Answer:
r = 1.37 billion feet
Step-by-step explanation:
It is given that,
A proposed design for a habitable Mars colony is a hemispherical biodome used to maintain a breathable atmosphere for the colonists.
The volume of biodome is 5.5 billion cubic feet of air.
It is in the shape of a hemisphere. The volume of a hemisphere is given by :
[tex]V=\dfrac{2}{3}\pi r^3[/tex], r = radius
V = 5.5 billion cubic feet
[tex]r^3=\dfrac{3V}{2\pi}\\\\r^3=\dfrac{3\times 5.5}{2\times 3.14}\\\\r=(\dfrac{3\times 5.5}{2\times 3.14})^{1/3}\\\\r=1.37\ \text{billion feet}[/tex]
So, the radius of the biodome is 1.37 billion feet.
The radius of the biodome if it is required to contain 5.5 billion cubic feet of air is 1.38 billion feet and this can be determined by using the formula of the volume of the hemisphere.
Given :
A proposed design for a habitable Mars colony is a hemispherical biodome used to maintain a breathable atmosphere for the colonists.Volume of the biodome is 5.5 billion cubic feet.The following steps can be used in order to determine the radius of the biodome:
Step 1 - The formula of the volume of the hemisphere can be used in order to determine the radius of the biodome.
Step 2 - Formula of the volume of the hemisphere is given by:
[tex]\rm V =\dfrac{2}{3}\pi r^3[/tex]
where r is the radius of the hemisphere.
Step 3 - Now, substitute the value of V in the above formula in order to determine the value of 'r'.
[tex]\rm 5.5=\dfrac{2}{3}\pi r^3[/tex]
Step 4 - Simplify the above expression.
[tex]r^3=\dfrac{5.5\times 3}{2\pi}[/tex]
[tex]r = \sqrt[3]{\dfrac{16.5}{2\pi}}[/tex]
r = 1.38 billion feet
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Plz help with this questio!
Thanks!♡︎
Answer:
Week 3.
Step-by-step explanation:
Add up the hours for each week.
Week 3 is the highest at 36 hours.
Answer:
week 3
Step-by-step explanation:
week 3. it totals for 36 hours in this week
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60?
Hey There!! ☄️ The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
and a indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis
The graph is made narrower.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
The graph of f(x) = x2 is made narrower
The graph of f(x) = x2 is made narrower.
It is given that f(x) = x2 and g(x) = –3x2 – 36x – 60.
To find the transformations applied to the graph.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
Indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
So, the graph of f(x) = x2 is made narrower.
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Round the following number to the nearest hundred
123,456
Answer:
Hey!
Your answer is 123,500!
Step-by-step explanation:
TO ROUND TO THE NEAREST HUNDRED we need to look at the TENS column...
IN THIS CASE WE LOOK AT '5'...
If its bigger than 4 INCREASE THE DIGIT IN THE HUNDREDS PLACE BY ONE
If its smaller than 5 DECREASE THE DIGIT IN THE HUNDREDS PLACE BY ONE!
So as 5 is a digit that makes us ROUND UP...we change 4 to a 5 to have 123,500 as our answer!
HOPE THIS HELPS!
Which of the following graphs represent a function?
Graph A
Graph B
Graph
Graph
a. Graph A and Graph C
b. Graph A
C. Graph D
D. graph b and d
The graphs that represent functions are given as follows:
a. Graph A and Graph C.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we have that:
Graph B has one vertically aligned point, hence it is not a function.Graph D has multiple vertically aligned points, hence it is also not a function.Hence the graphs that represent functions are given as follows:
a. Graph A and Graph C.
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Answer: The only graphs that classify as function are Graph A and Graph C, so the answer is C. It's not possible for B and D to be functions.
Caleb bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it increased by 38%. During the second year the value of the stock decreased by 12%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.
Answer:
1.2144xx
Step-by-step explanation:
The multiplier of value for the first year was (1 +38%) = 1.38.
The multiplier of value for the second year was (1 -12%) = 0.88.
Then the multiplier of value for the two years was ...
1.38×0.88 = 1.2144
The value of the stock after 2 years was ...
