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antiseptic1488 [7]
2 years ago
12

1. tan a = cot(a + 10°)

Mathematics
1 answer:
Temka [501]2 years ago
7 0

Answer:

a=40+90n

Step-by-step explanation:

Use a cofunction identity on the right hand side or left hand side...

So \tan(a)=\cot(90-a).

We have the equation:

\tan(a)=\cot(a+10)

Make the above replacement:

\cot(90-a)=\cot(a+10)

Since cotangent has period 180 degrees, we can also write this as:

\cot(90-a+180n)=\cot(a+10)

So solving the following will give us a set of solutions for a:

90-a+180n=a+10

Add a on both sides:

90+180n=2a+10

Subtract 10 on both sides:

80+180n=2a

Divide both sides by 2:

40+90n=a

Symmetric property:

a=40+90n

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One - fifth as a percentage?
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Answer:    0.2

Step-by-step explanation:

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3 years ago
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. Ramu took a loan of 50000 rupees from a bank which charges 10% interest, compounded an- nually. He repaid 10000 rupees after o
Setler79 [48]

Answer:

= 30,550 rupee owed

Step-by-step explanation:

yr1 = 50000 x 0.10^1 = 5000

5000 - 10000 = 5000 credit from debt.

yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt

yr 3 = 50000 x 1.10^3 = 50 debit from debt

5000 + 500 = 15000 where 50,000 owed initially and yr1 and yr 2 paid in full interest of 5500 and we deduct this from his payment = 25000-5500 =

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50000-19500= 30,500 rupees owed + 50 rupee interest.

= 30,550 rupee owed

4 0
2 years ago
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Bret works for a printing company-each document takes 8 sheets of paper-he has 500 sheets-how many documents can he print
Juli2301 [7.4K]

Answer:

He can print 62 documents

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500/8=62.5

He can print only 62 documents because he cannot print half a document.

Hope this helps!

If not, I am sorry.

7 0
2 years ago
I don’t really get this question so if anyone knows it please help
Mars2501 [29]

Answer:

116.82\:\text{square inches}

Step-by-step explanation:

The window consists of a large square and 4 smaller triangles on the outside. The side length of this square is marked as 10, and therefore the area of this square is 10^2=100\:\mathrm{in^2}.

The area of a triangle is given by \frac{1}{2}\cdot b\cdot h. Since the problem states that the overlapping squares are congruent, both legs of the triangle will be 2.9 and intersect at a 90^{\circ} angle.

Thus, the sum of all four triangles is \frac{1}{2}\cdot 2.9\cdot 2.9\cdot 4=16.82\:\mathrm{in^2}.

Therefore, the area of the window is:

100+16.82=\boxed{116.82\:\mathrm{in^2}}

3 0
3 years ago
Solve the quadratic equation 3x²-3x-1=0?<br>(by using the square method)​
ohaa [14]

Answer:

x=1 and x=-1/3

Step-by-step explanation:

3x^2-2x-1=0\\\\3(x^2-\frac{2}{3}x-\frac{1}{3})=0\\ \\3(x^2-\frac{2}{3}x-\frac{1}{3}+\frac{4}{9})=3(\frac{4}{9})\\ \\ 3(x^2-\frac{2}{3}x+\frac{1}{9})=\frac{4}{3}\\ \\ 3(x-\frac{1}{3})^2=\frac{4}{3}\\ \\(x-\frac{1}{3})^2=\frac{4}{9}\\ \\x-\frac{1}{3}=\pm\frac{2}{3}

x-\frac{1}{3}=\frac{2}{3}\\ \\x=\frac{3}{3}\\ \\x=1

x-\frac{1}{3}=-\frac{2}{3}\\ \\x=-\frac{1}{3}

Therefore, x=1 and x=-1/3

8 0
2 years ago
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