Find the area of each figure
Answer:
24
Step-by-step explanation:
12*4/2
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Read more about Lagrange multipliers at:
https://brainly.com/question/4609414
On Monday Tiffany spent 5 2/8 hours studying. On Tuesday she spent another 2 1/8 hours studying. What is the combined length of time she spent studying
Answer:
7 3/8 hours
Step-by-step explanation:
5 + 2 = 7
2/8 + 1/8 = 3/8
Therefore, 7 + 3/8 =
7 3/8 hours
PLEASEEEE WILL GIVE BRAINLIEST TO FIRST RIGHT ANSWER!!!!!!!!!!
Find the solution of the system of equations.
x-y=-3
-8x+y=45
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the sum of 32 2/9+ 23 4/9
Answer:
The answer is 55 6/9, but when simplified, it is 55 1/3
Calculate the area of the triangular region determined by the points D(-4,3) E(-7,-8) F(-2, -3)
Answer:
The area is 27
Step-by-step explanation:
Area =1/2 [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]
Area =1/2 [2(-6 - 8) + 3(8 - 4) + 7(4 + 6)]
=1/2 [2(-14) + 3(4) + 7(10)]
=1/2 (-28 + 12 + 70)
=1/2 (54)
Area = 27
Segment AB and CD intersect at point E, measure of angle ABC =6x+20 and measure of angle DEB=10x. What is the value of x?
Answer:
x = 5
Step-by-step explanation:
6x + 20 = 10x
I hope this helps!
For a basic subscription, a cable television provider charges an activation fee of $60, plus $125 per month. What linear function represents the total cost of a basic cable subscription for t months? What is the total cost for two years of service?
Answer:
t=23
Step-by-step explanation:
12.5(20 + 35) - 38(16)
Answer:
79.5
Step-by-step explanation:
20+35=55
38*16=608
12.5*55=687.5
687.5-608=79.5
Hope this helps! Plz give brainliest! Also, pls sub to kgirl633 on yt.
Answer: 79.5
Step-by-step explanation:
A town has two shopping malls. A survey conducted on the shopping preferences of the town's residents showed that 62% of the residents visit Comet Mall, 73% of the residents visit Star Mall, and 48% of the residents visit both malls. The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is
Using Venn probabilities, it is found that:
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.In this problem, the events are:
Event A: Visits Comet Mall.Evenet B: Visits Star Mall.In this problem:
62% of the residents visit Comet Mall, hence [tex]P(A) = 0.62[/tex].73% of the residents visit Star Mall, hence [tex]P(B) = 0.73[/tex].48% of the residents visit both malls, hence [tex]P(A \cap B) = 0.48[/tex]The probability of either is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Hence:
[tex]P(A \cup B) = 0.62 + 0.73 - 0.48 = 0.87[/tex]
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.You can learn more about Venn probabilities at https://brainly.com/question/25698611
Answer:
87%.
Step-by-step explanation:
The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.
Can someone answer this no bots please I will give you brainliest… please
Answer: Alice
Step-by-step explanation: Alice won because she started furthest From the starting line.
What is the area, in square centimeters, of the shape below?
Express your answer as a fraction in simplest form.
Therefore, the area of the triangle is 4/9 cm².
Hoped this helped.
[tex]BrainiacUser1357[/tex]
The base of a triangle is v245 cm and its height is V20 cm. Find its area.
The given information of the base length and the height of the
rectangle are sufficient to find the area of the triangle.
Correct response:
The area of the triangle is 35 cm.²Methods used for finding the areaGiven that the parameters are;
The base of the triangle = [tex]\sqrt{245}[/tex] cm
The height of the triangle = [tex]\mathbf{\sqrt{20}}[/tex] cm
Required:
To find the area of the triangle
Solution:
[tex]Area \ of \ a \ triangle = \mathbf{ \dfrac{1}{2} \times base \times height}[/tex]Therefore, the area, A, of the given triangle is given as follows;
[tex]A = \dfrac{1}{2} \times \sqrt{245} \ cm \times \sqrt{20} \ cm= \dfrac{1}{2} \times \sqrt{4,900} \ cm^2= \dfrac{1}{2} \times 70 \ cm^2 = 35 \ cm^2[/tex]
The area of the triangle, A = 35 cm²Learn more about the area of plane shapes here:
https://brainly.com/question/8428727
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A rug in the classroom is 3/4 yard wide and 8/6 yards long. What is the area of the rug in square yards?
PLEASE BE ANSWERED IN 30 MINS TOPS
Answer:
i think area of the rug is 1 square yards
Step-by-step explanation:
area = 3/4×8/6
area = 2/2
area = 1 square yards
Just a little help please ☺️
Simplify
(3^8/3^5)3
3^9
3^39
3^10
3^6
[tex]\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9[/tex]
check whether the given fraction are equivalent
a) 7 /13 ,5/11
Answer:
No
Step-by-step explanation:
Not equivalent
7/13 ≠ 5/11
Which table correctly lists the reasons to prove angle 1 approximately equal to angle 3 comma given that stack A B with left right arrow on top intersects stack C D with left right arrow on top ?