1.2144xx
_____
Comment on the variable
We have used the variable given in the problem statement (xx). If you intend something different, replace xx with the variable you intend.
Give the first two solutions of the n-Queens problem for n = 6 Write it in the form (1,2), (2,2), (3,2)
Answer:
(1,2), (2,4), (3,6), (4,1), ( 5,3), (6,5)
Step-by-step explanation:
Given the first two solutions of the n-Queens problem for n = 6
The solution requires that no two queens share the same row, column, or diagonal and each variable lies in the domain [1,6] (6 rows).while finding a solution we must ensure that no two queens are not placed on the same row and in the same diagonal
hence the first two solutions can be expressed as :
(1,2), (2,4), (3,6),(4,1),( 5,3), (6,5)
Show how 10-6 helps solve 50-6
Answer:
The digit in the ones spot will come out to be 4.
Step-by-step explanation:
Since the are both an even number of ten, and you're subtracting 6, their both gonna come out to have a 4 in the ones spot in the number answer.
Well 50 is just 10 x 5 so...
if you solve 10 + 6 = 16 then you can do 50 + 6 = 56
The sum of a number and three is six less than twice that number
Answer:
Algebraic expression = x+3=2x-6
Step-by-step explanation:
Let the unknown number be x ;
[tex]x+3 =2x-6[/tex]
Further explanation
[tex]x+3=2x-6\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}x+3-3=2x-6-3\\\\Simplify\\x=2x-9\\\\Collect\:like\:terms\\x-2x =-9\\\\Simplify\\-x =-9\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{-9}{-1}\\\\x =9[/tex]
3 Question
Simplify this expression:
4(1 - 25) + 70 - 10.
Type the correct answer in the box
Answer:
-36
Step-by-step explanation:
4(1 - 25) + 70 - 10
PEMDAS
Parentheses first
4( -24) + 70 -10
Then multiply and divide
-96 + 70-10
Then add and subtract
-36
Hmm can you help me solve god bless you
Answer:
(3/2)x - 14
Step-by-step explanation:
If two lines are perpendicular, their slopes are mathematically negative reciprocals of one another.
Here the given line is y = (-2/3)x; the slope is -2/3, and the negative reciprocal of that is 3/2. The desired line will have this slope 3/2.
Using the slope-intercept form of the equation of a straight line, y = mx + b, we write out
-8 = (3/2)(4) + b, obtaining -8 = 6 + b, or b = -14.
The desired equation is (3/2)x - 14.
Write 927 as a mathematical expression in expanded form.
Answer:
900 + 20 + 7
Answer:
[tex]900+20+7[/tex]
Step-by-step explanation:
Write 927 as a mathematical expression in expanded form.
So we see the number 927. It has hundreds, tens, ones. So the only thing we have to do it separate the number by hundreds, tens, ones. So now, let's start!
Hundreds: [tex]900[/tex]
Tens: [tex]20[/tex]
Ones: [tex]7[/tex]
We have 900, 20, and 7. Let's try adding them up to make 927.
[tex]900+20+7[/tex]
[tex]=927[/tex]
This is how we do 927 in expanded form.
Hope this Helps!
The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,
Answer:
7th measurement = -26
Step-by-step explanation:
The sequence is 16, 9, 2, –5, ...,
First term( a)= 16
Second term=9
Common difference (d) = 9-16
Common difference= -7
The sequence is a arithmetic progression
For AP's ,the terms formula is
Term(n) = a + (n-1)d
Where n represent the term to be found
In this case,we Are looking for the 7th term , so n= 7
Term(7) = 16+ (7-1)-7
Term(7)= 16 +6(-7).
Term (7) = 16-42
Term(7) = -26
7th term =-26
What is another way to name plane T?
Answer:
plane EHV
Step-by-step explanation:
To find the other name of plane T, we have to find any three non-collinear points on the plane T.
It means we have to find any three points which lie on the plane T but in a single straight line.
From the given figure it is clear that points E, H and V lie on plane T and they are not collinear.
Therefore, the other name of plane T is plane EHV.
