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]
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Lester has 2 toy cars. Ivan has t times as many toy cars as Lester. Write an expression that shows how many toy cars Ivan has
Answer:
I=2t
Step-by-step explanation:
ivan has 2 times t
If the distance between A(0, 4) and B(3,a) is 5 units then find the value of a.
Answer:
Step-by-step explanation:
a = 0
So that AOB makes a right triangle with sides 3-4-5
Answer:
a = 8
Step-by-step explanation:
Calculate AB using the distance formula and equate to 5
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (0, 4 ) and (x₂, y₂ ) = B (3, a )
d = [tex]\sqrt{(3-0)^2+(a-4)^2}[/tex]
= [tex]\sqrt{3^2+(a-4)^2}[/tex]
= [tex]\sqrt{9+(a-4)^2}[/tex] , then
[tex]\sqrt{9+(a-4)^2}[/tex] = 5 ( square both sides )
9 + (a - 4)² = 5² = 25 ( subtract 9 from both sides )
(a - 4)² = 16 ( take square root of both sides )
a - 4 = 4 ( add 4 to both sides )
a = 8
38. In a certain school, 45% of the students are boys. 80% of the boys have brown hair while 50% of those with brown hair
are girls. What is the probability that a randomly selected girl does NOT have brown hair?
A) .19
B) .36
C) 55
D) .35
E) none of the above are correct
The probability that a randomly selected girl does not have brown hair is 34.54%.
Given that in a certain school, 45% of the students are boys, and 80% of the boys have brown hair while 50% of those with brown hair are girls, to determine what is the probability that a randomly selected girl does NOT have brown hair, the following calculation must be performed:
45 x 0.80 = 36% of the school are brown hair boys 36% of the school are brown hair girls 55 - 36 = 55 = 100 19 = X 19 x 100/55 = X 1900/55 = X 34.54 = X
Therefore, the probability that a randomly selected girl does not have brown hair is 34.54%.
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please help anybody hm
Answer:
The answer is 1
Step-by-step explanation:
R, P, Q act on the base AB, BC, CA triangles ABC in alphabetical order, respectively. Show that P sec A + Q sec B + R sec C = 0, if the fluid of this power system passes through the center of the triangle.
Answer:
(i) In △ABD and △ACD,
AB=AC ....(since △ABC is isosceles)
AD=AD ....(common side)
BD=DC ....(since △BDC is isosceles)
ΔABD≅ΔACD .....SSS test of congruence,
∴∠BAD=∠CAD i.e. ∠BAP=∠PAC .....[c.a.c.t]......(i)
(ii) In △ABP and △ACP,
AB=AC ...(since △ABC is isosceles)
AP=AP ...(common side)
∠BAP=∠PAC ....from (i)
△ABP≅△ACP .... SAS test of congruence
∴BP=PC ...[c.s.c.t].....(ii)
∠APB=∠APC ....c.a.c.t.
(iii) Since △ABD≅△ACD
∠BAD=∠CAD ....from (i)
So, AD bisects ∠A
i.e. AP bisects∠A.....(iii)
In △BDP and △CDP,
DP=DP ...common side
BP=PC ...from (ii)
BD=CD ...(since △BDC is isosceles)
△BDP≅△CDP ....SSS test of congruence
∴∠BDP=∠CDP ....c.a.c.t.
∴ DP bisects∠D
So, AP bisects ∠D ....(iv)
From (iii) and (iv),
AP bisects ∠A as well as ∠D.
(iv) We know that
∠APB+∠APC=180
∘
....(angles in linear pair)
Also, ∠APB=∠APC ...from (ii)
∴∠APB=∠APC=
2
180
∘
=90
∘
BP=PC and ∠APB=∠APC=90
∘
Hence, AP is perpendicular bisector of
Step-by-step explanation:
HOPE ITS HELP YOU
Help Plssss it is due tommorrow!!!!!
Answer:
none of the other answera are correct
inverse of
f(x)=6x+5
find the output (y) of the function y= - 4/15 x +24 if the input (x) is 120
[tex]\text{Given that,}\\\\y = -\dfrac 4{15} x + 24\\\\\text{When x = 120,}\\\\y = -\dfrac 4{15} (120) + 24\\\\\implies y = - \dfrac{480}{15} +24\\\\\implies y=-32+24 \\\\\implies y = -8[/tex]
Compute the fare without tip: 1 passenger, 9.5 miles. Round to nearest fifth of a mile when dividing.
$28.53
$26.60
$27.83
$25.23
The fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.
The given parameters:
Number of passenger = 1Total distance = 9.5 milesCost of first 0.2 mile = $0.75Cost of additional mile = $0.55Cost of a passenger = $1.50The fare without tip for the Metro Taxi is calculated as follows;
for the first 0.2 mile = $0.75the remaining distance = 9.5 - 0.2 = 9.3 miles[tex]cost \ of \ distance = \$ 0.75 \ \ + \ \ \frac{\$ 0.55}{0.2 \ mile} \times 9.3 \ miles\\\\cost \ of \ distance = \$ 26.325[/tex]
Cost of 1 passenger = $1.50
The total cost is calculated as follows;
total cost = $1.50 + $26.325
total cost = $27.83
Thus, the fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.
