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4 years ago

Lim as x goes to 0: (2sinxcosx)/(2x^2+x)=

1 answer:

8 0

$\displaystyle\lim_{x\to0}\frac{2\sin x\cos x}{2x^2+x}=2\left(\lim_{x\to0}\frac{\sin x }x\right)\left(\lim_{x\to0}\frac{\cos x}{x+1}\right)=2(1)\left(\frac1{0+1}\right)=2$

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The distance between Lincoln, NE, and Boulder, CO, is about 500 miles. The distance between Boulder, CO, and a third city is 200

GenaCL600 [577]

We know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)

Let

A------> Lincoln, NE

B------> Boulder, CO

C------> third city

we know that

in the triangle ABC

AB=500 miles

BC=200 miles

AC=x

Applying the Triangle Inequality Theorem

1) 500+200 > x------> 700 > x------> x < 700 miles

2) 200+x > 500----> x > 500-200------> x > 300 miles

the solution for x is

300 < x < 700

the interval is------> (300,700)

the possible distances, d, in miles, between Lincoln, NE, and the third city, are in the range between 300 and 700 miles

6 0

3 years ago

Read 2 more answers

An alloy of tin is 15% tin and weights 20 pounds. A second allow is 10% tin. How many pounds of the second alloy must be added t

Fofino [41]

Let x represent the amount to be added. The total amount of tin will be
15%·20 + 10%·x = 12%·(20+x)
(15%-12%)·20 = (12%-10%)·x
3%·20/2% = x
30 = x

30 pounds of 10% tin must be added to get a 12% mixture.

8 0

3 years ago

Which statement is true using Cavalieri’s principles ?

Kay [80]

Answer:

One of the benefits of Cavalieri's principle is that it allows us to determine the volume of an oblique prism (or oblique cylinder). When dealing with two prisms (or two cylinders), if the base areas are equal and the heights are equal, then the volume is V = Bh regardless of the overall shape.

( i cant see the answers well so estimate to the one that applies)

5 0

3 years ago

Volume of sphere Marcus is using small stone spheres

satela [25.4K]

<h2>Volume of Sphere</h2>

1. What is the radius of the stone sphere?

- To know what is the radius divide is by 2.

$\large \tt 6 \div 2 = 3$

Therefore, the radius of the stone sphere is 3in

2. What is the volume of the stone sphere?

- Using the formula in finding the Volume of Sphere $\tt V = \frac{4}{3}\pi r^3$ to get the answer. Where the volume of the sphere is $\tt\frac{4}{3}\:\:\:\:\pi$ multiplied by the cube of the radius.

$\tt V = \frac{4}{3}\pi r^3$
$\tt V = \frac{4}{3}\times 3.14\times 3in^3$
$\tt V = \frac{4}{3}\times 3.14\times 27in$
$\tt V = \frac{4}{3}\times 84.78in$
$\tt V = \frac{339.12in}{3}$
$\tt V = 113.04in^3$

Therefore, the volume of the stone sphere is 113.04in³

3. Another stone sphere for the garden has a diameter of 10 inches. What is the volume of the stone sphere? Use 3.14 for <em>π</em>, and round to the nearest hundredth.

- Using the formula in finding the Volume of Sphere $\tt V = \frac{4}{3}\pi r^3$ to get the answer. Where the volume of the sphere is $\tt\frac{4}{3}\:\:\:\:\pi$ multiplied by the cube of the radius.