A triangular prism, with bases consisting of equilateral triangles of side length s, has height h and a volume of 250. If the surface area of the prism includes the areas of all the sides and the bases, what value of s minimizes the surface area of the prism

Answers

Answer 1

Answer:

10

Step-by-step explanation:

Answer 2

The required value of s to minimize the surface area of the prism is given as 10.

What is a triangular prism?

A triangular prism has 2 triangles as their top and bottom and three other faces as rectangles. The volume of the prism is given as the product of its height and base area.

The given problem can be solved as follows,

The expression for the volume of the prism is given as,

V = √3/4 × s²h

Substitute V = 250 to obtain,

250 = √3/4 × s²h

⇒ s²h = 1000/√3                       (1)

And, the expression for the surface area is given by,

A = 3 × sh +  √3/4s²

Substitute h = 1000/(√3s²) in the above equation to obtain,

A = 1000√3/s + √3/4s²

In order to get the minimum area differentiate A with respect to s and equate it to zero to get,

dA/ds = 0

⇒ √3/2s - 500√3/s² = 0

⇒ s = 10

Hence, in order to minimize the area the the value of s is obtained as 10.

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Related Questions

in the problem find m<1​

Answers

Answer:

m∠1 = 124°

Step-by-step explanation:

If this is the case then m∠1 and m∠2 are congruent to each other with the same angle in which m∠2 is also 124°, if m∠3 is said to be 56°.  Also, a straight angle has to equal to 180° in which the first angle is classified as obtuse.

A TV has an original price of $599. Enter the new price after the given percent of change.

20% increase

The percent decrease is ? %

Answers

Answer:

The new price = $718. 8

Step-by-step explanation:

Original Price =  $599

Given that the increase is 20%.

i.e.

Thus,

The amount of 20% Percentage increase = 20/100 × 599

                                                                             = 0.2 × 599

                                                                              = $119.8

Therefore,

New price = Original price + 20% increase amount

                 = 599 + 119.8

                  = $718. 8

Therefore, the new price = $718. 8

Given: f(x) = 1/x+5 and g(x) = x - 2.
What are the restrictiorts of the domain of f(g(x))?
0 x4 -5
O X-3
OX= 2
There are no restrictions.

Answers

Answer:

The restriction of the domain of f(g(x)) is that x cannot be 3.

Step-by-step explanation:

The first step to solve this question is finding the function, replacing the values. So

[tex]f(x) = \frac{1}{x+5}[/tex]

[tex]g(x) = x - 2[/tex]

[tex]f(g(x)) = f(x - 2) = \frac{1}{x - 2 + 5} = \frac{1}{x - 3}[/tex]

The function is a fraction, which means that the restriction is that the denominator cannot be zero. So

[tex]x - 3 \neq 0[/tex]

[tex]x \neq 3[/tex]

The restriction of the domain of f(g(x)) is that x cannot be 3.

The temperature outside changed from 66°F to 42°F over a period of eight days. If the temperature changed by the same amount each day, what was the daily temperature change?

Answers

Now I don’t know if this is right but I’m pretty sure it’s just 24 with simple subtraction

Somebody please help me :(

Answers

Answer:

A, C, E

Step-by-step explanation:

Factory M makes 200 screwdrivers per hour.

Factory N makes 100 screwdrivers per hour.

At what point does an angle with measure 75º in standard position intersect with unit circle?
a.
(sin 75º, tan 75º)
b.
(cos 75º, tan 75º)
c.
(sin 75º, cos 75º)
d.
(cos 75º, sin 75º)

Answers

Answer:

d

Step-by-step explanation:

x=rcosθ

y=rsinθ

r=1

θ=76°

verify the identity

[tex]cot(x-\frac{\pi }{2} )[/tex] = - tan x

please show all steps

Answers

Answer:

Step-by-step explanation:

[tex]\tan (x-\frac{\pi }{2} )=\frac{tan~x-tan~\frac{\pi }{2} }{1+tan~x~tan~\frac{\pi }{2} } \\or~\cot(x-\frac{\pi }{2} )=\frac{1+\tan~x~\tan\frac{\pi }{2} }{\tan~x-\tan~\frac{\pi }{2} } \\divide~the~R.H.S. ~by~\tan ~x~\tan~\frac{\pi }{2} \\=\frac{\cot~x~\cot~\frac{\pi }{2} +1 }{\cot~\frac{\pi }{2} -\cot~x} \\\cot\frac{\pi }{2} =0\\\cot(x-\frac{\pi }{2} )=\frac{\cot~x ~\times~0+1}{0-\cot~x} \\\cot~(x-\frac{\pi }{2} )=-\frac{1}{\cot~x} =-\tan~x[/tex]

WILL DO ABSOLUTELY ANYTHING FOR THIS ONE HELP ASAP TIMES

Answers

Given:

The graph of a function [tex]y=h(x)[/tex].

