‼️GEOMETRY‼️
What is the approximate surface area of the largest sphere that can fit inside a cube with a side length of 18 inches?
1018 square inches
1356 square inches
4069 square inches
6104 square inches
Answers
Answer:
A.) 1018 square inches
Step-by-step explanation:
The largest sphere will have a diameter equaling the length of the cube (see picture).
If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:
[tex]SA=4\pi r^2[/tex]
For this formula, we need the radius of the sphere. Divide the diameter by 2:
[tex]\frac{18}{2}=9[/tex]
The radius is 9 inches. Plug this into the equation:
[tex]SA=4\pi *9^2[/tex]
Simplify the equation:
[tex]SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87[/tex]
Round the result to the nearest whole number:
[tex]1017.87[/tex] → [tex]1018[/tex]
The surface area is 1,018 inches².
:Done
Picture:
In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.
Related Questions
Write three expressions equivalent to 3^2 9^2
Answers
Answer:
0-^
Step-by-step explanation:
An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.
(a)
Write an exponential function for the number of people A who had watched the video n hours after the initial observation. (Enter a mathematical expression.)
Answers
Answer:
(a) The exponential function representing the number of people who had watched the video [tex]t[/tex] hours after the initial observation is [tex]n(t) = 129\cdot 1.3^{\frac{t}{3} }[/tex].
(b) As [tex]n(120) < 5\times 10^{6}[/tex], we conclude that this video is not going "viral".
Step-by-step explanation:
Statement is incomplete. The complete statement is:
An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.
(a) Write an exponential function for the number of people A who had watched the video n hours after the initial observation.
(b) A video is said to go "viral" if the number of people who have watched the video exceeds 5 million within 5 days (120 hours). Would this video be considered to have gone viral?
(a) From the statement of the problem we get the following relationship:
[tex]\frac{n_{i+1}}{n_{i}}= r^{[(i+1)-i]}[/tex] (Eq. 1)
Where:
[tex]n_{i}[/tex] - i-th number of people watching a video, dimensionless.
[tex]n_{i+1}[/tex] - (i+1)-th number of people watching a video, dimensionless.
[tex]r[/tex] - Increase ratio, dimensionless.
For Induction Theorem, we get the following relatioship for [tex]i = 0[/tex]:
[tex]\frac{n_{1}}{n_{o}} = r^{1-0}[/tex] (Eq. 2)
For [tex]i = m[/tex], the following relationship is constructed:
[tex]\left(\frac{n_{1}}{n_{o}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+1}}{n_{m}} \right) = r^{m}[/tex]
[tex]\frac{n_{m+1}}{n_{o}} = r^{m}[/tex](Eq. 3)
And for [tex]i = m+1[/tex], we have the following expression:
[tex]\left(\frac{n_{1}}{n_{0}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+2}}{n_{m}} \right) = r^{m+1}[/tex]
[tex]\frac{n_{m+2}}{n_{0}} = r^{m+1}[/tex](Eq. 4)
If we multiply (Eq. 3) by the (m+1)-th ratio based on (Eq. 1):
[tex]\left(\frac{n_{m+1}}{n_{o}}\right)\cdot \left(\frac{n_{m+2}}{n_{m+1}} \right) = r^{m} \cdot r[/tex]
[tex]\frac{n_{m+2}}{n_{o}} = r^{m+1}[/tex]
Which is (Eq. 4) and the exponential function is represented by:
[tex]n_{i+1} = n_{o}\cdot r^{i}[/tex], [tex]i\in \mathbb{N}_{O}[/tex] (Eq. 5)
As the number of people is increased at constant rate every 3 hours, we get that [tex]i[/tex] is:
[tex]i = \frac{t}{3}[/tex], [tex]t \in \mathbb{R}[/tex], [tex]t \geq 0[/tex] (Eq. 6)
Where [tex]t[/tex] is the time, measured in hours.
Then, the exponential function is:
[tex]n(t) = n_{o}\cdot r^{\frac{t}{3} }[/tex] (Eq. 7)
Where [tex]n_{o}[/tex] is the initial number of people watching the video, dimensionless.
If we know that [tex]n_{o} = 129[/tex] and [tex]r = 1.3[/tex], then the exponential function representing the number of people who had watched the video [tex]t[/tex] hours after the initial observation is:
[tex]n(t) = 129\cdot 1.3^{\frac{t}{3} }[/tex]
(b) If we know that [tex]t = 120\,h[/tex], then we evaluate the exponential function:
[tex]n (120) = 129\cdot 1.3^{\frac{120}{3} }[/tex]
[tex]n(120) = 4.659\times 10^{6}[/tex]
As [tex]n(120) < 5\times 10^{6}[/tex], we conclude that this video is not going "viral".
