MATHEMATICS MIDDLE SCHOOL

Verify cot x sec^4x=cotx +2tanx +tan^3x

Answers

Answer 1

Answer:

Answer:

See explanation

Step-by-step explanation:

We want to verify that:

$\cot(x) \: { \sec}^(4) x = \cot(x) + 2 \tan(x) + { \tan}^(3) x$

Verifying from left, we have

$\cot(x) \: { \sec}^(4) x = \cot(x) \: ( 1 + { \tan}^(2) x )^(2)$

Expand the perfect square in the right:

$\cot(x) \: { \sec}^(4) x = \cot(x) \: ( 1 + { 2\tan}^(2) x + { \tan}^(4) x)$

We expand to get:

$\cot(x) \: { \sec}^(4) x = \cot(x) \: + \cot(x){ 2\tan}^(2) x +\cot(x) { \tan}^(4) x$

We simplify to get:

$\cot(x) \: { \sec}^(4) x = \cot(x) \: + 2 ( \cos(x) )/(\sin(x) ) ) * \frac{{ \sin}^(2) x}{{ \cos}^(2) x} +( \cos(x) )/(\sin(x) ) ) * \frac{{ \sin}^(4) x}{{ \cos}^(4) x}$

Cancel common factors:

$\cot(x) \: { \sec}^(4) x = \cot(x) \: + 2 \frac{{ \sin}x}{{ \cos}x} +\frac{{ \sin}^(3) x}{{ \cos}^(3) x}$

This finally gives:

$\cot(x) \: { \sec}^(4) x = \cot(x) + 2 \tan(x) + { \tan}^(3) x$

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4. Frank bought lunch for $5.60 at a diner. He spent $2.00 to ride the bus to the mall and back, and spent $6.50 while he was at the mall. His friend Bill paid him back $5.00 that he had borrowed last week. If Frank arrived at home with $10.50 in his pocket, how much did he have when he left home that morning?

Answers

Frank had $19.60 dollars when he left home that morning. If you add the $5.60, $2.00, and $6.50 that he spent while he was away from home, because he had that money when he left, you get a total of $24.60. You should then subtract the $5.00 his friend gave him, since he didn't have that when he left home. This brings you to a total of $19.60, which is the amount Frank left home with.

he had $19.60
u take $5.00 of the amount he had at home then u add the rest
so 5.50+2.00+5.60+6.50=19.60
sorry if im not right

A video game store has a 20% sale on all video games. If the game you wanted cost $32.00,what would the discount be?

Answers

Multiply the decimal conversion of 20% by 32 to find the discount. 20% = 0.20, so 0.20*32 = 6.4. Therefore, the discount is $6.40.
Hope that helped.

You would do cross multiplication and your answer should be $6.40

Explain how you could add 678 + 303 using mental math

Answers

678 + 303 = 981

Here are a few examples to get you started:
600 + 300 = 900
78 + 3 = 81
900 + 81 = 981
Here's another one:
678 = 600 + 70 + 8
303 = 300 + 00 + 3
Add the ones place = 11
Add the tens place = 70
Add the hundreds place = 900
Now add 900 + 70 + 11 = 981
Hope this helps! :-)

The expression 14 6power ÷ 14 4power is equal to _____.

Answers

Answer:

196

Step-by-step explanation:

The teacher writes 10/12 on the board write this fraction in slimplest form

Answers

Answer: $(5)/(6)$

Step-by-step explanation:

Given fraction= $(10)/(12)$

Here numerator=10

Denominator=12

We know that 10 and 12 both are multiples of 2 such that

$10=2*5$

$12=2*6$

Therefore, to write the given fraction in simplest form, divide numerator and denominator by 2 , we get

$(10)/(12)=(5)/(6)$

5/6 because 10 divided by two is 5. And 12 divided by two is 6. So if you want to simplify the fraction, find a number that both are divisible by. So 10/12 divided by 2 equals 5/6 and 5/6 can't be simplified so the simplest form is 5/6. Hope this helped, ;)

Please answer quick!The perimeter of a rectangular herb garden is 74 feet. If the length of the garden is 5 feet longer than 3 times its width, what is the garden's width?

Answers

Answer:

Step-by-step explanation:

Using perimeter =2(l+b)

74=2(L+B)

From the question

Width(b)=x & length(l)=3x+5

So we have that

74 =2(3x+5+x)

Adding like terms we then have that

74 =2(4x+5)

Opening the bracket gives

74=8x +10

Collecting like terms

8x=74-10

8x= 64

Therefore

X=64/8

X=8feets

The width is 8feets

Answer:

8 feet.

Step-by-step explanation:

plug into missing values

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