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3 years ago

Prove Cos3x=cos^3(x)-3sin^2(x)cos(x)

1 answer:

3 0

$\cos3x=\cos^3x-3\sin^2x\cos x\\\\L_s=\cos(2x+x)=\cos2x\cos x-\sin2x\sin x\\\\=(\cos^2x-\sin^2x)\cos x-2\sin x\cos x\sin x\\\\=\cos^3x-\sin^2x\cos x-2\sin^2x\cos x\\\\=\cos^3x-3\sin^2x\cos x=R_s\\\\\text{Used:}\\\\\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta\\\\\cos2\alpha=\cos^2\alpha-\sin^2\alpha\\\\\sin2\alpha=2\sin\alpha\cos\alpha$

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Expand (2 + a)9 using Pascal’s triangle.

Natalija [7]

Answer:

Step-by-step explanation:

The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.

1 $(A + B) ^ 0$ = 1

1 1 $(A +B ) ^ 1 = 1A + 1B$

1 2 1 $(A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2$

By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is

1 9 36 84 126 126 84 36 9 1

Now, fill in AB in the gaps.

1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB

Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is

$1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B$

Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B

$1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9$

The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.

$A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9$

Hope you can learn the method

5 0

2 years ago

if an area can be washed at a rate of 4,900 cm2/ minute, how many square inches can be washed per hour?

Olenka [21]

Answer : 4.5 × 10⁴ square inches can be washed per hour.

Step-by-step explanation :

As we are given that an area can be washed at a rate of 4,900 cm²/min. Now we have to determine the square inches can be washed per hour.

Given conversions are:

1 cm = 0.39 in and 1 hr = 60 min

As, 1 cm² = (0.39)² in² and 1 min = 1/60 hr

So, $1cm^2/min=(0.39)^2\times 60in^2/hr$

$1cm^2/min=9.126in^2/hr$

Now we have to determine the square inches can be washed per hour.

As, $1cm^2/min=9.126in^2/hr$

So, $4900cm^2/min=\frac{4900cm^2/min}{1cm^2/min}\times 9.126in^2/hr=44717.4in^2/hr=4.5\times 10^4in^2/hr$

Therefore, 4.5 × 10⁴ square inches can be washed per hour.

4 0

2 years ago

The square ABCD has side length 20 cm,

bogdanovich [222]

Answer:

AE=22.4

Step-by-step explanation:

BE is 1/2 of BC

BC is 20 cm All sides of a square are equal

BE = 1/2 BC Property of a midpoint.

BE = 10

Now just use Pythagorus

AB^2 + BE^2 = AE^2

AE^2 = 20^2 + 10^2 Perform the sqrs

AE^2 = 400 + 100 Add the terms

AE^2 = 500 Take the square root of both sides

√AE^2 = √500

AE = 22.36

AE ≈ 22.4

6 0

2 years ago

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric f

likoan [24]

Step-by-step explanation:

Let x be the length and y be the width of the rectangular plot.

The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,

x+2y = 1500

x = 1500 - 2y ....(1)

We know that the area of a rectangular plot is given by :

A = xy ....(2)

Put the value of x from equation (1) in (2)

$A=(1500-2y)y\\\\A=1500y-2y^2$ .....(3)

For largest area, differentiate above area equation wrt y.

$\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375$

Put the value of y in equation (1).

x = 1500-2(375)

= 750 m

Put the value of y in equation (3).

$A =1500(375)-2(375)^2\\A=281250\ m^2$

Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.

3 0

3 years ago

Bob can body paint 12 cars in 3 weeks. How many cars can Bob body paint in 8 weeks?

Oksana_A [137]

Answer:

32 cars

Step-by-step explanation:

we know that he can paint 12 cars in 3 weeks.

that means that he can paint 4 cars per week.

4cars x 8weeks = 32 cars in 8 weeks

3 0

2 years ago

Read 2 more answers