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2 years ago

xed{\sf Trigonometry}" align="absmiddle" class="latex-formula">
Solve for x

$\\ \rm\rightarrowtail tan^{-1}x+2cot^{-1}x=\dfrac{2\pi}{3}$

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Mathematics

2 answers:

nadya68 [22]2 years ago

7 0

Step-by-step explanation:

Since, tan

−1

θ+cot

−1

θ=

∴tan

−1

x+2cot

−1

2π

⇒cot

−1

2π

⇒cot

−1

2π

−

⇒x=

Soloha48 [4]2 years ago

3 0

Answer:

→x=√3

Step-by-step explanation:

$tan^{-1} x+2cot^{-1} x=\frac{2\pi }{3} \\\\tan^{-1} x+2(\frac{\pi }{2}-tan^{-1} x)= \frac{2\pi }{3} \\\\-tan^{-1} x=\frac{2\pi }{3}-\pi \\\\-tan^{-1} x=-\frac{\pi }{3} \\\\tan^{-1} x=\frac{\pi }{3} \\\\x=tan\frac{\pi }{3} \\\\x=\sqrt{3}$

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Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

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3 years ago

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

1. 4 green+3red+2blue+1yellow = 10 total

if 3/10 are red, then 7/10 are not red. So the second option, 7/10

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===============================

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