Answer:
C(min) = 277.95 $
Container dimensions:
x = 2.822 m
y = 1.411 m
h = 3.52 m
Step-by-step explanation:
Let´s call x and y the sides of the rectangular base.
The surface area for a rectangular container is:
S = Area of the base (A₁) + 2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)
Area of the base is :
A₁ = x*y we assume, according to problem statement that
x = 2*y y = x/2
A₁ = x²/2
Area lateral on side x
A₂ = x*h ( h is the height of the box )
Area lateral on side y
A₃ = y*h ( h is the height of the box )
s = x²/2 + 2*x*h + 2*y*h
Cost = Cost of the base + cost of area lateral on x + cost of area lateral on y
C = 10*x²/2 + 8* 2*x*h + 8*2*y*h
C as function of x is:
The volume of the box is:
V(b) = 14 m³ = (x²/2)*h 28 = x²h h = 28/x²
C(x) = 10*x²/2 + 16*x*28/x² + 16*(x/2)*28/x²
C(x) = 5*x² + 448/x + 224/x
Taking derivatives on both sides of the equation we get:
C´(x) = 10*x - 448/x² - 224/x²
C´(x) = 0 10x - 448/x² - 224/x² = 0 ( 10*x³ - 448 - 224 )/x² = 0
10*x³ - 448 - 224 = 0 10*x³ = 224
x³ =22.4
x = ∛ 22.4
x = 2.822 m
y = x/2 = 1.411 m
h = 28/x² = 28 /7.96
h = 3.52 m
To find out if the container of such dimension is the cheapest container we look to the second derivative of C
C´´(x) = 10 + 224*2*x/x⁴
C´´(x) = 10 + 448/x³ is positive then C has a minimum for x = 2.82
And the cost of the container is:
C = 10*(x²/2) + 16*x*h + 16*y*h
C = 39.82 + 158.75 + 79.38
C = 277.95 $
HELP MATH ANSWER QUESTION
the answer is in the picture
help please show work
67 2/3% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?
Answer:
2/3
Step-by-step explanation:
2/3 is 66 2/3%
ANYONE KNOW THE ANSWER TO THIS??
Answer:
x = 14 is your answer
Step-by-step explanation:
76 = 7x-22, so to figure it out, you first move -22 to the other side and get
76+22 = 7x.
add them together and you get 98 = 7x
7x would be your equation, so divide 98 by 7 and you get your solution
x = 14 is your answer
Find the length of side x
Answer:
Step-by-step explanation:
tan(30) = x/1
sqrt(3) / 3 = x/1
x= sqrt(3) / 2
Select all the correct answers.
These examples show the application of the negative exponent property. Which two examples correctly apply this property?
Answer:
First one and Third one
Step-by-step explanation:
Answer is correct from Plato
The correct expressions are:
[tex]17^{-1/4}[/tex] [tex]= \frac{1}{17^{1/4}}[/tex]
[tex]y^{1/2}[/tex] [tex]= \frac{1}{y^{-1/2}}[/tex]
In the given expression,
Since we know that the rule of exponent,
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Therefore,
For the given expression,
[tex]17^{-1/4}[/tex]
Using the above property of exponent we can write it,
[tex]= \frac{1}{17^{1/4}}[/tex]
Hence this is the correct expression.
For the given expression,
[tex]y^{1/2}[/tex]
Using the above property of exponent we can write it,
[tex]= \frac{1}{y^{-1/2}}[/tex]
Hence this is the correct expression.
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Tính (1,5)4; ((-2)/3)3; (√3)5.
Step-by-step explanation:
câu trả lời là trong bức ảnh trên
Cos15°°- Sin 15°= 1/√2
Hope it's help you
To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?
10 (one-half x + 2) minus 5 = 3 (x minus 6) + 1
–32 and 2
–2 and 32
–2 and 2
–32 and 32
Answer:
-2 and -2
Step-by-step explanation:
Which operation should you perform first in the expression 7x2^3?
Answer:
Below,
Step-by-step explanation:
The exponent part is done first
7 x 2^3
= 7 * 8
= 56.