Note: There are many other possible names of plane T, EHV is one of them.
What is the sum of 637,391+372,088
Answer:
1009479
Step-by-step explanation:
637,391 + 372,088 = 1009479
Answer:
the answers 1009479
Step-by-step explanation:
Which property is illustrated by the equation –8 + 8 = 0?
additive inverse
additive identity
commutative property
distributive property
2. Richie solved the equation 24x + 18(x - 2) = 216 for x.
Some of his steps are shown below.
Step 1: 24x + 18(x - 2) = 216
Step 2: 24x + 18x - 36 = 216
Step 3: 42x - 36 = 216
Step 4: 42x = 252
List the steps Richie took to solve the equation.
the answer is 6 he nned to divide 42 and
252
Step-by-step explanation:
42x=252
x=252/4
x=6
well hope that helps
Answer: Answer is the steps
Step-by-step explanation:
Step 1: Richie rewrite the equation as 24x + 18(x-2) =216
Step 2: Richie applied the distributive property to eliminate the parentheses and got the equation 24x + 18x - 32 = 216
Step 3: Richie combine like terms to get the equation 42x -36 =216
Step 4: Richie added 36 to both sides to get the new equation 42x = 252
Richie was not done solving for x so in
Step 5: Richie should have divided both sides by 42 to get the final answer
x = 6.
What are the critical points for the plane curve defined by the equations x(t)=t 33−t22−2t−4y(t)=t32−2t+2
Answer:
The points are
[tex]t_1 = 0.7433[/tex]
[tex]t_2 = -0.299[/tex]
Step-by-step explanation:
From the question we are told that
The first equation is [tex]x(t) = 3t^3 -2t^2-2t -4[/tex]
The second equation is [tex]y(t) = 3t^2 -2t -2[/tex]
Now differentiating the first and second equation
[tex]\frac{dx(t)}{dt} = 9t^2 -4t-2[/tex]
and
[tex]\frac{dy(t)}{dt} = 6t-2[/tex]
Now
[tex]\frac{dy(t)}{dx(t)} = \frac{\frac{dy(t)}{dt} }{\frac{dx(t)}{dt} } = \frac{9t^2 -4t-2}{6t-2}[/tex]
at critical point
[tex]\frac{dy(t)}{dx(t)} = 0[/tex]
=> \frac{9t^2 -4t-2}{6t-2}=0[/tex]
=> [tex]9t^2 - 4t-2 = 0[/tex]
solving using quadratic formula we have that
[tex]t_1 = 0.7433[/tex]
and [tex]t_2 = -0.299[/tex]
the sum of a number and six is ten. find the number
The required number is 4.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The sum of a number and six is ten.
let the number be x.
So, x + 6 = 10
Now, solving for x
x = 10 - 6
x = 4
Hence, the value of x is 4.
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Write the phrase as an algebraic expression. Use the variable x to represent the unknown number. Seven times a number.
Answer:
7x.
Step-by-step explanation:
Seven times a number = 7x.
An algebraic expression for the given statement is 7x.
The given statement is seven times a number.
We need to write an algebraic expression for the given statement.
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Given that, use the variable x to represent the unknown number.
Now, seven times a number=7x
Therefore, an algebraic expression for the given statement is 7x.
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Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the
beach. He fell asleep halfway home. He didn't wake up until he still had half as far to go as he had already
gone while asleep. How much of the entire trip home was Samuel asleep?
Answer: One fourth of the entire trip.
Step-by-step explanation:
The initial distance is D.
" He fell asleep halfway home."
Then he fells asleep when the distance between his actual position and his house was half of D, or:
D/2.
"He didn't wake up until he still had half as far to go as he had already
gone while asleep."
So he wakes up when his actual position is a fourth of the initial distance:
(D/2)/2 = D/4.
Then if the entire trip has a distance D, and he was sleeping between:
D/2 - D/4 = 2D/4 - D/4 = D/4.
in a trip of a distance D, he was asleep a distance of D/4.
Then, returning to the question:
How much of the entire trip home was Samuel asleep?
This is equal to the quotient between the distance that he travels asleep and the total distance:
r = (D/4)/D = 1/4.
