Brad is hoping to package exactly 48 baseballs together. He sees the side of a box in his storeroom that is 2 x 3. What is he hoping the other dimension is? please help me out! I need the eqation and answer and a drawing of it too! Please help me out!
Answers
The given dimensions of the base of the box are 2 x 3 units.
Let h be the height of the box.
So, the volume of the box = 2 x 3 x h ...(i)
The shape of baseball is spherical and one baseball fits in a cubical box having the minimum dimensions equal to the diameter of the spherical ball.
Assuming the diameter of the baseball is d units.
So, the volume occupied by one baseball= volume of the cubical box having the side [tex]d[/tex] units.
[tex]=d^3[/tex] cubic units
So, the volume required to pack 48 baseballs
[tex]= 48 d^3 \cdots(ii)[/tex]
Assuming that all the baseballs fit in the box, i.e peripheral balls in every horizontal and vertical layer touched the box as shown in the figure.
So, the length, 3 units and the width, 2 units, must be the integral multiple of the diameter, [tex]d[/tex] units, of the baseball. i.e
The length, [tex]3 = ad\cdots(iii)[/tex]
The width, [tex]2=bd\cdots(iv)[/tex]
The height, [tex]h=cd\cdots(iv)[/tex]
where [tex]a,b[/tex] and [tex]c[/tex] belong to the natural number.
This required volume must be equals to the volume of the box.
From equations (i) and (ii),
[tex]2\times 3\times h=48d^3[/tex]
[from (iii) and (iv)]
[tex]\Rightarrow abhd^2=48d^3[/tex]
[tex]\Rightarrow h=\frac{48d^3}{6abd^2}[/tex]
[tex]\Rightarrow h=\frac{48}{ab}d[/tex]
On comparing with the equation (iv)
[tex]c=\frac{48}{ab}\cdots(v)[/tex]
Now, if the diameter of the baseball is unity,i.e, d=1 unit
( integer) and (integer) [from (iii) and (iv)]
(also an integer) [from (v)]
Now, the height of the box,
[tex]h=8 \times 1= 8[/tex] unit.
Hence, the other dimension of the box, is 8 units corrosponding to the unity diameter of the baseball.
Note the height of the box depends on the diameter of the baseball, so it will have infinite possible value for different value of the diameter.
For example, the value of height for d=1 unit has been shown.
and another example may be if units, then (integer) and (integer)
(also an integer) [from (v)]
Now, the height of the box,
[tex]h=2 \times 0.5= 1[/tex] unit. [from (iv)]
Here, the height of the box is 2 units corrosponding to 0.5 unit diameter of the baseball.
The possivle values of d can be taken for which [tex]a,b[/tex] and [tex]c[/tex] must be integers.
Related Questions
Th e NCAA recommends that a competition diving pool intended for use with two 1-m springboards and two 3-m springboards, in addition to diving platforms set at 5 m, 7.5 m, and 10 m above the water, have a width of 75 ft 1 in., a length of 60 ft, and a minimum water depth of 14 ft 10 in. What is the minimum volume of water such a pool would hold in cubic yards, to the nearest whole number?
Answers
Answer:
The volume of the swimming pool is approximately 2475 yd³ to the nearest whole number
Step-by-step explanation:
The given information are;
The width of the swimming pool = 75 ft. 1 in.
The length of swimming pool = 60 ft.
The depth of the swimming pool = 14 ft. 10 in.
Therefore;
The volume of the swimming pool = Width × Length × Depth
The volume of the swimming pool = 75 ft. 1 in. × 60 ft. × 14 ft. 10 in.
The volume of the swimming pool = 901 in. × 720 in. × 178 in. = 115472160 in.³
1 in.³ = 2.14335 × 10⁻⁵ yd³
∴ 115472160 in.³ = 115472160 in.³ × 2.14335 × 10⁻⁵ yd³/in³ ≈ 2474.969 yd³
Which gives;
The volume of the swimming pool ≈ 2475 yd³ to the nearest whole number.
Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10. She wrote the following to represent the situation with a linear equation. What kind of equation did she use?
Answers
Answer: Standard Form
Step-by-step explanation:
In the slope intercept form, you can only solve for one equation at a time.
Ex: y = -2.5x + 15
but when using standard you can easly get the answer for both ticket prices
Ex: 25x + 10y = 150
5r + 2g = 30 is the linear equation that best describes the scenario.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10.
