Answer:
[tex]V = 6746.30cm^3[/tex]
Step-by-step explanation:
Given
[tex]Surface\ Area = 1700cm^2[/tex]
Required
Determine the largest possible volume
Represent the dimension with:
[tex]Height = h[/tex]
[tex]Sides = x[/tex]
Surface Area with an open top is:
[tex]Surface\ Area = x^2+ 4hx[/tex]
Substitute 1700 for Surface Area
[tex]1700 = x^2+ 4hx[/tex]
Make h the subject
[tex]4hx = 1700 - x^2[/tex]
[tex]h = \frac{1700 - x^2}{4x}[/tex]
The volume (V) is calculated as:
[tex]V = x^2h[/tex]
Substitute value for h in [tex]V = x^2h[/tex]
[tex]V = x^2*\frac{1700 - x^2}{4x}[/tex]
[tex]V = x*\frac{1700 - x^2}{4}[/tex]
[tex]V = \frac{1700x - x^3}{4}[/tex]
[tex]V = \frac{1700x}{4} - \frac{x^3}{4}[/tex]
[tex]V = 425x - \frac{x^3}{4}[/tex]
[tex]V = 425x - \frac{1}{4}x^3[/tex]
Differentiate and equate to 0, afterwards
[tex]V' =425 - \frac{3}{4}x^2[/tex]
[tex]425 - \frac{3}{4}x^2 = 0[/tex]
[tex]\frac{3}{4}x^2 = 425[/tex]
Solve for [tex]x^2[/tex]
[tex]x^2 = 425 * \frac{4}{3}[/tex]
[tex]x^2 = 566.67[/tex]
Take the square root of both sides
[tex]x = \sqrt{566.67[/tex]
[tex]x = 23.80[/tex]
Substitute 23.80 for x in [tex]h = \frac{1700 - x^2}{4x}[/tex]
[tex]h = \frac{1700 - 23.80^2}{4*23.80}[/tex]
[tex]h = \frac{1133.56}{95.20}[/tex]
[tex]h = 11.91[/tex]
So, the largest possible volume is:
[tex]V = x^2h[/tex]
[tex]V = 23.80^2 * 11.91[/tex]
[tex]V = 6746.30cm^3[/tex]
what is 7 -7/8 by the way this is a fraction question
Answer: 6 1/8
Step-by-step explanation:
6 1/8 that's what I got but I'm not sure
What is the measure of an angle that is the supplement of angle C?
Answer:
15
Step-by-step explanation:
Answer:
the measure of an angle that is the supplement of angle C=180-165=15
What is tan K?
please show your work
a ladder is 6 ft 9 in tall how tall is it in inches
Answer:
81 in
Step-by-step explanation:
1 ft=12in
12x6=72in
72+9=81
An artist is creating tiles to use in a project. Each tile is to be in the shape of a right triangle. One of the legs of the tile is to be 3 Inches long. The hypotenuse is to be z Inches long.
Write an expression in terms of 3 that models the other leg of a tile.
Answer:
???
Step-by-step explanation:
Need help ASAP!! What is the value of x?
Answer:
98
Step-by-step explanation:
the exterior angle is equal to the sum of the opposite interior angles
-Sumin <3
Answer:
98
Step-by-step explanation:
53+45+x = 180
53+45=98
180-98=82
82 (interior)
82+98=180
x = 98
Which of these is equivalent to x + 1 + x + 2 + x + 3 + x + 4?
Answer:
what are the options?
Answer:
x + 1 + x + 2+ x + 3 + x + 4
4x + 10
2( 2x + 5)
hope it helps
What is the surface area and volume ?