Someone help please I can give brainlist?
Answers
Answer:
-2.4f - 21
Step-by-step explanation:
brainlest!!!!!!!!! please help me
all the choices are the same
please help thx!!!!!
Answers
Answer:
Graph 1- last option choice
Graph 2- first option choice
Graph 3- third option choice
Graph 4- second option choice
Hope this helps stay safe!
Step-by-step explanation:
When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".
Answer:
1. x < 1
2. x </= 1
3. x >/= - 1
4. x > 1
PLEASE HELP
Given: AABC with vertices A(5,-2), B(5, -7), and C(1, -2). Which set of
coordinates best repositions the triangle to make a coordinate proof easier?
o (0,0),(4,0), and (4.-5)
O (0,0).(-4,0), and (0, -5)
O(0,0). (0,4), and (5,0)
O (0,0),(4,0), and (0, -5)
None of the other answers are correct
Answers
Answer: (0,0),(0,4), and (5,0)
Step-by-step explanation:
It is easy to find lengths of horizontal and vertical segments and distances from (0,0) so always place one vertex at the origin and one or more sides on an axis.
This answer has an x intercept and y intercept.
Find the rate of change given the following
points.
(-1, 3) and (1,7)
Answers
Fred has $200. He wants to purchase a gym bag for $26 and as many pair of shoes as he can. Each pair of shoes is $45. What is the maximum number of pairs of shoes he can
purchase in addition to the gym bag?
Answers
Answer:
3 shoes
Step-by-step explanation:
You can set up an equation to solve this question like this:
200=45s+26
174=45s
174/45=s
s=3.867
You can't have a part of a shoe, so you have to round down to get 3 shoes
Answer:
3
Step-by-step explanation:
In order to get the answer to this question you subtract in till you can no longer subtract after subtracting the cost of the bag.
What we do know:
[tex]M=200[/tex]
[tex]B=26[/tex]
[tex]S=45[/tex]
[tex]200-26=174[/tex]
[tex]174-45=129[/tex]
[tex]129-45=84[/tex]
[tex]84-45=39[/tex]
[tex]S=3[/tex]
Hope this helps
Simplify (three^six)^eigthteen
Answers
Answer:
[tex](3^6)^{18}=3^{108}=3.38139191\times10^{51}[/tex]
Which of these graphs represents a function?
Answers
Answer:
C
Step-by-step explanation:
Each x value only corresponds with 1 y value
Mr. Jackson sold 3 computers in the first year . in the second year he sold 4 times more than the first and third year. He was able to sell 6 times as many monitors than the first year how many monitors did Mr. Jackson sell in three years?
Answers
what are all the factors of 32?
Answers
Xavier has a lunch food budget of $120 a month. He spends an average of $6 per day on lunch. Create a table and then a graph to represent the relationship. Then write an equation
where d represents the number of days and m represents that amount of money he had left.
Answers
Answer:
m= 120 - 6*d
Step-by-step explanation:
budget is $120 per 1 month, spends $6 per 1 day
on the the table you have 2 columns: one labele it "days" and one "$ spent" and fill it in:
days: 1,2,3,4,..
$ spent: 6, 6*2=12, 6*3= 18, 6*4= 32,...
on the graph lable the horizontal axis "days" and the vertical axis "$ spent"
now plot the points (1,6), (2,12),(3,18), ..., and draw a line trough them
the equation is
m= 120 - 6*d
so after 20 days for example, out of 120 will have m=120-6*20=120-120=0,
$0 wil have in 20 days
If g(x)=4x-5 find g(-3).
Answers
Answer: -17
Explanation: If g(x) = 4x - 5, then g(-3) = 4(-3) - 5 which simplifies to -17.
help me with this plzz i need answer asap
Answers
Answer:
oof this is easy
Step-by-step explanation:
Straight angles consists with
two right angles
2
Straight angles consists with
one obtuse angle and one acute angle
RESULT
My friend is wrong because a straight angle either consists with two right angles or one obtuse angle and one acute angle.
Find the equation of the line that passes through the following two points: (3, -7) and (7, 2)
Answers
Answer:
[tex]y=\frac{9}{4}x-\frac{55}{4}[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Given points: (3, -7), (7, 2)
(3, -7) = (x1, y1)
(7, 2) = (x2, y2)
To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.
First, let's find the slope. To do this, input the given points into the slope formula:
[tex]\frac{2-(-7)}{7-3}[/tex]
Simplify:
2 - (-7) = 2 + 7 = 9
7 - 3 = 4
[tex]\frac{9}{4}[/tex]
The slope is [tex]\frac{9}{4}[/tex].