Let "r" be the Number of reserved tickets she bought
and "g" be the number of general admission tickets she bought
Money spent od reserved ticket = 25 * r
Money spent in general tickets = 10 *g
Since she totals spent 150$
Thus, the equation will be
25r + 10g = 150
Divide by 5 into both the sides
5r + 2g = 30
therefore, The linear equation that represents the given situation is 5r + 2g = 30.
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3. If Greg forgives Chad's $3 debt to him, how does that affect how much money Chad has?
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Q: What is the measure of <8?
A)45
B)55
C)155
D)135
Please needed help asap!
Answers
Answer:
your answer should be, D.135
i hope this helps!
Answer:
D) 135
Step-by-step explanation:
--------------- = 180 degrees
It's split and the other half is 45 degrees.
All you have to do is subtract.
180-45=135
<8 = D) 135
( need help asap for a test) Ms. Smith bought a 5 pound bag of candy for her 6th grade classroom. She gave away 2 pounds of candy to her students during the first unit of instruction and ate 6 ounces of candy during planning.
(16 ounces = 1 pound)
How many ounces of candy does Ms. Smith still have in her bag?
A.
38 ounces
B.
42 ounces
C.
48 ounces
D.
54 ounces
Answers
Answer:
c
Step-by-step explanation:
5-2=3 3•16=48 48-6=42
Choose the equation below that represents the line passing through the point (−2, −3) with a slope of −6
Answers
Answer:
a
Step-by-step explanation:
:)
y-y1=m(x-x1) is the formula
I need help! PLEASE HELP!!
Answers
Answer:
Step-by-step explanation:
P = pizza slices
S= soda drinks
98 = 23*P + 31*S
a) name the transversal connecting 1 and 5
b) name the transversal connecting 7 and 14
c) name the transversal connecting 8 and 11
d) name the transversal connecting 7 and 15
e) name the transversal connecting 3 and 9
Answers
Answer:
a) Name the transversal connecting 1 and 5. Line r b) Name the transversal connecting 7 and 14. Line q c) Name the transversal connecting 8 and 11. Line s d) Name the transversal connecting 6 and 15. Line q e) Name the transversal connecting 3 and 9. Line p
Step-by-step explanation:
The angles pairs and the transversal connecting them are:
a. <1 and <5: transversal r.
b. <7 and <14: transversal q
c. <8 and <11: transversal s
<6 and <15: transversal q.
<3 and <9: transversal p.
Note the following about what a transversal is:
A transversal is a line that intercepts or cut-across two straight lines.A transversal will connect two angles that lie in two other straight lines the transversal intercepts.The two angles connected by a transversal can lie on opposite sides of a transversal or on same side along the transversal.Let's determine the transversal connecting the following given angles:
<1 and <5, is connected by transversal r.<7 and <14 is connected by transversal q<8 and <11 is connected by transversal s<6 and <15 is connected by transversal q<3 and <9 is connected by transversal pTherefore, the answers are:
a. <1 and <5: transversal r.
b. <7 and <14: transversal q
c. <8 and <11: transversal s
<6 and <15: transversal q.
<3 and <9: transversal p.
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I went to the grocery store to buy avocados. They were $3 for 4. How much will it cost me for 10?
Answers
Answer:
7.50$
Step-by-step explanation:
3+3+1.5=7.50$.
36÷2/3
pls help i no understand
Answers
Easiest way to do this is to put 36 over 1. Then cross multiply and get 3(36)/2(1) which is 108/2 and that comes out to 54.
Can anyone please help me with this?
Answers
What is the equation of this line?
A. y=43x−4
B. y=34x−4
C. y=−4x+34
D. y=−4x+43
Answers
Answer:
Y=4/3x - 4
Step-by-step explanation:
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the given line is y=(4/3)x-4.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope of the line can be calculated with the two points that are present on the line, in this case, these points are (3,0) and (0, -4). Therefore, the slope is,
Slope, m = (-4 - 0)/(0 - 3) = -4/-3 = 4/3
The y-intercept of the line is -4, therefore, the equation of the line can be written as,
y = mx + c
y = (4/3)x - 4
Hence, the equation of the given line is y=(4/3)x-4.
