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2 years ago

The diameter of a circle is 6 meters what’s is the circles area

Mathematics

2 answers:

elena55 [62]2 years ago

3 0

Answer:

A≈28.27m²

d Diameter

faust18 [17]2 years ago

3 0

Answer:

A≈28.27m²

d Diameter

Step-by-step explanation:

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

2 years ago

Allen wants to have a mean of 90 on his math quizzes. So far, he has scored 86, 94, 88, 95, and 89. What is the least score that

viva [34]

Answer:

Step-by-step explanation:

$\frac{86 + 94 + 88 + 95 + 89 + x}{6} = 90$

The mean would be the sum of all the math quiz grades divided by the number of quizzes taken.

Solve for x:

$86 + 94 + 88 + 95 + 89 + x = 540$

$452 + x = 540$

$x = 88$

Thus, Allen needs at least an 88 to obtain a mean of at least 90.

3 0

2 years ago

5) x-y+6; use x = 6, and y = 1

ankoles [38]

Answer:

-1

Step-by-step explanation:

substitute x for 6 and y for 1

which will be 6-1+6

using BODMAS

6-(1+6)

6-7= -1

6 0

2 years ago

This week luis made 80%of what he made last week. lf he made $72 this week, how much did he make last week

cestrela7 [59]

U just have to find original amount (100%) and that is the amount he made last week.

3 0

2 years ago

PLZ IM BEGGING YOU

antoniya [11.8K]

Answer:

200

Step-by-step explanation:

5 0

2 years ago