A = 1
2 × (15 + 20) × 16
B = 1
2 × 15 × 20 × 10
C = 1
2 × (15 + 20) × 10
D = 1
2 × (10 + 16) × 20
Answer: a
Step-by-step explanation:
Which equation represents a slope of 4 and (5,-2)?
y-2=4(x-5)
y-5=4(x-2)
y+2=4(x+5)
y+2=4(x-5)
Answer:
Step-by-step explanation:
the formula is named the point slope formula for a reason. and you have show both of them in the question , the slope and the point are given
y - y1 = m(x-x1)
so for your answer
y-(-2) = 4(x-5)
y+2 = 4(x-5) is the right answer
michalle bought a new tablet for 360 last month now it priced at 280 what is the percent of change in price of the tablet
Answer:
Step-by-step explanation:
%change=100(280-360)/360
%change=-200/9%
%change=-22.22% (to nearest hundredth)
How much will 9 pencils cost if 6 pencils cost $1.68?
Answer:
$2.52
Step-by-step explanation:
1.68/ 6 = $0.28 each pencil
0.28 x 9 = $2.52
Marilyn and Frank each save $25 per month. Their savings are $3x and $2x respectively. What amount will be the sum of their savings 5 months from now?
Answer:yutu
gdffg
Step-by-step explanation:
uytyuytuyuyu dfgdgdg
Answer: the answer is b on the forum
Step-by-step explanation:
Use the substitution method to solve the system of equations.choose the correct ordered pair. x+2y=12 -x=-y-6
Answer:
Point Form: 8,2
Equation Form: x = 8, y = 2
Step-by-step explanation:
solve for the first variable in one of the equations, then substitute the result into the other equation.
Answer:
(8,2)
Step-by-step explanation:
write 16 + 32 = as a product of two factors using GCF and the distributive property
Answer:
16 (1+2)
Step-by-step explanation:
factors of 16: 1,2,4,8,16
factors of 32: 1,2,4,8,16,32
16 x 1 = 16
16 x 2 = 32
Solve the following system in any
manner.
4x + 8y = -3
6x + 12y= -7
Can someone please help me with this?
Answer:
No Solution.
Step-by-step explanation:
4x+8y=-3
6x+12y=-7
------------------
3(4x+8y)=3(-3)
-2(6x+12y)=-2(-7)
--------------------------
12x+24y=-9
-12x-24y=14
-------------------
0=5
no solution.
3. Jessie is looking for the volume of the cone
below, and she is using the formula V = (1/3)Bh.
Which of the following is the value of “B”?
Answer:
A
Step-by-step explanation:
The base is the circle.
To find the area of the circle, use pi*r^2
pi = 3.14
r = 6
Area = 3.14 * 6^2Area = 3.14 * 36Area = 113.04Answer:
C. 414.48
Step-by-step explanation:
1/3 x 3.14 x 6² x 11 = 4.14.48
how do u find surface area for this
Answer:
416.23
Step-by-step explanation:
A=a2+2aa2
4+h2=102+2·10·102
4+152≈416.22777
Answer:
find the areas of the individual triangles then add those ares
together.
Step-by-step explanation:
-6 x (1/3 + 1/3)What is the answer?
Answer:
−4
Step-by-step explanation
Answer:
−4
Step-by-step explanation:
-6 x (1/3 + 1/3)
Since 1/3 and 1/3 have the same denominator, add them by adding their numerators.
-6 x (1+1/3)
Add 1 and 1 to get 2.
-6 x (2/3)
Express -6 x (2/3) as a single fraction.
-6 x 2/3
Multiply −6 and 2 to get −12.
-12/3
Divide −12 by 3 to get −4.
−4
How to round 8.6023 in the nearest tenth?
Answer:
8.6
Step-by-step explanation:
https://www.you.tube.com/watch?v=32gDF10ZXOA
( it might be wrong pls dont report me just let me kno y its wrong )
Answer:
8.6
Step-by-step explanation:
First of all consider the thousands in the decimal which is 2. Since 2 is not greater than 5 we have to remove the number 2 and 3 from the 8.6023.
We're left with 8.60. Now we see that there's a 0 in the hundredths so since it's not greater than 5 we remove it.
Now we're left with 8.6 which is to the nearest tenth.
f – 5.2 1.6
answer pls
Answer: what u mean
Step-by-step explanation:
Answer:
huh what do you mean picture?
