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3 years ago

Evaluate:cos 45°/sec 30°+cosec30°

Mathematics

1 answer:

barxatty [35]3 years ago

3 0

Look at the trigonometry table for special angles.

From here, substitute the values in:

$\frac{\sqrt{2} }{2} / \frac{2\sqrt{3} }{3}} + 2$

Simplify:

$\frac{3\sqrt{2} }{4\sqrt{3} } + 2$

Rationalize:

$\frac{\sqrt{6} }{4} +2$

And this is your answer.

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Expand (2x+2)^6<br> How would you find the answer using the binomial theorem?

Yanka [14]

Answer:

Step-by-step explanation:

$\displaystyle\\\sum\limits _{k=0}^n\frac{n!}{k!*(n-k)!}a^{n-k}b^k .\\\\k=0\\\frac{n!}{0!*(n-0)!}a^{n-0}b^0=C_n^0a^n*1=C_n^0a^n.\\\\ k=1\\\frac{n!}{1!*(n-1)!} a^{n-1}b^1=C_n^1a^{n-1}b^1.\\\\k=2\\\frac{n!}{2!*(n-2)!} a^{n-2}b^2=C_n^2a^{n-2}b^2.\\\\k=n\\\frac{n!}{n!*(n-n)!} a^{n-n}b^n=C_n^na^0b^n=C_n^nb^n.\\\\C_n^0a^n+C_n^1a^{n-1}b^1+C_n^2a^{n-2}b^2+...+C_n^nb^n=(a+b)^n.$

$\displaystyle\\(2x+2)^6=\frac{6!}{(6-0)!*0!} (2x)^62^0+\frac{6!}{(6-1)!*1!} (2x)^{6-1}2^1+\frac{6!}{(6-2)!*2!}(2x)^{6-2}2^2+\\\\ +\frac{6!}{(6-3)!*3!} (2a)^{6-3}2^3+\frac{6!}{(6-4)*4!} (2x)^{6-4}b^4+\frac{6!}{(6-5)!*5!}(2x)^{6-5} b^5+\frac{6!}{(6-6)!*6!}(2x)^{6-6}b^6. \\\\$

$(2x+2)^6=\frac{6!}{6!*1} 2^6*x^6*1+\frac{5!*6}{5!*1}2^5*x^5*2+\\\\+\frac{4!*5*6}{4!*1*2}2^4*x^4*2^2+ \frac{3!*4*5*6}{3!*1*2*3} 2^3*x^3*2^3+\frac{4!*5*6}{2!*4!}2^2*x^2*2^4+\\\\+\frac{5!*6}{1!*5!} 2^1*x^1*2^5+\frac{6!}{0!*6!} x^02^6\\\\(2x+2)^6=64x^6+384x^5+960x^4+1280x^3+960x^2+384x+64.$

8 0

1 year ago

Marcy wants $205 in her bank account. If she has $85 now and adds $10 per week, how many weeks will it take her to reach her goa

DIA [1.3K]

Answer:

^^1 week and 5 days

Explanation:

If she has $85 now, and gains $10 per week, by the next week and 5 days, she should have her goal of $205. Hope it helps!

5 0

2 years ago

How many cups are in 16 quarts? 1 quart = 4 cups

GrogVix [38]

Answer:

Step-by-step explanation:

4 cups * 16 quarts = 64 cups

6 0

2 years ago

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The table below shows the transportation method of all of the employees who work at the mall. What percent of employees walk to

Pepsi [2]

Answer:

0.005 or 0.5% walk

Step-by-step explanation:

Total:

758 + 530 + 7 + 105 = 1400

To find how many employees walk:

7/1400 = 0.005

6 0

2 years ago

Shelby made 5 quarts of juice for a picnic .She said that she made1 1/4 of juice/Explain Shelby's mistake

Svetach [21]

<span>1 gallon= 4 quarts

She made 5 quarts of juice, that means that she has 1 gallon (4 quarts) and one quart left over!
which can be written as 1 1/4!
</span>

8 0

3 years ago

Read 2 more answers

Evaluate:cos 45°/sec 30°+cosec30°​

Evaluate:cos 45°/sec 30°+cosec30°