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
(3x+10)
(5x+10)
Set up an equation and solve for x.
Answers
[tex]/bold{Explanation:}[/tex] 3x+10 + 5x+10=180
8x+20=180
8x=160
x=20
Bob owed S225 on his store credit card. Ile made a payment of S75. Ilow much does Bob owe on his credit card? 0 -150 O 150 O 300 -300
Help me pleasee !
Answers
The answer is -300 because he owes -225 and then when he spends they subtract the amount he spent so the equation would be -225-75= the answer of -300
1. A tortoise is running on a long, moving sidewalk. Her pedometer doesn't report her speed, but she knows that—since she got on—she's been running for 40 minutes and that she's traveled 3 kilometers. Unfortunately, she realizes she left her suitcase on the ground just before she got on the sidewalk. Since she's too short to climb over the handrails, she decides to turn around and run at the same speed back to her suitcase. If it takes her 2 hours to return to her suitcase, how fast (in kilometers per hour) was the moving sidewalk moving? How fast (in kilometers per hour) was the tortoise running?
Answers
Answer:
the sidewalk speed q = 3km/hr
the tortoise speed p is 1.5 km/hr
Step-by-step explanation:
From the given information:
let the speed of the tortoise be p & the speed of the sidewalk be q
she's been running for 40 minutes (40/60 = 2/3) and that she's travelled 3 kilometres
Thus,
p + q = [tex]\dfrac{3}{\dfrac{2}{3}}[/tex]
p + q = 9/2
p + q = 4.5 ----- (1)
when returning, she travelled 3km in 2 hours
i.e. -p + q = 3/2
-p + q = 1.5 ----- (2)
Thus, by using the elimination method for equation (1) and (2)
p + q = 4.5 ----- (1)
-p + q = 1.5 ----- (2)
2q = 6
q = 6/2
q = 3 km/hr
From equation (1)
p + q = 4.5
p + 3 = 4.5
p = 4.5 - 3
p = 1.5 km/hr
Therefore, the sidewalk speed q = 3km/hr and the tortoise speed p is 1.5 km/hr
what is pi? will mark brainliest!!
Answers
Answer:
Short answer: 3.14 Long answer: First 1000 decimal places
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
Step-by-step explanation:
Answer:
The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159.
Hank draws a line with a zero slope through the points
(–2, 4) and (3, b). Which value of b could represent Hank’s second point?
–3
–1
4
9
Answers
Answer:
It's 4
Step-by-step explanation:
Answer:
The answer is C which is 4
Step-by-step explanation:
I just took the test and got it right
Hopefully this helps you
pls mark brainlest
which function has zeros of -8,1 and 3?
Answers
Answer:
A. y = (x - 3)(x + 8)(x - 1)
Step-by-step explanation:
To find zeros of a polynomial, we set the polynomial equal to zero.
We can eliminate C and D; as we set them equal to 0, we see that a root would be 0 due to x. Since we are not looking for a root of 0, those 2 answer choices are incorrect.
Between A and B, A is correct:
A
0 = (x - 3)(x + 8)(x - 1)
x = -8, 1, 3
B
0 = (x + 1)(x - 8)(x + 3)
x = -3, -1, 8
Answer:
Answer A is the correct one.
Step-by-step explanation:
Which function has zeros of -8,1 and 3? We convert each of these zeros into factors, as follows: (x + 8), (x - 1), (x - 3). Answer A is the correct one.
Which of the following is an example of direct variation?
y= cx
xy = c
y = czx
y= cx/z
Answers
Answer: Choice A) y = cx
The 'c' is the constant of variation
For example, if c = 2, then y = 2x is a direct variation. Whatever x is, we double it to get y. As x increases, so does y. As x decreases, then so does y. Both x and y increase/decrease together.
Direct variation equations always go through the origin, and they are always linear. The 'c' plays the role of the slope. You can think of y = cx as y = mx+b where b = 0 in this case and c = m.
Answer ASAP, Find the quadratic equations whose roots are ½ and -5/2
Answers
Answer:
4x^2+8x-5
Step-by-step explanation:
You work backwards to get (2x-1) which gets you the root 1/2 and (2x+5) which gets you the root -5/2 after this you foil what you have so (2x-1) times (2x+5). You do 2x times 2x which gives you 4x^2 2x times 5 which gives you 10x -1 times 2x which gives -2x and lastly -1 times 5 which gives you -5 now you combine like terms and get your final answer of 4x^2+8x-5
Asking for the answer to this algebra problem please! Tysm!
