Bill has a batting average of .290 write this decimal as a fraction in simplest form

How do I get this answer?

Keith_Richards [23]

Answer:

Step-by-step explanation:

Several trig identities are involved in the proof of this. This is the order in which they are used.

cos(2x) = cos²(x) -sin²(x)
cos²(x) +sin²(x) = 1
cos(x) = 1/sec(x)

<h3>Proof</h3>

Starting with the left side, we can transform it into the right side.

$2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}$

4 0

2 years ago

How many solutions are possible for a triangle with A = 113° , a = 15, and b = 8

statuscvo [17]

Answer:

One solution.

Step-by-step explanation:

To determine the number of possible solutions for a triangle with A = 113° , a = 15, and b = 8, we're going to use the law of sines which states that: "<em>When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C</em>".

Using the law of sines we have:

$\frac{sin(A)}{a} = \frac{sin(B)}{b}$

$\frac{sin(113)}{15} = \frac{sin(B)}{8}$

Solving for B, we have:

$sin(B)=0.4909$

∠B = 29.4°

Therefore, the measure of the third angle is: ∠C = 37.6°

There is another angle whose sine is 0.4909 which is 180° - 29.4° = 150.6 degrees. Given that the sum of all three angles of any triangle must be equal to 180 deg, we can't have a triangle with angle B=113° and C=150.6°, because B+C>180.

Therefore, there is one triangle that satisfies the conditions.

7 0

3 years ago

What are the types of roots of the equation below?<br> - 81=0

Tju [1.3M]

Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0. This can be obtained by finding root of the equation using algebraic identity.

<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,

⇒ x⁴ - 81 = 0

⇒ (x² + 9)(x² - 9) = 0

(x² - 9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

⇒ [x² - 3x + 3x - 9][x² - 3xi + 3xi - 9i²] = 0

⇒ (x² +0x - 9)(x² +0xi - 9(- 1)) = 0

⇒ (x² - 9)(x² + 9) = 0

⇒ x⁴ - 9x² + 9x² - 81 = 0

⇒ x⁴ - 81 = 0

Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

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5 0

1 year ago

Find the measure of angle d.<br> d°

QveST [7]

Answer:

Need points sorry <3

Step-by-step explanation:

3 0

3 years ago

Plz help. Write the slope intercept form of the equation

Fudgin [204]

Answer:

2nd option is correct

Step-by-step explanation:

x +2y=14

2y = -x + 14

y= -x/2 +7

3 0

3 years ago

Read 2 more answers