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3 years ago

Describe a situation where it is easier to use decimals than fractions and explain why

1 answer:

N76 [4]3 years ago

4 0

1) Their sizes are easier to compare. It's easy to see that 5.2 is less than 5.4, but comparing 6/54 to 13/52 takes a little more work.

2) Most physical objects are easier to measure as a decimal approximation. It might be easier to measure a piece of wood that's 0.21875 feet instead of 7/32 feet.

3) Decimals are expressed in fractions of powers of 10, and we use powers of 10 in our number system. Dividing 345 by 100 is easy to express as 3.45 rather than try to think of it as a fraction

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Evaluate exactly without the use of a calculator (remember to rationalize any denominators). a.(cos 60o)(sin 270o) + tan 225o b.

Rom4ik [11]

Given:

The trigonometric expressions are given as,

$\begin{gathered} a)\text{ }(\cos 60\degree)(\sin 270\degree)+\tan 225\degree \\ b)-\tan 240\degree+(cos45\degree)(\sec 135\degree) \end{gathered}$

Explanation:

The given expression can be rewritten as,

$=(\cos 60\degree)(\sin (360\degree-90\degree))+\tan (270\degree-45\degree)\text{ . . . . .(1)}$

Since, from the trigonometric ratios,

$\begin{gathered} \sin (360\degree-90\degree)=-\sin 90\degree \\ \tan (270\degree-45\degree)=\cot 45\degree \end{gathered}$

On plugging the obtained ratios in equation (1),

$=(\cos 60\degree)(-\sin 90\degree)+\cot 45$

Substitute the trigonometric values in the above equation.

$\begin{gathered} =\frac{1}{2}(-1)+1 \\ =-\frac{1}{2}+1 \\ =\frac{1}{2} \end{gathered}$

Hence, the exact value of the expression is 1/2.

The given expression can be rewritten as,

$=-\tan (270\degree-30\degree)+(\cos 45\degree)(\sec (90\degree+45\degree))\text{ . . . ..(2)}$

Since, from the trigonometric ratios,

$\begin{gathered} \tan (270\degree-30\degree)=\cot 30\degree \\ \sec (90\degree+45\degree)=-\csc 45\degree \end{gathered}$

On plugging the obtained ratios in equation (2),

$=-\cot 30\degree+(\cos 45\degree)(-\csc 45)$

Substitute the trigonometric values in the above equation.

$\begin{gathered} =-\sqrt[]{3}+\frac{1}{\sqrt[]{2}}(-\sqrt[]{2}) \\ =-\sqrt[]{3}-1 \end{gathered}$

Hence, the exact value of the expression is -√3-1.

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2 years ago

The difference of two numbers is 8. Five times the smaller number equals the greater numbers. Find the numbers.

alexgriva [62]

Answer:

feefef

Step-by-step explanation:

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3 years ago

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Tanzania [10]

Answer:

sepa

Step-by-step explanation:

i don’t know either

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4 years ago

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I need it now it’s important with number 7 and the button one

Sphinxa [80]

His model is incorrect because 20 x 7 is not 14, it is 140. If he had 140 instead of 14, he would have been correct.

I haven't done division like that in a long time, so this is what I think it will look like. I didn't add other work (multiplying 4 with #'s) but you can if you have to

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3 years ago

The radius of a garden in the shape of a regular pentagon is 18 feet. Find the area of the garden

bonufazy [111]

Think and do the math take your time

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3 years ago