2 years ago

You have 2 spreads, 3 meats, and 4 kinds of bread. How many different sandwiches can you make using one of each ingredient?

Mathematics

1 answer:

Blizzard [7]2 years ago

3 0

Answer:

Step-by-step explanation:

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

mash [69]

Let $a=\tan A$ and $b=\sin A$ . Then

$m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$

$\implies m^2-n^2=4\tan A\sin A$

and

$mn=(a+b)(a-b)=a^2-b^2$

$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

5 0

2 years ago

(GIVING BRAINLIEST AND 15 POINTS FOR ANSWER) Solve five and three sixths minus two and one third.

a_sh-v [17]

Answer:

three and three eighteenths

5 3/6 = 33/6

2 1/3 = 7/3 = 14/6

33/6 - 14/6 = 19/6 = 3 1/6 or 3 3/18

5 0

1 year ago

Which equation can be used to solve for x in the following diagram.

Romashka [77]

Answer:

11, A

Step-by-step explanation:

90 - 35 = 55

55/5 = 11

6 0

2 years ago

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3x+2(2x−1)=33<br> what is x?

klasskru [66]

Answer:

x = 5

Step-by-step explanation:

3x + 2(2x − 1)= 33

simplify

3x + 4x - 2 = 33

7x - 2 = 33

add 2 to both sides

7x - 2 + 2 = 33 + 2

7x = 35

divide both sides by 7

7x/7 = 35/7

x = 5

8 0

2 years ago

Which of the following techniques will provide the most consistently correct result?

AnnZ [28]

Please there are no options to be chosen from

4 0

1 year ago