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oksano4ka [1.4K]

2 years ago

15

The distance between the two places on a map is 4.5 in. If the scale on the map is 0.75 in: 4 miles, how far apart are the two p

laces in real life.

1 answer:

OLEGan [10]2 years ago

6 0

Answer:

24 miles

Step-by-step explanation:

Since 4.5 divided by 0.75 is 6, 6 times 4 is 24.

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) f) 1 + cot²a = cosec²a

notsponge [240]

Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

$\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}$

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

$\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}$

Another identity is:

$\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}$

Therefore:

$\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}$

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

$\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}$

Another identity:

$\displaystyle \large{\sin^2x+\cos^2x=1}$

Therefore:

$\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}$

Hence proved, this is proof by using identity helping to find the specific identity.

6 0

3 years ago

Helpppp pleases last question

iren2701 [21]

The perimeter is 40 cm. You would take the square root of 100 which is 10. 10 would be the length of each side since it is a square and all sides are equal.

8 0

2 years ago

How would i solve for this? it says im doing it wrong and have one more try left.

WITCHER [35]

Answer: 1 & 1/2

The whole part is 1

The fractional part is 1/2

======================================================

Explanation:

Write 1/2 as 2/4. Basically you multiply top and bottom by 2.

We have these three fractions: 1/4, 2/4, 3/4

Add them up: (1/4)+(2/4)+(3/4) = (1+2+3)/4 = 6/4 = 3/2

To go from 6/4 to 3/2, we divide both parts by 2.

Finally, convert the improper fraction 3/2 to the mixed number 1 & 1/2

6 0

3 years ago

Martin orders a pasta dish that is priced at $11.99. He also orders a drink. The total cost for the pasta and drink is $14.48. W

bixtya [17]

Answer:

14.48=11.99+y

or

y=14.48-11.98

Step-by-step explanation:

it should be one of these (the variable might be different)

y is the price of the drink

8 0

2 years ago

eli takes a typing test and types all 300 words in 1/10 hour.he takes the test a second time and types the words in 1/12 hour wa

Leokris [45]

He typed faster the second time because if you multiple 60 minutes by 1/10 and 1/12 of and hour separately, you get a smaller answer with 1/12 than by 1/10, and thereby a smaller answer.

Hope this helps!

5 0

3 years ago