Answer:
a) The length of its edge is 8 units.
b) The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
Step-by-step explanation:
a) The volume of a cube ([tex]V_{c}[/tex]), measured in cubic units, is defined by the following expression:
[tex]V_{c} = L^{3}[/tex] (1)
Where [tex]L[/tex] is the side length of the cube, measured in units.
If we know that [tex]V_{c} = 512\,u^{3}[/tex], then the length of its edge is:
[tex]L = \sqrt[3]{V_{c}}[/tex]
[tex]L = 8\,u[/tex]
The length of its edge is 8 units.
b) The volume of a sphere ([tex]V_{s}[/tex]), measured in cubic units, that fits snugly inside this cube is defined by:
[tex]V_{s} = \frac{\pi}{6}\cdot L^{3}[/tex] (2)
If we know that [tex]L = 8\,u[/tex], then the volume of the sphere is:
[tex]V_{s} \approx 268.083\,u^{3}[/tex]
The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube taken by the sphere is the ratio of the volume of the sphere to the volume of the cube. That is to say:
[tex]r = \frac{V_{s}}{V_{c}}[/tex]
If we know that [tex]V_{c} = 512\,u^{3}[/tex] and [tex]V_{s} \approx 268.083\,u^{3}[/tex], then the fraction of the cube that is taken up by the sphere is:
[tex]r = 0.524[/tex]
The result in percentage form is calculated by multiplying the result above by 100.
[tex]\% r = 52.4\,\%[/tex]
The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
Rob is saving to buy a new MP3 player. For every $11 he earns babysitting, he saves $8. On Saturday, Rob earned $33 babysitting. How much money did he save?
Answer:
21 dollars! I hope this helps with your math question!
Step-by-step explanation:
brainly highly appreciated!
Answer:
$30
Step-by-step explanation:
Guided Practice
Find the range of the function rule y=5x−2 for the domain.
{−1/2, 1/4, 2/5}
A.
{−1/2, 3 1/4, 4}
B.
{3/10, 9/20, 12/25}
C.
{− 4 1/2, −3/4, 0}
Answer:
C.
{− 4 1/2, −3/4, 0}
Step-by-step explanation:
domain
-1/2;1/4; 2/5
range
-5 1/2; (5/4-2);0
{-1/2, 1/4, 2/5}
take the derivative of the equation 4 times. f 4 (x)=0.
C
Step-by-step explanation:
if you put in the values (-1/2, 1/4, 2/5) in the function, it gives the answers in option C
consider the function g(x) = 54(1/3)x. evaluate g(0). what point does this indicate on the graph if g?
PLS I NEED TO KNOW FAST, How many degrees is X?
Answer:
To me it Looks about 50 degrees from 80 degrees but im not positive though but i hope this helps you in some way or form.
Step-by-step explanation:
HELPP (2) this is due in 4 mintues
Answer:
I think its A.
Step-by-step explanation:
SOMEONE PLEASE HELP WILL GIVE 25 POINTS
Answer:
Step-by-step explanation:
g(x) is vertical translation of f(x) by -12 units
Solve for x: 14x = 196.
(Only the number)
Answer:
14
Step-by-step explanation:
Answer:
the answer is X = 14
Step-by-step explanation:
So you need to single out the X
You do this by doing the opposite of X,
right now X is being multiplied by 14
The opposite of Multiplaction is division
That means you divide X by 14
But dont forget, what you do one side you do to the other.
This means you also Divide 196 by 14
196 ÷ 14 = 14
meaning X = 14
HELP HELP HURRY PLEASE !
Answer:
4
Step-by-step explanation:
5^2-3^2=16
sqrt16=4
Answer:
A. 4
Step-by-step explanation:
hypotenuse (h) = 5
base (b) = 3
perpendicular (p) = a = ?
We know
By using Pythagoras theorem
p = √( h² - b²)
a = √( 5² - 3²)
a = √(25 - 9)
a = √ 16
a = 4
HELP LOL IT MY LIL SIS HELPP
Answer:
what did ur lil sis do??? hurry call the police and get immediate help right away ok
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzz oh plzzzzzzzzz help
Answer:
y=13/11x+12/11 (assuming you want it in slope-intercept).
Step-by-step explanation:
estimate a 15% tip for a $60 bill
Answer:
the answer would be 15/100= .15 *60= 9 so the tip would be 9$
Answer the tax would be *.00 dollars if you estimate it
Step-by-step explanation:can I get marked brainlist
passes through (3,-6) and (-1,2) slope intercept form?
Answer:
2/1
Step-by-step explanation:
8/4 which is also 2/1
Simplify the expression by combining all the like terms 6+2x+5+4x
Answer:
6x+11
Step-by-step explanation:
6+2x+5+4x
4x+2x+6+5
(4x+2x)+(6+5)
6x+11
Answer:
6x +11
Step-by-step explanation:
group like terms (terms with the same variable and powers) together
(2x+4x) + (6+5)
6x +11
Please do number 11 for me.
(2.99548) x (1.8342)
Answer:
5.49430941
Step-by-step explanation:
Multiply together.
i hope this helps, good luck :)
Akira and Hideo are twins with different jobs. Akira earns five-eighths of what Hideo earns, but Akira's expenses are half of Hideo's. Akira ends up saving 40% of his income. What percentage of his income does Hideo save?