Mr. Armstrong went to Target to buy four pairs of dress socks. There was a 30% off sale
on the socks, and his total bill before tax was $14. What was the price of each pair of socks
before the sale?
Answer: $5
Step-by-step explanation:
We should note that since there was a 30% off sale, it means that he paid for 70% (100% - 30%) of the sales price.
Therefore, let the price of the socks be represented as x.
70% of x = 14
70/100 × x = 14
0.7 × x = 14
0.7x = 14
x = 14 / 0.7
x = 20
Therefore, the price of the socks was $20. Since there are 4 pairs, each pair will be:
= $20 / 4
= $5
I will give Brainliest or a Cookie, your choice
A ball is thrown into the air with an upward velocity of 44 ft/s. It’s height h in feet after t seconds is given by the function h=-16t^2 +44t+5. How long does it take the ball to reach its maximum height? What is the balls maximum height?
9514 1404 393
Answer:
1.375 seconds35.25 feetStep-by-step explanation:
A quadratic function y=ax^2 +bx +c is symmetric about the vertical line x=-b/(2a). That is the x-coordinate of the vertex (maximum or minimum).
Here, we have ...
h = -16t^2 +44t +5
t = -44/(2(-16)) = 11/8 = 1.375
It takes 1.375 seconds for the ball to reach its maximum height.
The height at that time is ...
h = (-16(11/8) +44)(11/8) +5 = (-22 +44)(11/8) +5 = 121/4 +5 = 141/4 = 35.25
The maximum height is 35.25 feet.
what is seven squared as an exponetial expression
Answer:
7^2
Step-by-step explanation:
Which pairs of expressions are equivalent
More the 1 answer
Answer:
The first 3 pairs of expressions are equivalent.
Step-by-step explanation:
Determine whether each expression is equivalent to 100t^2-0.5t
Answer:
[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{10^{t^{2}}}{100^{t}}[/tex].
[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}[/tex].
[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}[/tex].
Step-by-step explanation:
The expression to be evaluated is [tex]100^{t^{2}-0.5\cdot t}[/tex], we find by algebraic means the equivalent expression:
Possibility 1:
[tex]100^{t^{2}-0.5\cdot t}[/tex]
[tex]\frac{100^{t^{2}}}{100^{0.5\cdot t}}[/tex]
[tex]\frac{100^{t^{2}}}{(100^{0.5})^{t}}[/tex]
[tex]\frac{100^{t^{2}}}{10^{t}}[/tex]
[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{10^{t^{2}}}{100^{t}}[/tex].
Possibility 2:
[tex]100^{t^{2}-0.5\cdot t}[/tex]
[tex]\frac{100^{t^{2}}}{100^{0.5\cdot t}}[/tex]
[tex]\frac{(50\cdot 2)^{t^{2}}}{(25\cdot 4)^{0.5\cdot t}}[/tex]
[tex]\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}[/tex]
[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}[/tex].
Possibility 3:
[tex]100^{t^{2}-0.5\cdot t}[/tex]
[tex]\left(\frac{500}{5} \right)^{t^{2}-0.5\cdot t}[/tex]
[tex]\frac{500^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}[/tex]
[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}[/tex].
It is dinos birthday today. She is 9 years older than tyger. Altogether, their ages add up to 23 years. How old is dino?
Answer:
7
Step-by-step explanation:
Tyger = x
Dinos = x + 9
Total = 23
x + x+9 = 23
2x + 9 = 23
2x = 23 - 9
2x = 14
x = 14/2 = 7
I hope im right!!
Determine the domain of the following graph:
Answer:
[0,11)
Step-by-step explanation:
the function is defined over {0,11) because it includes x=0, but has an open dot at x=11.
Pls help reward the brainiest to right answers
Answer:
1. y=(4, 1)
2.y=(1/2, 2)
3. y=(-7.7, -1.3)
4.a=4, b=-13, c=3
5.x=the first one, i cant do all those symbols lol.
Step-by-step explanation: