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2 years ago

A parallelogram in a coordinate plane is reflected over the line y=5 and translated 2 units left and 1 unit down.

1 answer:

6 0

Answer: The resulting parallelogram is congruent to the original parallelogram regardless of the order of the transformations.

Step-by-step explanation:

A reflection and a translation are both rigid motions, meaning both transformations preserve congruency.

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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

3 years ago

PLEASE HELP WITH ALL QUESTIONS WILL GIVE BRAINLIEST AND WILL GIVE 33 POINTS

MrMuchimi

uh where the question?

6 0

3 years ago

The area of a rectangular swimming pool is 360 square feet. If the length of the swimming pool is 9 feet more than its width, fi

Inessa [10]

Answer:

l = 24ft

Step-by-step explanation:

A = lw

360 = (x + 9)(x)

360 = x^2 + 9x

0 = x^2 + 9x - 360

0 = (x + 24)(x - 15)

x ≠ -24 (length cannot be negative)

x = 15

l = 15 + 9

l = 24ft

7 0

3 years ago

Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castel sold

dmitriy555 [2]

One lemon meringue is $14 One apple pie is $4

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3 years ago

Find the midpoint on segment AB; A (0, 6), B (4, 2)

Bogdan [553]

Answer:

2,4

Explanation:

Because a midpoint is the middle of the line

8 0

3 years ago

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