You use the acronym PEMDAS:-
( E ( exponential) comes before M (multiply))
solve for x 7_3x=2x_3
[tex]7 - 3x = 2x - 3 = [/tex]
[tex]7 - 3x = 2x - 3 \\ 7 - 3x - 2x = - 3 \\ 7 - 5x = - 3 \\ - 5x = - 3 - 7 \\ - 5 = - 10 \\ x = \frac{ - 10}{ - 5} \\ x = 2[/tex]
HOPE IT HELPS!!!I NEED BRAINLIEST ✌️ PLZA box has three balls, one white and two red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:
a. Let F= the event of getting the white ball twice.
b. Let G= the event of getting two balls of different colors.
c. Let H= the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?
Answer:
See explaation
Step-by-step explanation:
Given
Represent the balls with the first letters
[tex]W =1[/tex]
[tex]R =2[/tex]
Solving (a): P(F) --- White balls twice
The event of F is:
[tex]F = \{(W,W)\}[/tex]
So:
[tex]P(F) = P(W) * P(W)[/tex]
[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(F) = \frac{1}{3} * \frac{1}{3}[/tex]
[tex]P(F) = \frac{1}{9}[/tex]
Solving (b): P(G) --- two different colors
The event of G is:
[tex]G = \{(W,R),(R,W)\}[/tex]
So:
[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]
[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(G) = \frac{1}{3} * \frac{2}{3} + \frac{2}{3} * \frac{1}{3}[/tex]
[tex]P(G) = \frac{2}{9} + \frac{2}{9}[/tex]
[tex]P(G) = \frac{4}{9}[/tex]
Solving (c): P(H) --- White picked first
The event of H is:
[tex]H = \{(W,R),(W,W)\}[/tex]
So:
[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]
[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(H) = \frac{1}{3} * \frac{2}{3} + \frac{1}{3} * \frac{1}{3}[/tex]
[tex]P(H) = \frac{2}{9} + \frac{1}{9}[/tex]
[tex]P(H) = \frac{3}{9}[/tex]
[tex]P(H) = \frac{1}{3}[/tex]
Solving (d): F and G, mutually exclusive?
We have:
[tex]F = \{(W,W)\}[/tex]
[tex]G = \{(W,R),(R,W)\}[/tex]
Check for common elements
[tex]n(F\ n\ G) = 0[/tex]
Hence, F and G are mutually exclusive
Solving (e): G and G, mutually exclusive?
We have:
[tex]G = \{(W,R),(R,W)\}[/tex]
[tex]H = \{(W,R),(W,W)\}[/tex]
Check for common elements
[tex]n(G\ n\ H) = 1[/tex]
Hence, F and G are not mutually exclusive
There are 5,000 books in the town's library. Of these, 4,700 are fiction. To find the percent of the books that are fiction, first set up the percent equation. Then find the percent.
Answer:
94%
Step-by-step explanation:
4,700/5,000 x 100%
0.94 x 100% = 94%
Answer:
94%
Step-by-step explanation:
find the equation of straight line passing through each of the following pairs of points
a) (2,4) and (7,2)
Answer:
The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Slope:
Having two points, the slope is given by the change in y divided by the change in x. Points (2,4) and (7,2), so:
Change in y: 2 - 4 = -2
Change in x: 7 - 2 = 5
Slope: [tex]m = \frac{-2}{5} = -\frac{2}{5}[/tex]
So
[tex]y = -\frac{2}{5}x + b[/tex]
(2,4)
This means that when [tex]x = 2, y = 4[/tex]. So
[tex]y = -\frac{2}{5}x + b[/tex]
[tex]4 = -\frac{2}{5}(2) + b[/tex]
[tex]b = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5}[/tex]
The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]
Question 1 of 10
The number √3 goes on forever with no repeating pattern; therefore, it is
rational.
A. True
B. False
SUBMIT
Answer:
False
Step-by-step explanation:
Rational number :
A rational number is a number which can be represent as p/q of two integers where q is not equal to zero
Example: 2/3
[tex]\sqrt{3}[/tex] = 17320508075........ and it keeps extending. Since it does not terminate or repeated after the decimal point.
Therefore [tex]\sqrt{3}[/tex] is an irritational number,
Hence given statement is FALSE
four times the difference of 15 and 6
Answer:
36
Step-by-step explanation:
9 is the difference
9 times 4 is 36
Subtraction is a mathematical operation. The statement "Four times the difference of 15 and 6" is equal to 36.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The statement "Four times the difference of 15 and 6" can be expressed as,
= 4 × (15 - 6)
= 4 × (9)
= 36
Hence, The statement "Four times the difference of 15 and 6" is equal to 36.