To find the y-intercept, input the slope and one of the given points(in this example I'll use point (7, 2)) into the equation and solve for b:
[tex]2=\frac{9}{4}(7)+b[/tex]
[tex]2=\frac{63}{4}+b[/tex]
[tex]-\frac{55}{4} =b[/tex]
The y-intercept is [tex]-\frac{55}{4}[/tex].
Now that we know the slope and the y-intercept, we can write the equation:
[tex]y=\frac{9}{4}x-\frac{55}{4}[/tex]
h+ j(j – h); use h = 2, and j = 6
Answers
Answer: 32
2+6(6-2)
8(4)
32
Write the equation of the line through (3,9) and (-2,9)
Answers
Answer:
y = 9
Step-by-step explanation:
y-y1 = m(x-x1)
m is the slope =y2-y1/x2-x1=9-9/-2-3=0
pick any number out of the given two for (x1, x2)
y-9 = 0*(x-3) so
y-9 = 0 add 9 to both sides
y = 9
What is the slope in the linear equation y= -3x +7?
Answers
Answer:
-3
Step-by-step explanation:
the coefficient of the x term is the slope in any equation that is in slope intercept form
Answer:
-3 is the slope
Step-by-step explanation:
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -3x+7
-3 is the slope and 7 is the y intercept
hey im new , who can show me how to use this ,thanks
Answers
Answer:
Sure, if u want to ask a question click question, however you need to answer questions to recieve points in order for you to ask questions. So answers some questions then you can ask
Step-by-step explanation:
Find the total cost to the nearest cent.
$49.95 pair of shoes; 5% tax
Answers
Answer:
$52.45
Step-by-step explanation:
the tax is $2.50, if we add that to $49.95 we get $52.45
Total cost will be $52.45.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
Cost of shoes = $49.95
Tax = 5%
Now,
The value of tax = 49.95 × 5%
= 49.95 × 5/100
= 2.50
So, Total cost = $49.95 + $2.50
= $52.45
Thus, Total cost will be $52.45.
Learn more about the percentage visit:
https://brainly.com/question/24304697
#SPJ5
PLEASE HELPP THIS IS IN A DIFFERENT language TO MY BRAin I swear My brain is LagGiNg RN
Answers
Answer:
A
Step-by-step explanation:
the first number in slope intercept is the slope and the second number is the y-intercept
Answer:
The answer is Choice a
Step-by-step explanation:
Estimate the answers to these calculations (167.8 x 24) /38
Answers
Answer:
105.978947368
Step-by-step explanation:
Sara used a number line to add. She started counting at 10, and then she counted until she
was over the number -4 on the number line. If Sara is modeling addition, what number did
she have to add to 10?
Answers
Answer:
-14
Step-by-step explanation:
You need a piece of paper to measure 56.34 cm. If you tape
two together that each measure 35.87 cm, how much do you
need to cut off?
Answers
Answer:
20.47.
Step-by-step explanation:
You need to 56.34, by 35.87. And you get your answer. 20.47!
Are the ratios 30:15 and 32:12 equal?
Answers
Answer:
No, they are not
Step-by-step explanation:
:(
Which three lengths could be used to form a right triangle?
15, 15, 48
19, 36, 57
51, 68, 85
7, 10, 14
Answers
Answer:
7, 10, 14 would be the answer
is the relation function?
choose the correct answer
marking brainlist
Answers
Answer:
Not a function because an output has two different inputs
Step-by-step explanation:
. Are the expressions 3(m - 2) + 2(m - 2) and 5(m - 2) equivalent expressions?
Answers
Then
Factor it you get 5(m -2) so yes the expressions are equivalent
Aubrey’s monthly bank statement shows a total of $51 in fees for ATM withdrawals. If Audrey made 17 withdraws, what is Audrey charged for each withdrawal?
Answers
Answer:
Audrey was charged $3 for each withdrawal.
Step-by-step explanation:
We have to calculate the amount of money charged on one transaction.
In order to find the amount for one ATM withdrawal, the total amount for ATM withdrawals will be divided by number of withdrawals.
Given
[tex]Total\ ATM\ withdrawal\ fees = \$51\\Total\ withdrawals = 17\\Amount\ for\ one\ withdrawal = \frac{Total\ fees}{No.\ of\ withdrawals}\\= \frac{51}{17}\\= \$3[/tex]
Hence,
Audrey was charged $3 for each withdrawal.
Find the value of in the triangle shown below
9, 7, and x around the triangle
Answers
Answer:
Step-by-step explanation: 56
Answer:
130 is correct
Step-by-step explanation: