What is tan 330°? for algebra 2 with trig in it.

What are the coefficients for the binomial expansion of (a + b)^3?

sashaice [31]

Answer:

Required coefficient :coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

Explanation:

Formula for binomial expansion is $(a+b)^n=^nC_0\cdot a^n\cdot b^0+^nC_1\cdota^(n-1)\cdot b^1+------b^n$

We will substitute the values a=a, b=b and n=3 in the formula for binomial expansion we will get

$^3C_0\cdot a^3\cdot b^0+^3C_1\cdot a^2\cdot b^1+^3C_2\cdot a^1\cdot b^2+^3C_3\cdot a^0\cdot b^3$

After simplification of the terms we will get

$a^3+3\cdot a^2\cdot b+3\cdot a\cdot b^2+b^3$

Since, $^nC_r=\frac{n!}{(r!)(n-r)!}$

Therefore the required coefficient : coefficients of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

5 0

2 years ago

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Write 8,000,000 in scientific notation ?

Alex_Xolod [135]

Answer:

A: 8 x 10^6

Step-by-step explanation:

4 0

2 years ago

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Need help on this ASAP! It’s due right now someone please help

Diano4ka-milaya [45]

Answer:

Part a would be "C" and part b would be "C" I believe

Step-by-step explanation:

(a):it is a constant speed, then decline, then back to constant.

(b):constant then he gets slower.

3 0

2 years ago

PLSSSSSSSSSSSSSSSSSSSSS

Veseljchak [2.6K]

I believe that the correct answer would be A

Hope this helped love <3

4 0

2 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

2 years ago