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3 years ago

1. What is the length of the shortest side if the perimeter of the rectangle is

Mathematics

2 answers:

Studentka2010 [4]3 years ago

6 0

Answer:

12 inches

Step-by-step explanation:

hope this helpes

alex41 [277]3 years ago

4 0

Answer:

12 inches

loveluttss. plss mark as brainliest

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This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl

Lostsunrise [7]

First,

tan(θ) = sin(θ) / cos(θ)

and given that 90° < θ < 180°, meaning θ lies in the second quadrant, we know that cos(θ) < 0. (We also then know the sign of sin(θ), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < θ/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(θ/2) > 0 and sin(θ/2) > 0.

Now recall the half-angle identities,

cos²(θ/2) = (1 + cos(θ)) / 2

sin²(θ/2) = (1 - cos(θ)) / 2

and taking the positive square roots, we have

cos(θ/2) = √[(1 + cos(θ)) / 2]

sin(θ/2) = √[(1 - cos(θ)) / 2]

Then

tan(θ/2) = sin(θ/2) / cos(θ/2) = √[(1 - cos(θ)) / (1 + cos(θ))]

Notice how we don't need sin(θ) ?

Now, recall the Pythagorean identity:

cos²(θ) + sin²(θ) = 1

Dividing both sides by cos²(θ) gives

1 + tan²(θ) = 1/cos²(θ)

We know cos(θ) is negative, so solve for cos²(θ) and take the negative square root.

cos²(θ) = 1/(1 + tan²(θ))

cos(θ) = - 1/√[1 + tan²(θ)]

Plug in tan(θ) = - 12/5 and solve for cos(θ) :

cos(θ) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(θ/2) and tan(θ/2) :

sin(θ/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(θ/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

3 0

2 years ago

1/4 x 2/5 x 3/6 x 4/7 x 5/8 x 6/9 x 7/n=?

postnew [5]

Answer:

c. $\frac{1}{12n} = {[12n]}^{-1}$

Step-by-step explanation:

$[\frac{1}{4}][\frac{2}{5}][\frac{1}{2}][\frac{4}{7}][\frac{5}{8}][\frac{2}{3}][\frac{7}{n}] = \frac{560}{6720n} = [12n]^{-1} = \frac{1}{12n}$

$\frac{2}{3} = \frac{6}{9}\\ \\ \frac{1}{2} = \frac{3}{6}$

* To make this simpler, reduce these two fractions in lowest terms.

I am joyous to assist you anytime.

8 0

3 years ago

What is the distance from C to D? A. 5 units B. 1 unit C. 25 units D. 7 units

Vera_Pavlovna [14]

Answer:

Option A

Step-by-step explanation:

According to the distance formula , for any 2 points P & Q whose coordinates are (x¹ , y¹) and (x² , y²) respectively. So ,

$PQ = \sqrt{(x^{2} - x^{1} )^{2} + (y^{2} - y^{1})^{2} }$

NOTE = HERE x² , y² DOESN'T MEAN THE SQUARES OF x & y . THEY ARE JUST COORDINATES.

According to the question ,

Coordinate of C = (2 , -1)

Coordinate of D = (5 , 3)

Using distance formula ,

$CD = \sqrt{(5-2)^{2} + (3 -(-1))^{2} }$

$=> CD = \sqrt{3^{2} + 4^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5$

5 0

3 years ago

Find the greates common factor of the following monomials:2r^4s^2 and 36r^4s^3

ki77a [65]

The greatest common factor is 2 $r^{4} s^{2}$

This is because we start by taking the largest factor that goes into both coefficients. Since the first coefficient is 2, we have to try 2 and 1. Since 2 is larger and goes into 36 evenly, we use that.

Then we use the smallest number of each variable. There are 4 r's in both equations. So, that is the number that we take. There are 2 s's in the first term, so we take that number.

6 0

3 years ago

PLZZZ HELPP anyonee plzzzz

mihalych1998 [28]

Answer:

The correct answer is B

Step-by-step explanation:

its is B because when dividing fractions the division symbol changes into a multiplication sign and the fraction on the right flips

High Hopes^^

Barry-

8 0

3 years ago

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