Answer:
10
Step-by-step explanation:
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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in the problem find m<1
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 ? %
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.
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?
Somebody please help me :(
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)
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
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
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.
Step-by-step explanation:
given
g(r)= -1 -7r
g ( 6) = - 1 - 7 * 6
= - 1 - 42
= - 43
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
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%
Find the distance from C to G.
4
86
7
64
3
32
Answer: 64/3
Step-by-step explanation:
PLS HELP WILL MARK BRAINLIST
Determine which is the better buy. (picture below)
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 $0.359Find 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 $0.32Make a conclusion:
Because $0.32 is less than $0.359, Cheese B is the better buy.
I hope this helps!
Please answer the question :)
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
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
Answer:
3x is greater then 3 because 3x has 3 of x and 3 is plain 3
plz answer my question
A. 3(x+2)=18 B. 3x+6=18
Answer:
B
Step-by-step explanation:
3x6 is 18 so therefore its B
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.
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.
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
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?
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
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
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
Answer:
i believe its 9 too
Step-by-step explanation:
Find x & y so that quadrilateral is a parallelogram. (Look at image)
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
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?
Answer:
1 hour and 53 minutes
Step-by-step explanation:
Your welcome
Write an equation for the following table.
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.
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.