Then he was asleep in 1/4 of the entire trip.
For each relation, indicate whether it is reflexive or anti-reflexive, symmetric or anti-symmetric, transitive or not transitive.
a. The domain of the relation L is the set of all real numbers. For x, y ∈ R, xLy if x < y.
b. The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.)
Answer:
(a)
L is not reflexive, L is anti-reflexive
L is not symmetric.
L is not anti-symmetric
L is transitive.
(b)
D is reflexive
D is not symmetric.
D is anti-symmetric
D is transitive.
Step-by-step explanation:
a)
Given that;
domain of the given relation L is the set of all real numbers
For x , y ∈ R , xLy if x less than y.
relation L, where xLy if x less than y, For x, y ∈ R
so For every x ∈ R, it is then false that x less than x.
That is (x, x) does not belongs to L.
∴ L is not reflexive, L is anti-reflexive.
For every x,y ∈ R, if (x,y) ∈ L (i.e. x < y), then (y, x) does not belongs to L, since it is false that y < x.
∴ L is not symmetric.
For every x ∈ R, we can say its false that x less than x. That is (x, x) does not belongs to L.
∴ L is not anti-symmetric.
For every x,y,z ∈ R, if (x, y) ∈ L(i.e. x < y) and (y, z) ∈ L(i.e. y < z), then (x, z) ∈ L, since it is true that x<z when x<y and y<z.
∴ L is transitive.
b)
Also lets consider a relation D, where xDy if there is an integer n such that y = xn, For x, y ∈ Z.
Now
For every x ∈ Z, it is true that x = x × 1. That is (x, x) belongs to D.
∴ D is reflexive,
For every x,y ∈ Z, if (x,y) ∈ P (i.e. y=x × n), then (y, x).
if (x,y) ∈ D, then there exist an integer n such that y=x × n.
Then x = y × (1/n).
Thus, (y,x) does not belongs to D, since 1/n is not an integer, but it is a real number.
∴ D is not symmetric.
For every x,y ∈ Z, if (x,y) ∈ D (i.e. y=x × n), then (y, x) also belongs to D only when x=y. where n=1.
∴ D is anti-symmetric.
For every x,y,z ∈ Z, if (x,y) ∈ D (i.e. x × n1= y), and (y,z) ∈ D (i.e. y × n2 = z), then (x,z)∈ D.
if (x,y) ∈ D, then there exist an integer n1 such that y=x × n1.
if (y,z) ∈ D, then there exist an integer n2 such that z=y × n2.
Thenz = (x × n1) × n2 ⇒ z=x × (n1 × n2).
where (n1 × n2) is an integer. Thus (x,z) ∈ Z
∴ D is transitive.
How can you prove that a conjecture is false?
Answer:
In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers avoid going down blind alleys and learn how to modify conjectures to produce provable theorems.
Step-by-step explanation:
Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased
Answer:
The answer is B: $29.35x + $17.45y
Rosanne makes 1 1 2 liters of strawberry lemonade. She pours 1 4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2 5 of the remaining lemonade. How much lemonade does Rosanne's brother drink?
Answer:
1/2 liter
Step-by-step explanation:
If she starts with 1 1/2 liters and removes 1/4 liter, the remaining amount is ...
(1 1/2) -(1/4) = 1 2/4 -1/4 = 1 1/4 . . . liters.
The brother drinks 2/5 of that, so drinks ...
(2/5)(1 1/4 L) = (2/5)(5/4 L) = 2/4 L = 1/2 L
Rosanne's brother drinks 1/2 L of the lemonade.
A hot air balloon starts at a height of 6 feet above the ground and then rises at a rate of 20 feet each minute. Which equation gives the height h in feet as a function of time t in minutes? Oh=6t Oh = 20$ Oh=20t + 6 Oh=6+ 20
Answer:
The height h it will travel in t minutes
Height h = 6 + 20(t)
Oh=20t + 6
Step-by-step explanation:
A hot air balloon starts at a height of 6 feet above the ground and then rises at a rate of 20 feet each minute.
