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2 years ago

What is the coefficient of x7 in the expansion of (1 + x)11?

1 answer:

eduard2 years ago

4 0

You can choose to expand the equation to find the coefficient of x7 but that would take a lot of time. Here is a useful tactic that can help;

11C(something)(1)(x)⁷ ----> This gives the coefficient of x⁷
11C7(1)⁴(x)⁷ ----> You know that pascal's triangle is equal on both sides
11C7×1⁴ = coefficient of x⁷ (just ignore x⁷)
330x1⁴=330

This means that the coefficient of x⁷ is 330. You can double check by expanding the equation. If you do not understand what I did there, you can ask me how I got to the solution.

Hope I helped :)

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What is the area of the shaded triangle inside the square? Round your answer to the nearest square inch.

Semenov [28]

Answer:

Step-by-step explanation:

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2 years ago

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Solve the equation for all real values of x. cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

Step-by-step explanation:

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

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3 years ago

The base of an isosceles triangle is 7 cm longer than the legs. Find the legs if the perimeter of the triangle is 43 cm.

Archy [21]

An isosceles triangle is a triangle that has one pair of equal sides. The Formula in finding the perimeter of a triangle is PΔ=S₁+S₂+S₃. Since two legs are missing, and the given are the base and perimeter, we will use the formula : S₁+S₂ = PΔ-S₃, where: S₁+S₂ are the legs and S₃ is the base.
Substitute values:
S₁+S₂ = 43cm - 7 cm
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since S₁ and S₂ are equal, divide 36cm by 2. Therefore S₁ and S₂ measures 18cm.
Check: PΔ=S₁+S₂+S₃
 = 18cm + 18 cm + 7cm
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3 years ago

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One morning, John drive 5 hours before stopping to eat. After lunch, he. increased his speed by 10 mph. If he completed a 500-mi

Marrrta [24]

So he drove 5hrs, before lunch, now, he was going at speed, say "r", after he ate, he sped up by 10mph, so, his rate is whatever "r" is, plus 10, or " r + 10 ", after lunch

we know the whole trip took 10hrs, so, is 5hrs before lunch and 5hrs after lunch

we also know the whole trip was 500miles, so if he drove, say "d" miles before lunch, after lunch he drove the slack after lunch, or " 200 - d "

recall, your d = rt, distance = rate * time

$\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
\textit{before lunch}&d&r&5\\
\textit{after lunch}&500-d&r+10&5
\end{array}
\\\\\\

\begin{cases}
\boxed{d}=5r\\
500-d=(r+10)5\\
----------\\
500-\boxed{5r}=(r+10)5
\end{cases}
\\\\\\
\cfrac{500-5r}{5}=r+10\implies 100-r=r+10$

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mr Goodwill [35]

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