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4 years ago

14 T 1,000 lb. + 2 T 1,000

Mathematics

1 answer:

Olegator [25]4 years ago

6 0

The answer will be 17 tons.

Step-by-step explanation:

Since we have given that

14 T 1,000 lb. + 2 T 1,000 lb.

As we know that

$1\ ton=2000\ lbs\\\\14\ tons=2000\times 14\ lbs\\\\14\ tons=28000\ lbs$

So, 14 T 1,000 lb. is given by

$28000\ lbs+1000\ lbs\\\\=29000\ lbs$

Similarly,

$1\ ton=2000\ lbs\\\\2\Tons=2\times 2000\ lbs\\\\2\ tons=4000\ lbs$

so,

2T 1,000 lb. is given by

$4000+1000\\\\=5000\ lbs$

So, 14 T 1,000 lb. + 2 T 1,000 lbs is given by

$29000+5000\\\\=34000\ lbs\\\\=\frac{34000}{2000}\\\\=17\ tons$

Hence, the answer will be 17 tons.

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Answer:

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Step-by-step explanation:

Let w be the width ( in meters ) of the container,

⇒ Length of the container = 2w,

If h be the height of the container,

So, the volume of the container = length × width × height

= 2w × w × h

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According to the question,

$2w^2h=10$

$\implies h=\frac{10}{2w^2}=\frac{5}{w^2}$

Now, the area of the base = length × width

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Area of sides = 2 × length × height + 2 × width × height

$=2\times 2w\times h+2\times w\times h$

$=4w\times \frac{5}{w^2}+2w\times \frac{5}{w^2}$

$=\frac{20}{w}+\frac{10}{w}$

$=\frac{30}{w}$

Since, material for the base costs $20 per square meter and material for the sides costs $12 per square meter,

Hence, total cost,

$C(w) = 2w^2\times 20 +\frac{30}{w}\times 12$

$C(w)=40w^2+\frac{360}{w}$

Differentiating with respect to w,

$C'(w) = 80w - \frac{360}{w^2}$

Again differentiating with respect to w,

$C''(w) = 80 +\frac{720}{w^3}$

For maxima or minima,

C'(w) = 0

$80w - \frac{360}{w^2}=0$

$80w^3-360=0$

$80w^3=360$

$\implies w=\sqrt[3]{\frac{360}{80}}=1.65096362445\approx 1.651$

For w = 1.651, C''(w) = positive,

Thus, cost is minimum for width 1.651 meters,

And, the minimum cost = C(1.651) = $40(1.651)^2+\frac{360}{1.651}=\$327.081706869\approx \$ 327.08$

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This is also true about the Earth and the moon.

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3 years ago

Amy's favorite lotion cost $30 for four fluid ounces at the same time what would she expect to pay for a quart of lotion

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Assuming that 1 quart= 32 Fluid Ounces,
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I hope this helps you