Based on the right application of the reflexive property and subtraction property of equality, the table that correctly lists the reasons to prove that m∠1 ≅ m∠3 is: the table in option B (See attachment below).
The reflexive property of equality states that:
a + b = a + b.
Since m∠1 + m∠2 = 180°, and m∠2 + m∠3 = 180°, therefore, based on the reflexive property, we would have:
m∠1 + m∠2 = m∠2 + m∠3.
Thus, subtracting m∠2 from both sides of the equation will leave us with: m∠1 = m∠3 (subtraction property of equality).
Therefore, based on the right application of the reflexive property and subtraction property of equality, the table that correctly lists the reasons to prove that m∠1 ≅ m∠3 is: the table in option B (See attachment below).Learn more about the reflexive property on:
https://brainly.com/question/1601404
what is the value of y if x = 4
Answer:
5aaaaaaaaaaaaaaaaaaaaaaaa
HELPP PLS I NEED THIS WUICK ILL GIVE BRAINLEST
Answer:
x = 20
Step-by-step explanation:
(2x+10) = 180 - 130
2x + 10 = 50
2x= 40
x = 20
hope this helps! :)
the sum of kyras and calebs age is 37. calebs age is equal to twice the quantity of kyras age decreased by 4. let k represent kyras age.
Help me out please!!!!!!
Step-by-step explanation:
y = 2x + 9
y = -x - 3
there are multiple ways to solve this.
let's follow the approach that both x-expressions must be equal :
2x +9 = -x - 3
3x = -12
x = -4
y = -x - 3 = 4 - 3 = 1
A palm tree is 30 feet tall and casts a 48 foot shadow. The woman standing next to the palm tree casts a shadow similar to that of the palm tree. How tall is the woman if she casts an 8 foot shadow?
Answer:
48 feet foot I took the testttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt oh yeah yeah yeah
Step-by-step explanation:
Simplify.
(–28xy) ÷ (–4)
−7xy
17ab
−17ab
7xy
If any doubt leave a comment
The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the
equation. Include the phrases, "Isolate the variable by -" "Simplify," and "Isolate
the variable term by -" in your answers.
Original equation
7x +3 - 52
7x +3-3-52-3
7x = 49
7x49
TT
x = 7
Answer:
The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the
Step-by-step explanation:
Simplifying
7x + 3 = 52
Reorder the terms:
3 + 7x = 52
Solving
3 + 7x = 52
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + 7x = 52 + -3
Combine like terms: 3 + -3 = 0
0 + 7x = 52 + -3
7x = 52 + -3
Combine like terms: 52 + -3 = 49
7x = 49
Divide each side by '7'.
x = 7
Simplifying
x = 7
The scale model of a building is 8.5 inches tall. How tall is the actual building if the scale
used for the model is 1 inch = 150 feet?
Answer:
1,275
Step-by-step explanation:
Answer:
1275
Step-by-step explanation:
you do 8.5 multiplied by 150
Enter the value of x + 27.
х
1
o
1x + 27)
67°
1) Commutative Property of addition and multiplication: (Commutative, x; Commutative, +) ... 24) -6 + 10 = 4 25) - 8 - 12 = 20 26) -8 +6= -2 27) -7 - 5= -12.
I'm spending my last 10 points on this please help me
Answer:
Rate of sales tax = 6% of $60
Sales tax = [tex]\frac{6}{100}[/tex] × 60
= $3.60
Over six months, a family's electric bills averaged $55 per month. The bills for
the first five months were $57.60, $60, $53.25, $50.75, and $54.05. What was
the electric bill in the sixth month? Find the median, mode, and range of the
six electric bills.
Does anyone get this??
Answer:
the answer is 12m
Step-by-step explanation:
u know the side c and side B.
C=15m but u have to square it which is 225
B=9m but u have to square it which is 81. then subtract 82 from 225.which will give u 144 which is a perfect square route of 12
It costs $10 to rent a canoe and $5.50 to use the canoe for an hour. You have $21. Write an equation that represents the number h of hours you can rent the canoe.
Answer:
21 = 10 + 5.5h
Step-by-step explanation:
Total cost = initial cost + hourly cost
21 = 10 + hourly cost
hourly cost = 5.5 per hour, or 5.5 * h as we add 5.5 for each hour
21 = 10 + 5.5h
Answer:
Step-by-step explanation:
$10 + $5.50h ≤ $21
Let h stand for the hours the canoe is rented.
Fixed cost = $10, regardless of h.
$5.50h for the cost of n hours of rental.
Total cost = $10 + $5.50h
The total cannot exceed $21, legally.
So we should write:
$10 + $5.50h ≤ $21
If $10 + $5.50h ≥ $21 then ║║║║║║║