - 3= -3x
y = -3x + 3
Playland Park charges $25 admission plus $2 per ride. Funland Park charges $35 admission plus $1 per ride. For what number of rides is the total cost the same at both parks? Does any body know the answer to this question?
Answer:
10 rides
Step-by-step explanation:
Make an equation.
25 + 2x = 35 + 1x
Subract 1x from the 2x to get 1.
New Equation: 25 + 1x = 35
Subtract 25 from 35 to get 10.
New Equation: 1x = 10
Divide 1 from both sides.
Answer: 10 rides
Are these equivalent the the expression on the top right
Answer:
No
Yes
No
Yes
(choice 3 is a no)
There are 4 blood types, and not all are equally likely to be in blood banks. 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A person with type A blood can safely receive blood transfusions of type O and type A blood. If three donations are made, what is the probability that at least 1 of them can be safely used in a blood transfusion on someone with type A blood? 0.0138 0.4390 0.5610 0.9862
Answer:
0.9862.
Step-by-step explanation:
For each donation, there are only two possible outcomes. Either it can be safely used in a blood transfusion on someone with type A blood, or it cannot. The probability of a donation being safely used is independent of other donations, which means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Type A blood:
Can receive from type O(49%) and from type A(27%), which means that:
[tex]p = 0.49 + 0.27 = 0.76[/tex]
If three donations are made, what is the probability that at least 1 of them can be safely used in a blood transfusion on someone with type A blood?
Three donations mean that [tex]n = 3[/tex]
This probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.76)^{0}.(0.24)^{3} = 0.0138[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0138 = 0.9862[/tex]
The answer is 0.9862.
The probability that at least 1 of them can be safely used in a blood is 0.9862.
Since, A person with type A blood can safely receive blood transfusions of type O and type A blood.
Given that,
49% of donations are type O blood
27% of donations are type A blood
So, [tex]p=0.49+0.27=0.76[/tex] and [tex]q=1-0.76=0.24[/tex]
Where p represent probability of success and q represent probability of unsuccessful.
Now use Binomial distribution,
[tex]P(X=r)=n_{C}_rp^{r} q^{n-r}[/tex]
Here three donations, it means that, n = 3
We have to find that the probability that at least 1 of them can be safely used in a blood.
So, [tex]P(X\geq 1)=1-P(X=0)[/tex]
[tex]P(X=0)=3_{C}_0(0.76)^{0} (0.24)^{3}=0.0138[/tex]
[tex]P(X\geq 1)=1-0.0138=0.9862[/tex]
Thus, The probability that at least 1 of them can be safely used in a blood is 0.9862.
Learn more about Binomial distribution here:
https://brainly.com/question/11388449
nine times the difference between 4 and a number is24.what is the number.
Answer:
9×24-4
216-4
212
Step-by-step explanation:
I am not sure, but it might help you
Answer:
n = [tex]\frac{4}{3}[/tex]
or (because the wording is kind of confusing)
n = [tex]\frac{20}{3}[/tex]
Step-by-step explanation:
9(4 - n) = 24
36 - 9n = 24
-9n = -12
n = [tex]\frac{4}{3}[/tex]
or (because the wording is kind of confusing)
9(n - 4) = 24
9n - 36 = 24
9n = 60
n = [tex]\frac{20}{3}[/tex]
Samantha is 3 years older than her twin sisters. Next year the sum of age ages of all 3 sisters will be 45. how old is Samantha now?
The trapzeoids below are congruent figures. What is the value of W
Answer:
2
Step-by-step explanation:
3w=6
w=6÷3
w=2
Then number of pandas in the world is decreauing at a rate of
about 0.5% every year. If in one year there are 3000 pandas in
the world, how many will be there in 4 years? Round to the
nearest whole number.
Answer:
2998 Panda's will be left in 4 years.
Step-by-step explanation:
0.5 x 4 =2
3000-2=2998
what is the mean of the ages of the dance instructors?
IM GIVING BRAINLIEST‼️
Answer:
the answer to this is 25
Answer: 25
To find mean you first need to add up all the ages, which gives you 125. Then you divide that number by how many people. In this case it's 5, so divide 125 by 5 which gives you 25. And that's your answer.
Hope this helped you!
Does this situation involve a permutation or a combination, then solve? Selecting 4 out of 50 minions to compete in a dancing competition.
Answer:combination
Step-by-step explanation: just did the assignment