The complete question is below:
Compute the fare without tip: 1 passenger, 9.5 miles. Round to nearest fifth of a mile when dividing.
Metro Taxi: first 1/5 mi= $0.75, each additional 1/5 mi= $0.55, each additional passenger= $1.50.
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They are similar or not similar and why?
Answer:
Yes its similar because if you look at all the numbers they are all the same but the shape is just turned around
please consider brainliest <3
Answer:
Step-by-step explanation:
Yes its similar because if you look at all the numbers they are all the same but the shape is just turned around
love ELVIS
Broccoli costs $1.50 per pound at a store. How much money does 32 onces of broccoli cost
Answer:
$3.00
Step-by-step explanation:
1 pound = 16 ounces
2 pounds = 32 ounces
1.5 x 2 = 3
Ms. Lee takes out a loan to start a business. She borrows $5,000 at a simple annual interest rate of 6.5% for 5 years. What is the total amount of interest Ms. Lee must pay?
Answer:
6625
Step-by-step explanation:
We know that: P = 5000
R = 6.5%
T = 5
Formulate and substitute: I = 5000rt
Calculate the product or quotient: 5000 x (1 + 0.325)
Calculate the sum or difference: 5000 x 1.325
Calculate the product or quotient: 6625
What's the Answer ~
[tex] \sf \tiny{14 + 14 \div 7}[/tex]
Step-by-step explanation:
remember the priorities of the different mathematical operations
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
so,
14 + 14/7 = 14 + 2 = 16
Hey there!
14 + 14 ÷ 7
14 ÷ 7 = 2
= 14 + 2
= 16
Therefore, your answer is: 16
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
12 A train in France can travel at a speed
of 217.4 miles per hour. A train in
China can travel 1.23 times this speed.
How fast can the train in China travel
in miles per hour?
I WILL MARK YOU AS BRAINIEST IF YOU ANSWER THIS QUESTION WITH AN ANSWER AND EXPLANATION + 100 points
Answer: 267.402
Step-by-step explanation:
The answer is 267.402 because 217.4 times 1.23 = 267.402.
Answer:
267 mph
Step-by-step explanation:
Multiplication
i hope this helps have a great day :)
esterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?
Answer:6 six graders were late. 10% would be 12, and half of that is 6. You need to divide that in half because 5 is half of 10.
Answer:
6 sixth graders at school where late
Step-by-step explanation:
5% = 0.05
0.05(120) = 6
PLEASE HELP TEST DUE SOON⚠️
What is the equation for the line in slope intercept form
Answer:
The answer should be [tex]y=mx+b[/tex]
Step-by-step explanation:
[tex]y=mx+b[/tex] is the only thing I can think of when your talking about the equation of the line in intercept form, but I'm 85% sure this is correct.
Hope this helps!
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Have a great day/night/afternoon!
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If 2 of the triangle sides are 8 m and one side is 6 m what kind of triangle is it
Answer:
An isosceles triangle has two side lengths the same and one different.
Step-by-step explanation:
How can I solve for t?
Answer:
This is not possible with 2 equal symbols
Which of these actions would decrease heat transfer between two objects?
increasing the temperature of the warmer object
increasing the area of their contact
reducing the thermal energy of the cooler object
reducing the time of their contact
(Fr ran out of free answers)
Answer:
increasing the area of their contact
what is n? solve for n+5=2n-6
Answer:
n = 11
Step-by-step explanation:
n+5=2n-6
you add 6 on both sides and you get
n+11=2n
you then subtract n on both sides and get
11=n
Step-by-step explanation:
n+5 = 2n - 6 -> Original equation
5 = n - 6 -> Take n away from both sides
11 = n -> Add 6 to both sides
n = 11 -> Final answer
*Remember, we are trying to get n by using inverse operations.
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark ( 1 ) as the fraction bar if necessary.
10
(-4,8).
(-6,-4)
Answer here
Answer:
slope = 6
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (-6, - 4) and (x₂, y₂ ) = (- 4, 8) ← 2 points on the line
m = [tex]\frac{8-(-4)}{-4-(-6)}[/tex] = [tex]\frac{8+4}{-4+6}[/tex] = [tex]\frac{12}{2}[/tex] = 6
The slope of the line given in the task content is; m = 6.
What is the slope of the line?The slope of the line is the rate of change of the dependent variable with respect to the independent variable.
On this note, the slope of the equation is;
Slope, m = (-4-8)/(-6-(-4))
m = -12/-2
m = 6.
