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kondaur [170]
2 years ago
7

Please help

Mathematics
2 answers:
alexandr402 [8]2 years ago
3 0
\bf 3\sqrt[3]{2a} -6\sqrt[3]{2a}\qquad \stackrel{add ing~like-terms}{\implies }\qquad -3\sqrt[3]{2a}
Grace [21]2 years ago
3 0

Answer:

-3\sqrt[3]{2a}

Step-by-step explanation:

We have been given a  radical expression 3\sqrt[3]{2a} -6\sqrt[3]{2a} and we are asked to write our given expression in simplest form.

Using exponent property \sqrt[n]{x}=x^{\frac{1}{n} we can write our given expression as:

3*(2a)^{\frac{1}{3}}-6*(2a)^{\frac{1}{3}}

Since we can add or subtract variables with same powers and we have like bases and like exponents for our given expression, so we can subtract 6*(2a)^{\frac{1}{3}} from 3*(2a)^{\frac{1}{3}}

-3(2a)^{\frac{1}{3}}

Using exponent property x^{\frac{1}{n}=\sqrt[n]{x} we will get,

-3\sqrt[3]{2a}

Therefore, our given radical expression simplifies to -3\sqrt[3]{2a}.

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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
I need help with this one please help asap thank you
frozen [14]
(a) is the first one. 48 I would say 8 mins
(b) is the second one. 10 I would say is 96
4 0
3 years ago
Find AC. Show Your Work.​
kolbaska11 [484]

Check the picture below.

7 0
2 years ago
Seven times a number decreased by three-fourths of the same number is 25. What is the number?
Tomtit [17]

Answer:

103/28

Step-by-step explanation:

Let the number be 'x'

Equation:-

7x - 3/4 = 25

7x = 25 + 3/4

7x = 100/4 + 3/4

7x = 103/4

x = 103/(4 x 7)

x = 103/28

5 0
3 years ago
Read 2 more answers
Michael has 265 baseball cards. He wants to put them in packs of 9 cards each. How many cards will he have left over?
viktelen [127]
Michael will have 4 cards left because 265/9=29.4444444... then i do 29 (from the 29.4444) times 9 which gives me 261 and i did 265-261.
6 0
3 years ago
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