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How do I factor
x ^5−x^ 4+3x−3
Answers
Help? Find angle psw
Answers
find the area of the equilateral triangle.if its perimeter is 24cm
Answers
Answer:
16√3 cm²
Step-by-step explanation:
The perimeter of a triangle is the sum of its all three sides. Since this is an equilateral triangle, all sides are equal.
Let's consider one side of the triangle to be 'x'
Givent that, the perimeter is 24cm,
The equation should be x + x + x = 24
⇒3x = 24
∴ x = 8 cm
To find the area of the triangle, we need to find the height, and for that, we can use trigonometry.
Since it is an equilateral triangle, all angles are exact 60°.
let's draw a line and mark it as 'h'.
we can use sine formula to find out the opposite i.e. h
sin∅ = opposite ÷ hypotaneous
sin 60° = h ÷ 8
h = 8 sin 60°
h= 4√3
Now, let's find the area
Area = 1/2 × base × height
Area = 1/2 × 8 × 4√3
area= 16√3 cm²
a) What is y=mx+b?
b) What does the m stand for?
c) What does the b stand for?
d) Where do I find the x & y?
e) If I get two coordinate points how do I find the slope? What is the formula?
f) If I get a graph, how do I find the slope?
Answers
b) the m is the slope of the line.
c) the b is the y-intercept
d) the x-axis is horizontal, the y-axis is vertical.
e) m = rise/run = y2-y1/x2-x1
f) pick 2 points on the graph & determine their coordinates. find the difference in the y-coordinates (the rise) & the difference in the x-coordinates (the run) & divide them.
x - 13 = 22 linear equations
Answers
Answer:
x = 35
Step-by-step explanation:
x - 13 = 22
Add 13 to each side
x - 13+13 = 22+13
x = 35
See attachment for math work and answer.
A circuit board manufacturer rejects a 100-ohm resistor if its measured resistance is 0.15 ohm or more away from 100 ohms. Resistors A and B are rejected. Resistor A's resistance differs from 100 ohms by +0.15 ohm. Resistor B's resistance differs from 100 ohms by -0.78 ohm. Which resistor has a resistance closer to 100 ohms?
Answers
Answer:
Resistor A has a resistance closer to 100
Step-by-step explanation:
Here, we want to know which of the two resistors have a resistance closer to 100 ohms
To know the resistance closer to 100, we need to know the absolute value of the resistances
-0.78 has a resistance of 100 - 0.78 = 99.22
The 15 ohms resistor has resistance of 100 + 0.15 = 100.15
Since 100.15 is closer to 100 than 99.22, due to the absolute value of both, then the +0.15 ohm resistor is closer to 100
Find the average rate of change of g(x)=3x^2 ver the interval [-5, -3].
Answers
Answer:
ill help
Step-by-step explanation:
How do you write a linear equation given the slope and a point that
is not the y-intercept?
Edge 2020
Answers
Answer:
point slope form
Step-by-step explanation:
hi! we can use point slope form:
y-y1=m(x-x1)
where m is the slope, x1 is the x-coordinate of the given point, and y1 is the y-coordinate of the given point.
example:
slope is 4
ordered pair is (2,3)
y-3=4(x-2)
y-3=4x-8
y=4x-5
hope this helps!
From 24 grams to 96 grams ( percent change )
Answers
Answer:
i think it is 300%
Step-by-step explanation:
(URGENT!! PLS HELP) The color of paint used to paint a race car includes a mixture of yellow and green paint. Scotty wants to lighten the color by increasing the amount of yellow paint 30%. If a new mixture contains 3.9 liters of yellow paint, how many liters of yellow paint did he use in the previous mixture?
Answers
Answer:
3 litersStep-by-step explanation:
Let the initial amount of yellow paint be x
Then we have x increased by 30% equals 3.9 liters:
x + 0.3x = 3.91.3x = 3.9x = 3.9/1.3x = 3 litersThe points in the table lie on a line. Find the slope of the line.
Answers
The slope of the line is [tex]-\frac{3}{4}[/tex]
First, you must find 2 points.
(-6,8) (-2,5)
Then, you must substitute the value of the points in.
[tex]\frac{5-8 }{-2+6}[/tex]
Finally, simplify the fraction.
[tex]-\frac{3}{4}[/tex]
If you are given the graph of a line and are asked to write the equation of a
perpendicular line, does it matter what the y-intercept will be for the equation
you write? Explain why or why not.
