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11Alexandr11 [23.1K]
3 years ago
12

Jade takes 5 minutes more than twice as long as Binh to ride to their friend’s house. If Binh takes x minutes to ride to his fri

end’s house, how long will it take Jade?
Mathematics
1 answer:
skad [1K]3 years ago
6 0

Answer:

It will take Jade (2x + 5) minutes

Step-by-step explanation:

Let us find the expression that represents the time Jade will take

∵ Binh takes x minutes to ride to his friend’s house

∴ The time Binh takes = x minutes

∵ 5 more means + 5

∵ Twice means × 2

∵ Jade takes 5 minutes more than twice as long as Binh to ride to their

   friend’s house

→ Multiply the time Binh takes by 2 and add the product by 5

∵ Binh takes x minutes

∴ The time Jade takes = 2 × x + 5

∴ The time Jade takes = 2x + 5 minutes

∴ It will take Jade (2x + 5) minutes

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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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Answer: The equation parallel to the line is y=3x+8

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y=mx+c

5= 3(-1)+c

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The equation become y=3x+8

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