Answers
Answer:
b
Step-by-step explanation:
i did the math
Please help me with this. This is my last one and when you are answering PLEASE SHOW STEPS FOR BRAINSLT. THIS IS DUE TOMORROW
Answers
X= -2
Explanation: the photos are in order :)
Answer:
x = -2
Step-by-step explanation:
3/5 +3/10x = 4/5 + 2/5x
Step 1. Change every fraction into the same denominator
6/10 + 3/10 x = 8/10 + 4/10x
Step 2. Subtract 3/10x
6/10 = 8/10 + 1/10x
Step 3. Subtract 8/10
-2/10 = 1/10x
x = -2
What else would need to be congruent to show that triangle EFG is equal to triangle JKL by SSS?
Answers
Answer:
EF = JK
Step-by-step explanation:
Please help ASAP
Drag and drop the numbers into the correct locations
Answers
Answer:
first box: -1
second box: √-1
Step-by-step explanation:
the imaginary number equals √-1 and when you square it, the roots would go away, leaving you with -1.
HIJ is equal to STR What is the perimeter of STR?
Answers
Answer:
Do you have a picture to show ?
m² - 9m +8
(Factoring)
show steps
Answers
Answer:
I really dont know sorry love <3
Step-by-step explanation:
Find the equation of the line passing through the point (–1, 0) and parallel to the line y = –1∕2x + 3∕7
Answers
Answer:
y = -1/2x - 1/2
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Step 1: Define
y = -1/2x + 3/7
Point (-1, 0)
Step 2: Find parallel line
Parallel lines have the same slope as the original but different y-intercepts.
m = -1/2
y = -1/2x + b
0 = -1/2(-1) + b
0 = 1/2 + b
b = -1/2
Step 3: Write parallel line
y = -1/2x - 1/2
19. A package of 12 confetti eggs costs $2.88.
At this rate, what is the cost of 1 confetti egg?
Answers
Answer:
0.24$
Step-by-step explanation:
Each egg costs 1/12 of 2.88.
So either you multiply 2.88 by 1/12
or you divde 2.88 by 12
Answer:
0.24
Step-by-step explanation:
you would divide 2.88 by 12 hope this helps.
can someone PLEASE answer this
Answers
the correct answer is the last one. hope this helped
Answer:
y = 3x+1
Step-by-step explanation:
Slope:
Change in y = 6
Change in x = 2
6/2=3
Y intercept:
when x is 0 y is 1, so the y intercept is 1
therefore the answer is y = 3x+1
4x - 8 = 12
4x - 8 + 8 = 12 + 8
4x = 20
4/4x = 20/20
x=
Answers
Answer:
x=5
Step-by-step explanation:
If 4x=20 then all we need to do is to divide both sides by 4 and we get x=5. Also, if replace x with 5 within any of the equations it works.
Hope this helps!
The solution is: The value of x is: x=5
Here, we have,
given that,
the expression is: 4x - 8 = 12
we get,
4x - 8 = 12
or, 4x - 8 + 8 = 12 + 8
or, 4x = 20
now, we have,
If 4x=20 then all we need to do is to divide both sides by 4 and we get x=5.
i.e. 4x/4 = 20/4
or, x = 5
Also, if replace x with 5 within any of the equations it works.
Hence, The solution is: The value of x is: x=5
To learn more on Expression click:
brainly.com/question/14083225
#SPJ6
Gcf of 16abc^2, 28abc
Answers
Answer:
4abc..............................
1. Multiply (3)(−4)(2). (5 points)
Answers
Answer:
-24
Step-by-step explanation:
Answer-24
Step-by-step explanation:
3 x -4 x 2
6 x -4 =
-24
In the function f(x) = 3x + 2, f(5)
A. 15
B. 16
C. 17
D. 19
Answers
Answer:
C. 17
Step-by-step explanation:
3 times 5 is 15 , then you add 15 plus two which equals 17.
Answer:
C. 17
Step-by-step explanation:
In the equation f(5)=3x+2, you substitute 5 for x.
Which makes the equation f(5)=3(5)+2
Simplified f(5)=17 after you multiply 3(5) and add 2.
Hope this helps!
I need help with this please!!
