Answer:
The dimensions that give the minimum surface area are:
Length = 14cm
width = 14cm
height = 14cm
And the minimum surface is:
S = 1,176 cm^2
Step-by-step explanation:
A regular rectangular prism has the measures: length L, width W and height H.
The volume of this prism is:
V = L*W*H
The surface of this prism is:
S = 2*(L*W + H*L + H*W)
If the base of the prism is a square, then we have L = W
Then the equations become:
V = L*L*H = L^2*H
S = 2*(L^2 + 2*H*L)
We know that the volume of the figure is 2744 cm^3
Then:
V = 2744 cm^3 = H*(L^2)
In this equation, we can isolate H.
H = (2744 cm^3)/(L^2)
Now we can replace this on the surface equation:
S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))
S = 2*L^2 + 4(2744 cm^3)/L
Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.
S' = 2*(2*L) - 4*(2744 cm^3)/L^2
This is equal to zero when:
0 = 2*(2*L) - 4*(2744 cm^3)/L^2
0 = 4*L*L^2 - 4*(2744 cm^3)
4*(2744 cm^3) = 4*L^3
2744 cm^3 = L^3
∛(2744 cm^3) = L = 14cm
Then the length of the base that minimizes the surface is L = 14.
Then we have:
H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm
Then the surface is:
S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2
What are the solutions to the equation below
Answer:
x = -1.434, x = -0.232
Step-by-step explanation:
What is the answer to this problem
Answer:
791.68
Step-by-step explanation:
have a nice day! :)
A 12-sided solid has equal-sized faces numbered 1-12
a. Find P(number greater than 10).
b.Find P(number less than 5)
c. If the 12-sided solid is rolled 200 times, how many times would you expect either a 4, 6, or 9 to be rolled?
Answer:
a) [tex]P(x > 2) = \frac{1}{6}[/tex]
b) [tex]P(x < 5) = \frac{1}{3}[/tex]
c) 50 times
Step-by-step explanation:
Given
[tex]S = \{1,2,3,4,5,6,7,8,9,10,11,12\}[/tex]
Solving (a): P(x > 10)
First, list all outcomes of x
[tex]x = \{11,12\}[/tex] --- 2 outcomes
So, the probability is:
[tex]P(x > 2) = \frac{2}{12}[/tex]
Simplify
[tex]P(x > 2) = \frac{1}{6}[/tex]
Solving (b): P(x < 5)
First, list all outcomes of x
[tex]x = \{1,2,3,4\}[/tex] --- 4 outcomes
So, the probability is:
[tex]P(x < 5) = \frac{4}{12}[/tex]
Simplify
[tex]P(x < 5) = \frac{1}{3}[/tex]
Solving (c): Expected outcome of 4, 6 or 9 in a roll of 200
We have:
[tex]n = 200[/tex]
First, list all outcomes of x
[tex]x = \{4,6,9\}[/tex] --- 3 outcomes
So, the probability is:
[tex]P(x ) = \frac{3}{12}[/tex]
Simplify
[tex]P(x ) = \frac{1}{4}[/tex]
The expected number of rolls (E(x)) is calculated as:
[tex]E(x) = P(x) * n[/tex]
[tex]E(x) = \frac{1}{4} * 200[/tex]
[tex]E(x) = 50[/tex]
Find the side length x of the shelf
Answer:
the length of x must be 10
Step-by-step explanation:
Factorise x^2-3x
plz help me
x^2 - 3x = x ( x - 3 )
ʜᴏᴘᴇ ʏᴏᴜ ɢᴇᴛ ᴡᴇʟʟ
whats is the circumference of a circle with a diameter of 2 feet use 3.14 for π
Answer:
Hope it helps you!!!
Please mark as brainliest!!!!
Step-by-step explanation:
The formula for finding the circumference of a circle is pi x diameter. So it would be 3.14 x 2. And when you calculate it you get 6.28.
Answer:
6.28
Step-by-step explanation:
Yes or No pick come on and answer
Answer:
The answer is yes to both!
Hope that helps - we're studying the Pythagorean theorem right now! :)
Step-by-step explanation:
Answer:
please give the picture so only I can able to answer
What is the volume of the triangular prism shown below?