Answers
Answer:
Yes
Step-by-step explanation:
It does matter because when it comes to perpendicular lines the equations for the lines with have opposite y-intercepts. So if you had y=2x +3 the perpendicular line would be y=-1/2x +3.
Yes, the y-intercept of the equation written does matter and can be determined if a point on the line is given.
According to the question;
We are required to determine; does it matter what the y-intercept will be for the equation you write when given the graph of a line and are asked to write the equation of a perpendicular line.Although, according to line geometry;
The slope of two perpendicular lines are related as follows;
m1 m2 = -1The y-intercept of the perpendicular line does matter when writing the equation of the line and can be determined if a point on the perpendicular line is given.
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What is the name of the lake located at letter B on the map above? Answer is C :)
Answers
Answer:
the answer is C. lake Texoma
hope this helps
please please please i need help !!!
Answers
Answer: Choice B
h(c) = 1 for at least one c between -3 and 4
====================================================
Explanation:
Draw an xy axis system. Plot the points (-3,-1) and (4,2) on this grid. These points come from the fact that h(-3) = -1 and h(4) = 2. These are the endpoints of the h(x) function.
Next, draw horizontal lines through both points. Also, draw vertical lines through the two points as well. A rectangle will form.
The region inside this rectangle is all we care about.
We're told that h(x) has endpoints mentioned earlier, and h(x) is continuous, so that means we have some curve or line through the two points. One such example is shown below. There are infinitely many possible curves to draw out as long as they stay in the rectangle.
----------------------
After you have your h(x) function curve drawn, draw a horizontal line through y = 1 on the y axis. This is the dashed line in the diagram below.
This horizontal line crosses the green h(x) curve at one point or more. In my example, it does so at one point only. However, you could easily draw h(x) so that it crosses y = 1 as many times as you want (just have it squiggle up and down multiple times).
This shows that h(c) = 1 is possible when [tex]-3 \le c \le 4[/tex]. Here c is playing the role of x since it is the input of a function. The h(c) is the output, so that's the y value.
This says that for some input between -3 and 4, it's possible to get an output of 1.
-------------------------
Here's a real world example of the intermediate value theorem.
Let's say the endpoints are A and B, and they are two towns.
The h(x) curve is a road connecting the towns.
To go from A to B, or vice versa, we need to cross over some border that is between the towns. The border in this case is the dashed horizontal line in the diagram.
side note: A special use of the intermediate value theorem is to show that a root exists on some interval (if you know the function changes between positive to negative, or vice versa).
A rectangular tank has a length of 12 feet, width of 8 feet, and height of 5 feet. Frankie filled the tank with water at a rate of 4 cubic feet per minute. At this rate, how long will it take Frankie to completely fill the tank without overflowing it?
Answers
Answer:
Step-by-step explanation:
12 x 8 x 5 = 480/4= 120 minutes or 2 hours
Carson was shopping online for bow ties to wear with his school uniform he bought a certain number of ties that each cost $12.50 and paid a flat rate of 19 for shipping and handling he has 220 in his bank account before buying the tie write the expression to represent how much money Carson spell on low tide be sure to Define your variable
Answers
Given :
Carson was shopping online for bow ties to wear with his school uniform he bought a certain number of ties that each cost $12.50 and paid a flat rate of 19 for shipping and handling.
He has $220 in his bank account before buying the tie.
To Find :
Maximum number of ties he can buy.
Solution :
Let, price of buying x ties is y.
y = 19 + (12.50)x
It is given that he has $200 in his bank account.
So, price of buying tie ≤ $200
y ≤ 200
19 + (12.50)x ≤ 200
(12.50)x ≤ 200 - 19
x ≤ 14.48
Since, number of tie cannot be in decimal.
x ≤ 14
Therefore, maximum tie he can buy is 14.
Hence, this is the required solution.
PLEASE HELP!! MATH FINAL + NO EXPLANATION NEEDED :))
Answers
Answer:
C.
Step-by-step explanation:
Michael rents a car for one day. The charge is $30 plus the $0.12 per mile. He wants to spend exactly $105. How many miles can he drive?
Answers
Answer:
He can drive 625 miles
Step-by-step explanation:
Total spent: $105
$105- $30 charge = $75
$75/$0.12 per mile charge
= 625 Miles