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4 years ago

Finding diffrence and writing in simplest form of 4 1/2-3 5/6

1 answer:

5 0

You need to find the common denominator between 1/2 and 5/6. 2 can be divided by 6 3 times so a common denominator is 6. 5/6 is in the correct form. Half of six is 3. so 4 3/6 minus 3 5/6. Put them into improper fractions

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Prove that sin^4x - cos^4x = 2sin^2x - 1

Liula [17]

Step-by-step explanation:

Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation

Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)

LHS = sin^4x - cos^4x = (sin²x)² - (cos²x)²

= (sin²x - cos²x)(sin²x + cos²x)

= sin²x - (1 - sin²x) since sin²x + cos²x = 1

= 2 sin²x - 1

= RHS

Hence proved.

5 0

3 years ago

Use logarithmic differentiation to find the derivative of the function. y = x2cos x Part 1 of 4 Using properties of logarithms,

Arisa [49]

ANSWER

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

EXPLANATION

The given function is

$y = {x}^{2} \cos(x)$

We take natural log of both sides;

$ln(y) = ln({x}^{2} \cos(x) )$

Recall and use the product rule of logarithms.

$ln(AB) = ln(A ) + ln(B)$

This implies that:

$ln(y) = ln({x}^{2} ) + ln( \cos(x) )$

$ln(y) = 2 ln({x} ) + ln( \cos(x) )$

We now differentiate implicitly to obtain;

$\frac{ {y}^{'} }{y} = \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) }$

Multiply through by y,

${y}^{'} = y( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) })$

Substitute y=x²cosx to obtain;

${y}^{'} = {x}^{2} \cos(x) ( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) } )$

Expand:

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

7 0

4 years ago

If a triangle has a height of 12 inches in the base of 5 inches what is the area

tatiyna

<span>The area of the triangle with height 12 inches and the base of 5 inches is 30 square inches. The area (A) of a triangle with height, h, and base, b, is: A = h * b / 2. We know that h = 12 in and that b = 5 in. Therefore, the area of this triangle will be: A = 12 in * 5 in / 2 = 60 in^2 / 2 = 30 in^2. The area of the triangle is 30 square inches.</span>

4 0

3 years ago

Which property of inequalities states that if x ≤ 5 and 5 ≤ y , then x ≤ y?

katen-ka-za [31]

ANSWER

The Transitive Property of Inequalities.

EXPLANATION

The Transitive properties of inequalities says that,

If a≤b and b≤c, then a≤c.

The same thing applies to the given inequality.

if x ≤ 5 and 5≤ y, then x≤ y.

Therefore the correct answer is Transitive Property.

7 0

3 years ago

PLEASE HELP ASAP!!!!

Bond [772]

Answer: 518

Step-by-step explanation:

4 0

3 years ago