Initial height h0 = 6 feet
Then it travel 29 feet each minute
Rate = 20 feet/ minute
The height h it will travel in t minutes
Height h = 6 + 20(t)
The value, V(m), of a comic book m must be months after publication has an average rate of change of -0.04 between m=36 and m=60. Which statement must be true?
A) The value of the comic book decreased by a total of $0.04 between m=36 and m=60
B) The value of the comic book increased by a total of $0.04 between m=36 and m=60
C) The value of the comic book decreased by an average of $0.04 each month between m=36 and m=60
D) The value of the comic book increased by an average of $0.04 each month between m=36 and m=60
Answer:
A
Step-by-step explanation:
The average is over the months not added each month
(5x10) plus (2x1/100)
Answer:
2501/50
Decimal:50.02
Step-by-step explanation:
5 × 10 + 2× 1/100
5 × 10 = 50
2 × 1/100 = 1/50
50 + 1/50
50×50. 1
_____ + ___
50. 50
50 × 50 + 1 = 2501 meaning 2501 over 50 is your answer
Answer:
100
Step-by-step explanation:
Hope this helped! ;)
31, -32, 33, -11, 5 least to greatest
Answer: -32, -11, 5, 31, 33
Answer:
-32, -11, 5, 31, 33
Step-by-step explanation:
The smallest one is -32. I know this because it's:
A negativeIs the farthest back on a number lineThe next one is -11. -11 is the next smallest because it's:
A negativeIs larger than -32 (it's closer to 0 and the positives on a number line)The third one is 5. It's the third greatest because it's:
A positiveIs the closest positive option to 0.The fourth one is 31. It's the fourth greatest because it's:
A positiveIt's larger than 5, but smaller than 33The last one is 33. It's the greatest because it's:
A positiveIt's larger than all the other numbers-170=5(8n+6)
Help please !!
Answer:
Step-by-step explanation:
40n + 30 = -170
40n + 30 = -170
40n = -200
n = -5
Show all work to identify the asymptotes and zero of the function f(x)= 5x/x^2-25. Please answer ASAP!!!
Answers:
root: x = 0Vertical asymptotes: x = 5 and x = -5Horizontal asymptote: y = 0The term "root" is another way of saying "zero of a function"
============================================
Explanation:
To find the roots, we need to solve f(x) = 0 for x
f(x) = 0
5x/(x^2 - 25) = 0
5x = 0*(x^2-25)
5x = 0
x = 0/5
x = 0
Plugging x = 0 into f(x) leads to f(x) = 0.
The root is x = 0 meaning the x intercept is at 0 on the x axis number line. This is the origin (0,0).
---------------
To find the vertical asymptotes, set the denominator equal to 0 and solve for x
x^2 - 25 = 0
x^2 - 5^2 = 0
(x-5)(x+5) = 0 ... difference of squares rule
x-5 = 0 or x+5 = 0
x = 5 or x = -5
If either x = 5 or x = -5, then then the denominator x^2-25 is zero
We cannot divide by zero, so these values are excluded from the domain, and this produces the vertical asymptotes.
--------------
The horizontal asymptote is y = 0 because the degree of the numerator is 1, while the degree of the denominator is 2. The denominator's degree is larger, which leads to y = 0. The rules for finding the horizontal asymptote are
If m < n, then the horizontal asymptote is y = 0If m = n, then the horizontal asymptote is y = a/bIf m > n, then there is no horizontal asymptote (use polynomial long division to find the oblique asymptote)For those rules above, m and n are the degrees of the numerator and denominator respectively. The a,b refers to the leading coefficients of the numerator and denominator.
The asymptotes and zero of the function are ±5 and 0 respectively
Given the function below;
[tex]f(x)=\frac{5x}{x^2-25}[/tex]The vertical asymptotes occur at the point where the function goes large that is the denominator is zero.
If the denominator is zero, hence;
x^2 - 25 = 0
x^2 = 25
x = ±√25
x = ±5
Hence the asymptotes of the function is ±5
For the zero of the function;
[tex]\frac{5x}{x^2-25}=0\\5x = 0\\x = 0\\[/tex]
Hence the zero of the function is 0
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