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2 years ago

Solve the equation for x.

Mathematics

2 answers:

anzhelika [568]2 years ago

8 0

32x+64 = 160
32x = 96
x = 3

Afina-wow [57]2 years ago

6 0

The Answer for the given equation is 3

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6 inches per day .25 inches per hour

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3 years ago

I NEED THE ANSWERS PLZ

g100num [7]

Answer:

1. 32

2. 4.7

3. 3

Step-by-step explanation:

4*8=32

6.5-1.8= 4.7

18/6=3 or 18 divided by 6 = 3

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1 year ago

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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.

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2 years ago

Which of the following scenarios demonstrates an exponential decay? A. A tennis tournament in which after each round, half the p

Sliva [168]

Answer:

A. A tennis tournament in which after each round, half the players are eliminated.

Step-by-step explanation:

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A bag contains 10 red marbles, 15 yellow marbles and 5 green marbles. What is the probability of drawing a red or green marble f

Volgvan

Probability =

(number of ways it can come out the way you want)
divided by
(total number of ways it can come out).

Total number of ways to draw a marble = 30 (marbles in the bag).

Number of ways it can succeed = 15 (number of red or green ones)

Probability = 15/30 = 1/2 = 50% .

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2 years ago

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