Answer:
25%
Step-by-step explanation:
Let x represent Akira income and let y represent Hideo income.
Since Akira earns five-eighths of what Hideo earns, therefore Akira income is given by:
x = (5/8)y
Let a represent Akira expenses and let y represent Hideo expenses. Since Akira expenses is half of Hideo, hence:
a = (1/2)b; b = 2a
Given that Akira savings is 40% of his income, we have:
savings = income - expenses
40% of x = x - a
a = x - 0.4x
a = 0.6x
For Hideo:
Income = y, expenses = b = 2a
Savings = income - expenses
Savings = y - 2a
Savings = y - 2(0.6x) = y - 1.2x
Savings = y - 1.2(5/8)y
saving = y - 6y/8
savings = 2y/8 = 0.25y
Therefore Hideo saves 25% of his income
please help me, i’m super confused one what to do since my teacher did not explain well
Find the equation of the linear function represented by the table below in
slope-intercept form.
V
5
-10
8
A linear function in slope intercept form is
y = mx + c
To find the equation, you need m and c. This can be found by substituting the points you have.
For example, 5 = -1(m) + c and -7 = 2(m) + c
From here, do simultaneous equations
c = m + 5
-7 = 2(m) + m + 5
3m = -7 -5
m = -4
c = m + 5
c = 1
Rewrite the equation: (This is your answer)
y = -4x + 1
Write 546/61 as a mixed number.
Can you solve it
Answer:
8 58/61.
Step-by-step explanation:
546/61 = 8 remainder 58
so it's 8 58/61.
Zena wants to paint a rectangle on a wall to serve as the background for a mural. She has enough paint to cover 38.25 square feet of wall space. If the width of the rectangle is 4.5 feet, what is its maximum length? a 33.75 ft b 8.5 ft c 38.25 ft d 4.5 ft
Answer:
8.5 feet.
Step-by-step explanation:
it is 38.25 / 4.5
Answer:
8.5
Step-by-step explanation:
how much sit-ups can you do in 1 minutes?
Solve this inequality 3t < 327
Answer fasttt plsssssss
Answer:
25ax25b= 625
Solve for x. If anybody can, can someone help me out with this one? Thank you!!
Answer:
x=3
Step-by-step explanation:
Help please help help help:)
Answer:
1/8 of a pound
Step-by-step explanation:
(3/4) ÷ 6 = .125 = 1/8
The straight line L1 passes through the points with coordinates (6, 5) and (10, 3)
The straight line L2 passes through the origin and has gradient -3
The lines L1 and L2 intersect at point P
Find the coordinates of P.
Answer:
The coordinates of point p are:
x = -3.2
y = 9.6
Step-by-step explanation:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then if we know that L1 passes through the points (6, 5) and (10, 3) the slope of this line will be:
a = (3 - 5)/(10 - 6) = -0.5
Then this line will be something like:
y = -0.5*x + b
To find the value of b we can just replace the values of one of the points in the above equation. For example if we use the point (6, 5), this means that:
x = 6
y = 5
Then we get:
5 = -0.5*6 + b
5 = -3 + b
5 + 3 = b
8 = b
Then the equation for line L1 is:
y = -0.5*x + 8
Now, for line L2 we know that it has a gradient -3 (for linear equations, the gradient is the same as the slope)
Then line L2 has a slope equal to -3
y = -3*x + b
And we know that this line passes through the origin, (0, 0)
Then if we replace the values of that point in our equation, we get:
0 = -3*0 + b
0 = b
Then line L2 is:
y = -3*x
Then our two lines are:
y = -0.5*x + 8
y = -3*x
Now we want to find the point where these lines intersect. The lines will intersect in one point that belongs to both lines, then we can use the relation:
-0.5*x + 8 = y = -3*x
-0.5*x + 8 = -3*x
now we can solve this for x.
-0.5*x + 8 = -3*x
8 = -3*x + 0.5*x
8 = -2.5*x
8/-2.5 = x = -3.2
Now we need to evaluate one of the lines on this value, i will use line L2
y = -3*(-3.2) = 9.6
Then we can conclude that the lines do intersect in the point:
x = -3.2
y = 9.6
this point is written as: (-3.2, 9.6)
What is the answer please
Answer:
I would say 45
Step-by-step explanation:
180-90=90
90/2=45
What is the slope for this graph?*
(3,2)
|(1,2)
(-2,1)
(-1,2)
Answer:
the slope is 0
Step-by-step explanation:
Answer:
the answer is 0 .....,..........,..,
Trigonometric functions
Answer:
in mathematics,the trigonometric functions are real function which relate an angle of a right angle triangle to ratios of two side lengths.They are widely used in all sciences that are related to geometry,such as navigation,solid mechanics,celestial mechanics,geodesy,and many others.
Which is equivalent to the ratio 35:100
Answer:
D
Step-by-step explanation:
35:100
/5. /5
7:20
and you cant simply anymore
Answer: D. 7:20
Step-by-step explanation: Because 35 divided by 5 =7
And 100 divided by 5 =20
So the answer is (D.) 7:20
ZOOM IN IF YOU CANT SEE THE PIC. I NEED HELP ASAP!
Answer:
The answer is the last one!! 3/14
Step-by-step explanation: