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A circle has an area of 256pi. What is the diameter of the circle?

brilliants [131]

256pi
sqroot 256 = 16
16 * 2 = 32
The diameter of the circle is 32

5 0

3 years ago

79. Use properties of exponents to rewrite each expression as either an integer or as a quotient of integers p/q to show the exp

Nesterboy [21]

Answer:

See explanation below

Step-by-step explanation:

First we will going to rewrite 54 into its prime factors: 54 = 3³(2)

So, the expression $\frac{3\sqrt{54} }{3\sqrt{2} }$ can be written as:

$\frac{3\sqrt{3^32} }{3\sqrt{2} } =\frac{3(3^{3/2})2^{1/2} }{3(2^{1/2}) } =3^{3/2}=3\sqrt{3}$

<u>*We used the fact that a square root is like having a 1/2 exponent so we multiplied the exponents inside the root by 1/2 and then simplified them*</u>

7 0

4 years ago

Please help with these

Nookie1986 [14]

The values would be

sin2x = -3/5

cos2x = -4/5

tan2x = 3/4

What are double angles in trigonometry?

The double angle formulas are used to find the values of double angles of trigonometric functions using their single angle values. For example, the value of cos 30° can be used to find the value of cos 60°. Also, the double-angle formulas can be used to derive the triple-angle formulas.

Given: tanx = -3

Now as we know,

$sin2x=\frac{2tanx}{1+tan^2x}\\\\sin2x=\frac{2(-3)}{1+(-3)^2}\\\\sin2x=\frac{-6}{10}\\\\sin2x=\frac{-3}{5}$

Now

$cos2x=\frac{1-tan^2x}{1+tan^2x}\\\\cos2x=\frac{1-(-3)^2}{1+(-3)^2}\\\\cos2x=\frac{1-9}{1+9}\\\\cos2x=\frac{-8}{10}\\\\cos2x=\frac{-4}{5}$

And similarly, we can find the value of tan2x, as

tan2x = sin2x/cos2x

= (-3/5)/(-4/5)

= 3/4

Hence,

The values would be

sin2x = -3/5

cos2x = -4/5

tan2x = 3/4

To learn more about double angles in trigonometry, visit:

brainly.com/question/6277459

#SPJ1

6 0

2 years ago

The length of a swimming pool would be about

zubka84 [21]

It would be 12 yards :)

7 0

3 years ago

1. Assume O P || NM.

ipn [44]

1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming $\frac{ON}{LO} = \frac{PM}{LP} = 3$ using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

<h3>What is the Triangle Proportionality Theorem?</h3>

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

$\frac{ON}{LO} = \frac{PM}{LP}$

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, $\frac{ON}{LO} = \frac{PM}{LP} = 3$

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

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

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

Learn more about triangle proportionality theorem on:

brainly.com/question/24804474

4 0

3 years ago