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HELP THIS IS URGENT!!!!!!!!!!!!!1Fill in the blank so that the equation has the solution x=3
3x+ =5
Answer:
y = 3x + 5
Step-by-step explanation:
Since this is a linear function, its graph is a straight line stretching from - infinity to infinity on both x and y axes, hence domain and range is all real numbers from - infinity to infinity.
Marla was given the point (1,3), (2, 1), and (-2, -15). She was asked to find a quadratic function that fit these 3 given
points. Marla created a system of three equations with three variables to solve the problem and then used the
matrix functions on her graphing calculator to find the equation. Which equation can be written given these 3
points?
The linear equations [tex]c_{2}+c_{1}+c_{o} = 3[/tex], [tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] and [tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] can be written given the points [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex].
A quadratic function ([tex]p(x)[/tex]) is a second order polynomial of the form:
[tex]p(x) = \Sigma\limits_{i= 0}^{2} c_{i}\cdot x^{i} = c_{2}\cdot x^{2}+c_{1}\cdot x + c_{o}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable[tex]i[/tex] - Monomial index[tex]c_{i}[/tex] - i-th coefficientTo determine the value of all coefficients, we need three distinct points on plane and create a resulting system of linear equations.
If we know that [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex], then the system of linear equations is:
[tex]c_{2}+c_{1}+c_{o} = 3[/tex] (2)
[tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] (3)
[tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] (4)
The linear equations [tex]c_{2}+c_{1}+c_{o} = 3[/tex], [tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] and [tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] can be written given the points [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex].
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How many times does 13 go in to 33
Can you help? Please show work. Thank You.
Answer:
C. x+y=5; -2x+y=2
Step-by-step explanation:
The slope of the line in Table A is ...
m = (y2 -y1)/(x2 -x1)
m = (-6 -(-4))/(11 -9) = -2/2 = -1
The slope of the line in Table B is ...
m = (-8 -20)/(-5 -9) = -28/-14 = 2
We observe that the slopes have different signs. This means the signs of the terms in the standard form equation will be different from one equation to the other. The only pair of equations for which that is true is the pair in choice C.
Trying these equations on the first line of the tables, we see they match the table values.
Table A: 9 +(-4) = 5 . . . true
Table B: -2(9) +20 = 2 . . . true
_____
Additional comment
Neither equation in choice A has the correct slope for either table. The equations in choice B are inconsistent, both having slope -1, but different y-intercepts.
2. Find two equivalent ratios of the following ratios: a) 27 : 9 b) 7 : 35
Answer:
see explanation
Step-by-step explanation:
Equivalent ratios are found by multiplying or dividing the parts of the ratio by the same value.
27 : 9 ( divide both parts by 9 )
= 3 : 1
(b)
7 : 35 ( divide both parts by 7 )
= 1 : 5
In isosceles triangle the length of a leg is 17 cm, and the base is 16 cm. Find the length of the altitude to the base.
Answer:
altitude = 15 cm
Step-by-step explanation:
you can use the Pythagorean Theorem where you have a right triangle with a base of 8 (half of 16), a hypotenue of 17, and the altitude is 'a'
a² + 8² = 17²
a² + 64 = 289
a² = 225
a = [tex]\sqrt{225}[/tex]
a = 15
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Robert is ordering jerseys for the baseball team
A local company charges $5,25 for each jersey and $45 to create the design
An online company charges $7.75 for each jersey and $20 to create the design
For which number of jerseys is the cost the same at both companies?
A)26 jerseys
B)1 jersey
С)5 jerseys
D)10 jerseys
Answer: D) 10 jerseys
Step-by-step explanation:
Let j represent the number of jerseys and C for total cost
Local company eqn: C = 5.25j + 45
Online company eqn: C = 7.75j + 20
Set both sides equal to solve:
5.25j + 45 = 7.75j + 20
5.25j - 7.75j = 20 -45
- 2.5j = -25
[tex]\frac{-2.5j}{-2.5}=\frac{-25}{-2.5}[/tex]
j = 10
Therefore, the cost is the same for both companies when 10 jerseys are sold
do the values in this table represent a proportional relationship? x 2/4 6 8 y 1 2 3 4 yes, and the constant of proportionality is 12. yes, and the constant of proportionality is 2. no. i don't know.
Answer: No
Step-by-step explanation:
Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) – 6 = 0?
(u + 2)2 + 5(u + 2) – 6 = 0 where u = (x – 2)
u2 + 4 + 5u – 6 = 0 where u = (x – 2)
u2 + 5u – 6 = 0 where u = (x + 2)
u2 + u – 6 = 0 where u = (x + 2)
Answer:
we have
(x+2)^{2} +5(x+2)-6=0(x+2)
2
+5(x+2)−6=0
Let
u=(x+2)u=(x+2)
Substitute in the expression
(u)^{2} +5(u)-6=0(u)
2
+5(u)−6=0
therefore
the answer is
(u)^{2} +5(u)-6=0(u)
2
+5(u)−6=0 is equivalent to (x+2)^{2} +5(x+2)-6=0(x+2)
2
+5(x+2)−6=0