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PLEASE HELP ASAP Determine the period.
In mixture A of candy ingredients there are 3 parts of milk-chocolate for every Z parts peanut separate mixture B. there are 4 parts of nougat for every 3 parts of caramel equat parts of A and combined in one mixing bow what is the ratio of peanut butter to nougat in the bowl
Answer:
D. 7:10
Step-by-step explanation:
The Correct Answer
Consider the graph below: Point T(-2; 3) is a point on the Cartesian Plane such that B is the angle of inclination of OT. T(-2;3) у х 2.1 Calculate the following without the use of a calculator: a) tanſ b) 13 sin B.cosB (2)
Answer:
(a) - 3/2
(b) - 78/25
Step-by-step explanation:
According to the trigonometry, the tangent of any angle is the ratio of rise to the run of the right angle triangle .
The sine of an angle is the ratio of rise to the hypotenuse of the right angle triangle.
The cosine of an angle is the ratio of run to the hypotenuse of the right angle triangle.
(a)
[tex]tan\beta = \frac{3}{-2} = \frac{-3}{2}[/tex]
(b)
[tex]13 sin\beta cos \beta = 13\times \frac{3}{\sqrt{3^2+2^2}}\times\frac{-2}{\sqrt{3^2+2^2}}\\\\13 sin\beta cos\beta = \frac{- 78}{25}[/tex]
06.04 find the area of the image below a.24.6 units b.25.8 units c.26.3 units d.27.5 units
Pic added
Solve for x.
L
20x + 10
850
K
J
3
8
Answer:
Option (3)
Step-by-step explanation:
By applying the property of inscribed angle and intercepted arc in the given circle,
"Measure of an inscribed angle is half the measure of the intercepted arc"
[tex]m(\angle LKJ)=\frac{1}{2}m(\text{arc LJ})[/tex]
[tex]85=\frac{1}{2}(20x+10)[/tex]
[tex]170=20x+10[/tex]
[tex]20x=160[/tex]
[tex]x=8[/tex]
Therefore, Option (3) is the correct option.
A TRIANGLE HAS SIDE LENGTH 3, 8 AND 9. FIND THE ANGLE MEASUREMENTFOR THE ANGLE CROSS FROM THE SIDE WITH LENGTH OF 8.
Answer:tu culo
Step-by-step explanation:
Which expression can be modeled using the number line?
Answer:
7 x 1/10 = 7/10
Step-by-step explanation:
There are 7 "bumps" on the number line, and each "bump" moves the line 1/10.
This can also be modeled as
1/10 + 1/10 + 1/10 +1/10 +1/10 +1/10 +1/10 = 7/10
please help its urgent
Answer:
Step-by-step explanation:
18x-6=120
18x=120+6
18x=126
x=126÷18
x=7
Which is equivalent to f/125)*? O 125+ 0 1254 125" C. 125/11
Answer:
I think choose (1)
[tex]125 ^{ \frac{1x}{3} } [/tex]
What is the answer. I need it ASAP u have to choose 3 answers
please help meeeeeeeeeeeeeeeeee
pt 1
Answer:
Completing the square
Step-by-step explanation:
The proof is lengthy, and I don't think you came here to see that whole proof. Here it is anyway to show you the process of completing the square.
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/a/quadratic-formula-proof-review
Evaluate the expression for the given value of the variable.
3x + 4 when x = 2
5y - 3.6 when y = 4
7z4+ 1.05 when z = 1.2
20 - b3.2when b = 5.2
Answer:
I NOT 100% SURE BUT I THINK ITS .B)
Step-by-step explanation:
Please can you help me
Answer:
[tex]x = 24.75[/tex]
Step-by-step explanation:
Required
Find x
To find x, we have:
[tex]\angle PQR + \angle RPQ + \angle QRP = 180[/tex] -- angles in a triangle
Because [tex]\bar {PR}[/tex] is extended to S, then:
[tex]\angle QRS = \angle QRP[/tex]
So, we have:
[tex]2x + 6 + x - 7 + 5x -17 = 180[/tex]
Collect like terms
[tex]2x + x + 5x = 180 + 17 + 7-6[/tex]
[tex]8x = 198[/tex]
Divide by 8
[tex]x = 24.75[/tex]
If 12 muffins cost $27, how much would 2 muffins cost?