8 cm
3 cm
13 cm
A 143 cm
B 312 cm
C 156 cm
D
Not here
Answer:
156 cm
Step-by-step explanation:
PLEASE HELP I NEED IT TO PASS THIS CLASS
Answer:
∠ 1 = 99°, ∠ 2 = 81°, ∠ 4 = 81°
Step-by-step explanation:
∠ 1 and ∠ 3 are vertical angles and are congruent, then
∠ 1 = 99°
∠ 1 and ∠ 2 are adjacent angles and sum to 180° , so
∠ 2 = 180° - 99° = 81°
∠ 2 and ∠ 4 are vertical angles and are congruent, so
∠ 4 = 81°
26. FUNDRAISING The Art Club receives $10 plus $2
for every sculpture they sell for a fundraiser. The
expression 2x + 10 represents the amount the Art
Club receives if they sell x sculptures.
Factor 2x + 10.
Answer
x+5
Step-by-step explanation:
2x+10 = 2(x+5)
what is the square root of 56?
Answer:
2 square root 14
Step-by-step explanation:
The square root of 56 is 2 square root 14. 56 = 4 * 14, and 4 can be square rooted into an integer.
Circle O has a arc length 34 inches sub tended by an angle of 78 degrees. Find the length of the radius, x, to the nearest tenth of an inch
Answer: 25 in.
Step-by-step explanation:
Given
Arc length is 34 inches
The angle subtended by the arc is [tex]78^{\circ}[/tex]
arc length l subtending an angle [tex]\theta[/tex] is given by
[tex]\Rightarrow l=\dfrac{\theta }{360^{\circ}}\times 2\pi R[/tex]
Put the values
[tex]\Rightarrow 34=\dfrac{78^{\circ}}{360^{\circ}}\times 2\pi R\\\\\Rightarrow R=24.97\approx 25\ in.[/tex]
y is an integer.
Write down all the solutions of the inequality. -8 < 2y < 0
Answer:
y = - 3, - 2, - 1
Step-by-step explanation:
Given
- 8 < 2y < 0 ( divide each interval by 2 )
- 4 < y < 0
Then y can equal - 3, - 2, - 1
Find the base area of a square pyramid
whose base has a side length of 12cm.
A) 148 B) 144
C) 143
D) 140
Answer:
B) 144 cm^2
Step-by-step explanation:
riverview soccer team won 10 games and drawn 2 out of 18 games so far this season. what is the probability they will lose their next game
Which is an example of a statistical question?
Questions
Question 1 How many pets does Alisha have at home?
Question 2 How old were you when you got your first pet?
Question 3 Do you like having a pet?
Question 4 What is Alisha’s pet’s name?
A question 1
B question 2
C question 3
D question 4
Answer:
Question 2
Step-by-step explanation:
divdtihcdyuvftujvfujvfubf
Answer:
2
Step-by-step explanation:
1. Find the area of each circle. Use 3.14 for A. Round to the nearest tenth.
5cm
RE
Answer:
78.5 cm²Step-by-step explanation:
Area of circle:
A = πr²A = 3.14*5² = 78.5 cm²−4x−6=−5y+2
Write a formula for g(x), in terms of x.
Please
What is the Volume PLEASE HELP!!!!
Answer:
a
Step-by-step explanation:
its a because 12cm×10cm×9cm = 1,080cm
Solve the right triangle. Round decimal answers to the nearest tenth.
The main question isn't supplied.
Answer:
Kindly check explanation
Step-by-step explanation:
A right - angled triangle is one which has one of its angles being 90°. Once we have a right angled triangle, the rule of Pythagoras can be applied in other to solve problems relating to obtaining sides of the triangle while trigonometric relations including :
Sinθ = opposite / hypotenus
Tanθ = opposite / Adjacent
Cosθ = Adjacent / Hypotenus
To obtain the angle θ; depending on which of the sides are given.
From Pythagoras :
c² = a² + b²
Where, c = hypotenus and the longest side if the triangle.
What is the value of cose in the diagram below?
a)3/5
b)3/4
c)4/5
d)4/3
Find the solution of the system of equations.
−2x+9y= -17
-x - 3y = -1
Answer:
x = 4 and y = −1
(4, -1)
Step-by-step explanation:
I going to solve this system of equations by elimination. (You could also solve by substitution too.)
Multiply the first equation by 1, and multiply the second equation by -2.
1(−2x+9y= -17)
-2(-x - 3y = -1)
Becomes:
−2x + 9y = −17
2x + 6y = 2
Add these equations to eliminate x:
15y = −15
15y/15 = -15/15
y = -1
Now we solve for x:
-x -3(-1) = -1
-x + 3 = -1
-3 -3
-x = -4
x = 4
Hope this helped!