To find:

The interval where [tex]h(x)>0[/tex].

Solution:

From the given graph graph it is clear that, the function before x=0 and after x=3.6 lies above the x-axis. So, [tex]h(x)>0[/tex] for [tex]x<0[/tex] and [tex]x>3.6[/tex].

The function between x=0 and x=3.6 lies below the x-axis. So, [tex]h(x)<0[/tex] for [tex]0<x<3.6[/tex].

Now,

For [tex]-1<x<0[/tex], the graph of h(x) is above the x-axis. So, [tex]h(x)>0[/tex].

For [tex]0<x<1[/tex], the graph of h(x) is below the x-axis. So, [tex]h(x)<0[/tex].

For [tex]1<x<2[/tex], the graph of h(x) is below the x-axis. So, [tex]h(x)<0[/tex].

Only for the interval [tex]-1<x<0[/tex], we get [tex]h(x)>0[/tex].

Therefore, the correct option is A.

The Question is above.

Answers

Step-by-step explanation:

given

g(r)= -1 -7r

g ( 6) = - 1 - 7 * 6

= - 1 - 42

= - 43

Yes he is correct I

Diana buys 5 sodas every week. Which of the following expressions shows the total number of sodas she buys in y weeks? (4 points)

Group of answer choices

5y

Fraction y over 5

5 + y

5 + 5y

Answers

Answer:

Shalom Guys I will try my best to answer this! ok i think it would be #2 have a great day i hope i could help the squad says hi!

                         ~Piper Rokelle

Step-by-step explanation:

Circle the fraction equal to 0.1%

Answers

0.1 as a fraction in simplest form is 1/10. For this answer, you simply have to replace the point with 10 in the denominator.

Find the distance from C to G.
4
86
7
64
3
32

Answers

Answer: 64/3

Step-by-step explanation:

PLS HELP WILL MARK BRAINLIST

Determine which is the better buy. (picture below)

Answers

Answer:

Cheese B

Step-by-step explanation:

Find the cost of 1 slice for Cheese A:

Set up a proportion: [tex]\frac{3.59}{10} = \frac{x}{1}[/tex]  Cross multiply, then divide: 3.59 × 1 = 3.59, 3.59 ÷ 10 = 0.359So, the cost of 1 slice of Cheese A is $0.359

Find the cost of 1 slice for Cheese B:

Set up a proportion: [tex]\frac{5.12}{16} = \frac{x}{1}[/tex]  Cross multiply then divide: 5.12 × 1 = 5.12, 5.12 ÷ 16 = 0.32So, the cost of 1 slice of Cheese B is $0.32

Make a conclusion:

Because $0.32 is less than $0.359, Cheese B is the better buy.

I hope this helps!

Please answer the question :)

Answers

Answer:

the lenght of the shortest side is 12

Step-by-step explanation:

So first add them all up becuase perimeter

3x+3x+5x-4+5x-4

You’ll get 16x-8

16x-8=56

16x=64

x=4

So then plug it in

3x=3*4=12

5x-4=5*4-4=16

so 12 is the shortest side

Pls help this is due by midnight

Answers

Answer:

Cost of four DVD= 36.7, but due to 25% discount it cost 27.57. Then add 7.75 taxes and he payed 29.71. Answer is 29.71

Step-by-step explanation:

Answer:

$27.71

Step-by-step explanation:

Price of 1 DVD: $9.19

Price of 4 DVDs: 4 * $9.19 = $36.76

Discount: 25%

Now we find 25% of $36.76.

25% of $36.76 =

= 0.25 * $36.76

= $9.19

The 25% discount amounts to $9.19. We now subtract $9.19 from $36.76 to find the discounted price.

$36.76 - $9.19 = $27.57

Now we need to apply the 7.75% tax to $27.57.

7.75% of $27.57 =

= 0.0775 * $27.57

= $2.14

The sales tax is $2.14.

Now we add the sales tax amount to the total discounted price.

