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3 years ago

12

A tractor trailer weighs 80,000 pounds. Two tractor trailers come upon a bridge with a sign saying it can only handle 100 tons.

How many tons are still available before the bridge reaches its weight limit?
How many tons are there. ONLY TONS!

1 answer:

Lyrx [107]3 years ago

6 0

Answer:

there are 20 tons before the bridge reaches its limit because you get 80 tons in total weight

Step-by-step explanation:

you would first multiply 80,000 pounds by 2 which gives you 160,000 pounds then you divide that by 2,000 because a ton is equal to 2,000 pounds

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3 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

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Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

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Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

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So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

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Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

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$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

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$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

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$y = \frac{\sqrt {10}}{2}$

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3 0

3 years ago

A bike is bought for $1200 and sold 10 months later for $940.

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Value

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or

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Step-by-step explanation:

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