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katovenus [111]
3 years ago
8

Please help . I’ll mark you as brainliest if correct!!!!!

Mathematics
1 answer:
topjm [15]3 years ago
6 0

Answer:

Step-by-step explanation:

hi

pls find below

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An open metal tank of square base has a volume of 123 m^3
snow_lady [41]

Answer:

  a) h = 123/x^2

  b) S = x^2 +492/x

  c) x ≈ 6.27

  d) S'' = 6; area is a minimum (Y)

  e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

  V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

  123 = x^2·h

  h = 123/x^2

__

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}

__

c) The derivative of the area with respect to x is ...

S'=2x-\dfrac{492}{x^2}

When this is zero, area is at an extreme.

0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583

__

d) The second derivative is ...

S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6

This is positive, so the value of x found represents a minimum of the area function.

__

e) The minimum area is ...

S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78

The minimum area of metal used is about 117.78 m².

3 0
2 years ago
In Triangle ABC, AC is extended through C to D. If
DENIUS [597]

Answer:

X  = 5 unit

Step-by-step explanation:

Given as , ABC is a Triangle ,

AC extended to through C to D

∠BAC = 6x + 10

∠ABC = 6x - 10

∠BCD = ∠ 8x + 20

When c extended to D then , ∠BCD is an external angle

∵ <u>External angle = Sum of opposite internal angles</u>

Or ,∠BCD = ∠BAC + ∠ABC

Or, ∠ 8x + 20 = 6x + 10 + 6x - 10

Or, ∠ 8x + 20 = 12x

Or, 12x - 8x = 20

∴ 4x = 20

So, x = \frac{20}{4} = 5

Hence the value of X = 5  unit  Answer

8 0
2 years ago
Simplify -2a(7a^5-5a+5)
olga_2 [115]
Here here here here here here here

3 0
2 years ago
One positive number exceeds three times another positive number by 5. The product of the two numbers is 68. Find the number
kati45 [8]

Answer:12

Step-by-step explanation:

Let the numbers be a and b

a-3b=5 ........equation (1)

There product is :

ab=68 ..........equation (2)

From equation (1)

a-3b=5

Make a the subject of the formula

a=5+3b. ........equation (3)

Substitute equation (3) into equation (2)

(5+3b)b=68

3(b^2)+3b-68=0

The product is -204b^2(17 and -12)

(b+17)(b-12)=0

b=-17 or b=12

So the number is 12

6 0
3 years ago
The midpoint of y and 31 is -5. what is y
pochemuha
Y = -41.
EXPLANATION.
if -5 is the midpoint, it must be -5 + 36.
Because there is 36 numbers between 31 and -5.
So -5 + 36 = -41.
4 0
3 years ago
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