$27.57 + $2.14 = $29.71

Answer: $27.71

What reason justifies 3x>3

Answers

Answer:

3x is greater then 3 because 3x has 3 of x and 3 is plain 3

plz answer my question

Answers

4R+12

When you diffuse (multiply) the 4 to the rest of the number r become 4r and 3 becomes 12 giving you the equivalent of 4r+12

A. 3(x+2)=18 B. 3x+6=18

Answers

Answer:

B

Step-by-step explanation:

3x6 is 18 so therefore its B

what the quest but I guess A or B but I

The perimeter of a rectangle is 98 feet. The ratio of its length to its width is 5:2.
Find the area of the rectangle.​

Answers

Answer:

the area is 50

Step-by-step explanation:

value of the 5:2

PLEASE ANSWER ASASP AND GIVE BRAINLEST!!!!!!!!!!!!!
The equation c = 2.5t represents the cost, c, for t tickets to the school play. Does a value of 3.5 for t make sense in this situation? Explain your reasoning.

Answers

Answer:

No

Step-by-step explanation:

Number of tickets can only be represented by integer values. A value of 3.5 for t would imply you can purchase three and a half tickets, which isn't possible.

any help for math lesson

Answers

Answer:

12.5

Step-by-step explanation:

We can turn this into a cross - multiplication problem.

n / 7.5 = 25 / 15

All we have to do is cross multiply to get 15n = 7.5*25

As a result, we get 15n = 187.5

Divide by 15 on both sides to get 12.5

Double check

We can double check this answer by dividing 15/7.5 and 15/7.5, because ratios are the same if they are just multiplied versions of themselves

So, we get 2 for both answers, meaning that 12.5 is correct

200-3.5 x 2.8 what is the product?

Answers

Answer:

190.2

Explanation:

3.5x2.8=9.8

200-9.8=190.2

Answer:

how do you find the product of 3.5 x 2.8

Step-by-step explanation:

explain how you got it.

4^(x-1)+4^(x)+4^(x-1)=84

Answers

Answer:

7.66

Step-by-step explanation:

Just open the parenthesis.

4x-4+4x+4x-4=84

Now simplify and solve

12x-8=84

12x=92

x= 7.66

Need help only on odds please

Answers

Answer:

Step-by-step explanation:

1) (i) HG ≅ ST ;      GI ≅ TR ;           IH ≅ RS

ΔHGI ≅ ΔSTR     by  S S S congruent

(ii) ∠H ≅ ∠S      ;  HG ≅ ST       ; ∠G ≅ ∠T

ΔHGI ≅ ΔSTR     by A S A -> Angle Side Angle congruent.

3) LM ≅ XY ;          MK ≅ YZ  ;      KL ≅ ZX

ΔLMK ≅ ΔXYZ Side Side Side congruent

∠K ≅ ∠Z  ;    KL ≅ ZX  ;    ∠L ≅ ∠X

ΔLMK ≅ ΔXYZ     by Angle Side Angle congruent

Which one should I choose

Answers

Answer:

i believe its 9 too

Step-by-step explanation:

Find x & y so that quadrilateral is a parallelogram. (Look at image)

Answers

Answer:

x = - 6 y = 13

Step-by-step explanation:

we know when the diagonals bisect it divides into two equal parts so

-4x - 2 = -3x + 4

-4x + 3x = 4 + 2

- x = 6

x = - 6

Now

2y + 8 = 3y - 5

3y - 2y = 8 + 5

y = 13

Hope it will help :)❤

Find the least common multiple of: 6, 3, 2

Answers

least common multiple of 6,3,2 is 6.

- 6 is the smallest number that is divisible by all three.

Answer:

.5

Step-by-step explanation:

The movie starts at 3:15 p.m. and ends at 5:08 p.m. How long is the movie?

Answers

Answer:

1 hour and 53 minutes

Step-by-step explanation:

Your welcome

Write an equation for the following table.

Answers

Answer:

y= 38x

Step-by-step explanation:

It is going up by 38 each time. There is no b value (y=mx + b), because if you times 6 by 38, you get 228. You don't need to add any remainders.

91 points need help now . Emanuel put 12 marbles on one pan
of a scale. On the other pan, he put
4 marbles, then he added 8 more
marbles to that side. Each of the-
marbles weighs 1 ound. Is the scale
balanced? Explain.

Answers

Answer: I believe the scale is balanced.

Step-by-step explanation: I stated that because since the other side of the scale contained 12 marbles that were 1 pound each that would be 12 pounds and then since 4+8=12 12 pounds of marbles were also put on the other side.

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