Solve. 1/2(4x + 2/5) = 4/5
Answer:
[tex]\frac{1}{2}(4x + \frac{2}{5} ) = \frac{4}{5}\\2x + \frac{1}{5} = \frac{4}{5}\\\frac{10x + 1}{5} = \frac{4}{5}\\10x + 1= 4\\10x = 3\\x = \frac{3}{10}[/tex]
Answer:
x = 3/10
Step-by-step explanation:
Given equation,
→ 1/2(4x + 2/5) = 4/5
Let's solve the problem,
→ 1/2(4x + 2/5) = 4/5
→ 2x + (1/5) = 4/5
→ 2x = (4/5) - (1/5)
→ x = (3/5) × (1/2)
→ [ x = 3/10 ]
Thus, the value is 3/10.
natalie bought a 3/4 pound for flour for baking she used 2/3 of the flour to make cookies how many pounds of flour did she use
PLEASE HELP ASAP WILL MARK BRAINLIEST
Answer:
1) .11111
2) 5/9
3) 122/495
4) rational- .167167, 2/9
irrational- π, [tex]\sqrt{225}[/tex]
5) 5.75
What is the least possible quotient when two distinct
integers from the set
{-5,-3, -2,0,+1,+6,+18}
are divided?
I NEED THIS ASAP
Answer:
18 ÷ (-2) = -9
Step-by-step explanation:
18 ÷ (-2) = -9 is the least possible quotient.
To meet the requirement, we should divide the biggest positive number by smallest negative number
Show that the statement is true. If JK has endpoints J(9,0) and K(-3,-4), then the midpoint M of JK lles In Quadrant IV.
URGENT!!!!!!!
Answer:
True
Step-by-step explanation:
J(9 , 0) ; K(-3 , -4)
Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
[tex]= (\frac{9+(-3)}{2},\frac{0+(-4)}{2}\\\\\\= (\frac{6}{2},\frac{-4}{2})\\\\=(3 , -2)[/tex]
(3 , -2) lies in quadrant IV
Solve the rational equation: 2x/x-4-2x-5/x^2-10x+24=-3/x-6
A. X=-0.64, x=1.44
B. There is no solution.
C. X=4, x=6
D. X=6.08, x=-0.58
Heellpppp plsss; timed test
Answer:
D. X=6.08, x=-0.58
Step-by-step explanation:
Given the rational expression
[tex]\frac{2x}{x-4}-\frac{2x-5}{x^2-10x+24} = \frac{-3}{x-6}\\\frac{2x}{x-4}-\frac{2x-5}{x^2-4x-6x+24} = \frac{-3}{x-6}\\\frac{2x}{x-4}-\frac{2x-5}{x(x-4)-6(x-4)} = \frac{-3}{x-6}\\ \\\frac{2x}{x-4}-\frac{2x-5}{(x-4)(x-6)} = \frac{-3}{x-6}\\Rerrange;\\\frac{2x-5}{(x-4)(x-6)} = \frac{2x}{x-4}+ \frac{3}{x-6}\\\frac{2x-5}{(x-4)(x-6)} = \frac{2x(x-6)+3(x-4))}{(x-4)(x-6)}\\[/tex]
Cancel out the denominator on both sides
[tex]2x-5 = 2x(x-6)+3(x-4)\\Expand\\2x-5 =2x^2-12x+3x-12\\2x-5 = 2x^2-9x-12\\Equate \ to \ zero\\2x^2-9x-12-2x+5 = 0\\2x^2-11x - 7 = 0\\[/tex]
Factorize
[tex]x = -(-11)\pm\frac{\sqrt{(-11)^2-4(2)(-7)} }{2(2)}\\x = 11\pm\frac{\sqrt{121+56} }{4}\\x = 11\pm\frac{\sqrt{177} }{4}\\x = 11\pm\frac{13.3 }{4}\\x = \frac{11+13.3}{4} \ and \ x = \frac{11-13.3}{4} \\x = 6.08 \ and \ - 0.58[/tex]
Hence the required solution is X=6.08 and -0.58
please help me i dont understand it
Answer:
B
Step-by-step explanation:
Its B I think Here go your answer.
The sum of twice a number, n, and 14 is 30. Write an equation that models this
statement. Then explain how you might use reasoning to find the value of n.
Answer:
2n +14 = 30 I can use inverse operations and solve for n.
Step-by-step explanation:
twice means 2 so twice a number,n, means 2 times n thus 2n.
sum means add so, 2n + 14
is means equal so 2n + 14 = 30
If you solve it you will find n = 8