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3 years ago

What is the fraction of 2 1/4

Mathematics

2 answers:

Fofino [41]3 years ago

7 0

Answer:

9/4

Step-by-step explanation:

Multiply the denominator which is 4 by the whole number which is 2.

4 x 2 = 8

Next add the numerator to the 8.

8 + 1 = 9

The 9 is now the numerator and keep the original denominator.

9/4

icang [17]3 years ago

3 0

Answer:

9/4

Step-by-step explanation:

2 1/4 = 9/4 From mixed fraction to an improper fraction: "the numerator of the improper fraction" = "denominator" xx "the whole number" + "the numerator of the mixed fraction" The denominator remains as it is. So 2 1/4 = (4 xx 2 + 1)/4 = 9/4

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Question:

I will answer the following two questions.

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Step-by-step explanation:

Question 1: $\sin(x)+1=\cos^2(x)$

Question 2: $\sin(x)+1=\cos(2x)$

Question 1:

$\sin(x)+1=\cos^2(x)$

I will use a Pythagorean Identity so that the equation is in terms of just one trig function, $\sin(x)$ .

Recall $\sin^2(x)+\cos^2(x)=1$ .

This implies that $\cos^2(x)=1-\sin^2(x)$ . To get this equation from the one above I just subtracted $\sin^2(x)$ on both sides.

So the equation we are starting with is:

$\sin(x)+1=\cos^2(x)$

I'm going to rewrite this with the Pythagorean Identity I just mentioned above:

$\sin(x)+1=1-\sin^2(x)$

This looks like a quadratic equation in terms of the variable: $\sin(x)$ .

I'm going to get everything to one side so one side is 0.

Subtracting 1 on both sides gives:

$\sin(x)+1-1=1-\sin^2(x)-1$

$\sin(x)+0=1-1-\sin^2(x)$

$\sin(x)=0-\sin^2(x)$

$\sin(x)=-\sin^2(x)$

Add $\sin^2(x)$ on both sides:

$\sin(x)+\sin^2(x)=-\sin^2(x)+\sin^2(x)$

$\sin(x)+\sin^2(x)=0$

Now the left hand side contains terms that have a common factor of $\sin(x)$ so I'm going to factor that out giving me:

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Now this equations implies the following:

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$\sin(x)=0$ when the $y$ -coordinate on the unit circle is 0. This happens at $0$ , $\pi$ , or also at $2\pi$ . We do not want to include $2\pi$ because of the given restriction $0\le x$ .