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3 years ago

∫ 5cos(x) - 2sec²(x) dx

Mathematics

1 answer:

daser333 [38]3 years ago

5 0

$\bf \displaystyle \int [5cos(x) - 2sec^2(x)]dx\implies 5\int cos(x)dx~-~2\int sec^2(x)dx
\\\\\\
5sin(x)-2tan(x)+C$

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A scale on a hiking map shows that 1.5 inches represents 4 miles

Alexxandr [17]

Answer: 24 miles.

Step-by-step explanation:

1. You must keep on mind that, according the scale on the map, 1.5 inches represents 4 miles. Then, you can set up the following ratio:

$\frac{1.5}{4}=\frac{6}{x}$

Where x is the number of actual miles asked

2. You must solve for x, as following:

$(1.5)(x=4*6\\x=\frac{24}{1.5}\\x=16$

3. Therefore, 6 inches on the map represents 24 miles.

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4 years ago

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Anestetic [448]

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4 years ago

A 12 cm x 2 cm rectangle sits inside a circle with radius of 8 cm.

hammer [34]

Answer:

Diagram was not given.

Still I had drawn it, hope may it will helpful to you. So as per my diagram I had solved the sum.

The area of the shaded region is 176.96 ≈ 178 cm²

Step-by-step explanation:

Given:

radius of the circle = r = 8 cm

length of the rectangle = L = 12 cm

breadth of the rectangle = B = 2 cm

To Find:

Area of shaded region = ?

Solution:

$\textrm{Area of rectangle} = Length\times Breadth\\= L\times B\\= 12\times 2\\= 24\ cm^{2}$

$\textrm{Area of Circle} = \pi \times (radius)^{2} \\=\pi \times r^{2}\\=3.14\times 8^{2}\\=200.96\ cm^{2}$

Now, The Area of Shaded region will be

$\textrm{Area of Shaded region}=\textrm{Area of Circle}-\textrm{Area of Rectangle}\\=200.96 - 24\\=176.96\ cm^{2} \\=178\ cm^{2}\........... \textrm{Rounded to tenth}$

The area of the shaded region is 176.96 ≈ 178 cm²

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o-na [289]

I believe that Charlotte bikes 499.2 meters and Mary biked 123.6 meters, so Charlotte would’ve biked 375.6 more meters.

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