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3 years ago

20points!!!! 3 2/3 + 2.3 =

Mathematics

1 answer:

Slav-nsk [51]3 years ago

6 0

5.96666 or 6 because if you round it that’s what it’ll be

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If i drive at a constant rate and go 100 miles in 2 hours, write an equation that could represent the number of miles, m, per ho

Ipatiy [6.2K]

100 miles ............... 2 hours
x miles ................1 hour

x = 100 m / 2 h = 50 m / h

5 0

3 years ago

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

Write the trigonometric expression <br> Cos (arcsin (u))<br> As an algebraic expression in u

makvit [3.9K]

When we use arcsine, we are finding the angle while giving the trigonometric ratio.

Arcsin(u) = theta can be rewritten as:

sin(theta) = u

Sine is opposite over hypotenuse, so u/1 means that the side opposite to theta (the y value) is u, and the hypotenuse is 1.

We can use Pythagorean Theorem to find the adjacent (x value).

1^2 - u^2 = x^2

x = sqrt(1-u^2)

Back to the original question, we are trying to find cos(arcsin(u)). We just solved all the sides for our triangle using arcsin(u). Now we need to do cos(u).

Cosine is adjacent over hypotenuse.

So our answer is sqrt(1-u^2)/1

Or just sqrt(1-u^2)

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3 years ago

ASAP ILL GOVE 10 POINTS

murzikaleks [220]

Answer:

Step-by-step explanation:

Took the test on AP3X

7 0

2 years ago

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The movie theater sold 50 buckets of popcorn last Wednesday. 60 people watched movies that day, and 40 of those people ate popco

STALIN [3.7K]

Answer:

Step-by-step explanation:

60/40Ⅹ50=70

I hope this helps

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2 years ago