Answers
Answer:
The correct choices would be A, C, D & F. Correct me if I'm wrong :)
A local supermarket sells shrimp $9.49/lb and beef for $5.99/lb Todd buys s pounds of shrimp and b pounds of beef. Which of the following inequalities represents that Sandy only has $65 to spend?
Answers
Answer: 9.49s + 5.99b ≤ 65
Plz mark brainliest:)
Write in slope-intercept form with the given information. Show all work. Passes through (-8,3) with a slope of -2
Answers
Answer:
y=-2x-13
Step-by-step explanation:
y=mx+b
3=-2(-8)+b
3=16+b
3-16=b
-13=b
(3^8 ⋅ 2^−5 ⋅ 9^0)^−2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 3^28
Answers
Answer:
I agree with the first answer.
Step-by-step explanation:
Answer:
(38 ⋅ 2−5 ⋅ 90)−2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 328 ((38 ⋅ 2−5 ⋅ 90)−2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 328 (
Step-by-step explanation:
Evaluate the following expression. Express your answer in simplest form. 3/16 + 5/8 × 1/2
Answers
Answer:
1/2
Step-by-step explanation:
We have to follow the order of operations. Since there are no parenthesis or exponents, we do multiplication first. to multiple fractions, we multiply the two numerators (top parts), which in this situation would get us 5*1=5. Then, we multiply the two denominators (bottom parts), which would get us 8*2=16. then we put the first result over the second, and we get 5/16. since the two denominators are the same, we don't need to change anything. we can just add the numerator, and get 8/16, which simplifies to 1/2.
11) What is the y-intercept of the function that passes through the given
coordinates: f(12)=2 and f(15)=3,
Answers
Answer:
The y-intercept is -2
Step-by-step explanation:
Here, we want to find the y-intercept of the function that passes through the given points
The first thing to do here is to get the coordinates of the needed point;
That would be ; (12,2) and (15,3)
It is just like writing f(x) = a ; x would
be x-value while a will be the y-value
The equation of the line passing through the points will be
y = mx + b
where b represents the y-intercept
Let us start by looking at the slope m
m = (y2-y1)/(x2-x1)
m = (3-2)/(15-12) = 1/3
So the line would be;
y = x/3 + b
now to get b, select any of the points, input the x value and the y value
2 = 12/3 + b
2 = 4 + b
b = 2-4
b = -2
1/2a + 1/3a =5 please help :)
Answers
Answer:
a=6
Step-by-step explanation:
1/2a+1/3a=5
5/6a=5
a=6
hope this helps
brainliest?
Answer:
a=6
Step-by-step explanation:
1/2a + 1/3a =5
Multiply each side by 6 to clear the fractions
6(1/2a + 1/3a) =5*6
3a +2a = 30
Combine like terms
5a = 30
Divide by 5
5a/5 = 30/5
a = 6
4. Write the equation of a line that passes through the point (-8, 2) and is parallel to the
line 3x – 2y = 12.
Answers
Answer:
3x - 2y = - 28
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x - 2y = 12 ( subtract 3x from both sides )
- 2y = - 3x + 12 ( divide all terms by - 2 )
y = [tex]\frac{3}{2}[/tex] x - 6 ← in slope- intercept form
with slope m = [tex]\frac{3}{2}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 8, 2) into the partial equation
2 = - 12 + c ⇒ c = 2 + 12 = 14
y = [tex]\frac{3}{2}[/tex] x + 14 ← equation in slope- intercept form
Multiply through by 2
2y = 3x + 28 ( subtract 2y from both sides )
0 = 3x - 2y + 28 ( subtract 28 from both sides )
- 28 = 3x - 2y , that is
3x - 2y = - 28 ← equation in standard form
-3²-7· -3+6
will give brainiest
please!!! i need it answered
Answers
Answer
18
Step-by-step explanation:
I hope this helps
Answer:
18
Step-by-step explanation:
Use the order of operations here to solve your expression.
First do Parentheses, then Exponents, Multiplication and Division, and Addition and Subtraction. An easy way to remember this is PEMDAS.
Let's dive right in,
[tex]-3^{2}-7*-3+6\\-9-7*-3+6\\-9+21+6\\12+6\\18[/tex]
In conclusion, the value of this expression is 18. Hope this helped :D
Edit: fixed an error (did 3^2 instead of -3^2)