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3 years ago

Plz prove this for me.....

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

3 0

I've answered your other question as well.

Step-by-step explanation:

Since the identity is true whether the angle x is measured in degrees, radians, gradians (indeed, anything else you care to concoct), I’ll omit the ‘degrees’ sign.

Using the binomial theorem, (a+b)3=a3+3a2b+3ab2+b3

⇒a3+b3=(a+b)3−3a2b−3ab2=(a+b)3−3(a+b)ab

Substituting a=sin2(x) and b=cos2(x), we have:

sin6(x)+cos6(x)=(sin2(x)+cos2(x))3−3(sin2(x)+cos2(x))sin2(x)cos2(x)

Using the trigonometric identity cos2(x)+sin2(x)=1, your expression simplifies to:

sin6(x)+cos6(x)=1−3sin2(x)cos2(x)

From the double angle formula for the sine function, sin(2x)=2sin(x)cos(x)⇒sin(x)cos(x)=0.5sin(2x)

Meaning the expression can be rewritten as:

sin6(x)+cos6(x)=1−0.75sin2(2x)=1−34sin2(2x)

You might be interested in

You are at a coffee shop and notice that as the temperature of the room gets colder, more people order hot beverages. From this

mina [271]

Answer:

negative relationship.

Step-by-step explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

Cause and effect can be defined as the relationship between two things or events in which an occurrence one (cause) leads to the occurrence of another (effect).

A negative relationship or correlation can be defined as the relationship between two variables in which there exist an inverse relationship between them i.e as one variable increases, the other decreases and vice-versa.

In this scenario, you are at a coffee shop and notice that as the temperature of the room gets colder, more people order hot beverages. From this observation, you conclude that there is a negative relationship between the temperature and hot beverage sales at this coffee shop because for the temperature to get colder it would decrease and for the hot beverages to be hot, its temperature must be increased.

7 0

3 years ago

Please help me because I don't understand how to do it.:)

shutvik [7]

Answer:

y= 1/3 x +5

Step-by-step explanation:

To find the slope, we take two points

(0,5) and (15,10)

The slope is found by the formula

m = (y2-y1)/ (x2-x1)

= (10-5)/(15-0)

= 5/15

= 1/3

The slope is 1/3

The y intercept is found when x=0

When x=0 y=5

The slope intercept form of the line is

y=mx+b where m is the slope and b is the y intercept

y= 1/3 x +5

3 0

3 years ago

A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t

andreyandreev [35.5K]

Answer:

r = 2.632 cm
h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

r² = 3V/(πh)

The lateral surface area of the cone is ...

A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

dT/dh = -18V²/h³ +3πV

This will be zero when ...

3πV = 18V²/h³

h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

Interestingly, the ratio of h to r is √2.

8 0

3 years ago

A dance studio teaches students a contemporary dance form. It is observed that the probability of students from this studio beco

Helen [10]

$\mathbb P(X=75)=\dbinom{120}{75}0.69^{75}(1-0.69)^{120-75}\approx0.0239$

or about a 2.4% chance.

5 0

3 years ago

Read 2 more answers

Simplify.<br> 3/3-n - n/n-3

Black_prince [1.1K]

$\frac{3}{3-n}- \frac{n}{n-3}= \frac{3}{3-n}-(- \frac{n}{3-n})= \frac{3}{3-n}+\frac{n}{3-n}= \frac{3+n}{3-n}$

8 0

3 years ago