All categories

1 year ago

The coefficient of x³ in the expansion of (3 +bx )⁵ is −720. Find the value of the constant b.

Mathematics

1 answer:

Molodets [167]1 year ago

3 0

Answer:

b = -2

Step-by-step explanation:

We need to use the binomial theorem, to expand

the expression (3 + bx )⁵ :

(3 + bx )⁵ = 3⁵ + 5(3)⁴(bx)¹ + 10(3)³(bx)² + 10(3)²(bx)³ + 5(3)¹(bx)⁴ + (bx)⁵

= 243 + 5×81×(bx)¹ + 10×27×(bx)² + 10×9×(bx)³ + 5×3×(bx)⁴ + (bx)⁵

= 243 + 405(bx)¹ + 270(bx)² + 90(bx)³ + 15(bx)⁴ + (bx)⁵

= 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵

Then

(3 + bx )⁵ = 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵

Then

The coefficient of x³ in the expansion of (3 + bx )⁵ is 90b³

Comparing the coefficients :

90b³ = -720

Then

b³ = (-720) ÷ 90 = -8

Then

b³ = -8

Then

b = -2

You might be interested in

Araceli had 61 pennies and then lost 12. Now she wants to buy a treat that costs 4 sevenths of the pennies she has left. How man

igor_vitrenko [27]

The treat would cost 7 cents of your 49

8 0

3 years ago

-3.6,-5.4,-8.1,-12.15 arithmetic or geometric or neither.

Brums [2.3K]

Answer:

Geometric Sequence

Step-by-step explanation:

1. Check the difference.

The difference between the 1st and 2nd term

$( - 5.4) - ( - 3.6) = - 1.8$

The difference between the 2nd and 3rd term

$( - 8.1) - ( - 5.4) = - 2.7$

The difference is not the same. Therefore, it is not an arithmetic sequence.

2. Check the ratio

The ratio between the 1st and 2nd term

$( - 5.4) \div ( - 3.6) = 1.5$

The ratio between the 2nd and 3rd term

$( - 8.1) \div ( - 5.4) = 1.5$

The ratio is the same. Therefore, it is a geometric sequence.

8 0

2 years ago

A factory makes candles. Each candle is in the shape of a triangular prism, as shown below. If the factory made 35 such candles,

Llana [10]

Number of candles =(total volumes used by the company)/(volume of one candle)
volume of one candle =5cm*2cm*12cm=120cm^3
hence number of candles =5040/120
, ,=42candles

5 0

2 years ago

Which is answer if not know please solve for mw

Vlad1618 [11]

<h3>Answers:</h3><h3>Area of parallelogram = 63</h3><h3>Area of triangle = 34</h3><h3>Area of trapezoid = 84</h3><h3>The trapezoid has the largest area</h3>

==================================================

Work Shown:

area of parallelogram = base*height

area of parallelogram = 9*7

area of parallelogram = 63

----------

area of triangle = (1/2)*base*height

area of triangle = (1/2)*10*6.8

area of triangle = 34

----------

area of trapezoid = height*(base1+base2)/2

area of trapezoid = 6*(13+15)/2

area of trapezoid = 6*(28)/2

area of trapezoid = 168/2

area of trapezoid = 84

5 0

3 years ago

Please help with this, i tried to solve for x, and it didnt give me any of those answers

DedPeter [7]

Let's solve your equation step-by-step.4(1−x)+2x=−3(x+1)Step 1: Simplify both sides of the equation.4(1−x)+2x=−3(x+1)Simplify: (Show steps)−2x+4=−3x−3Step 2: Add 3x to both sides.−2x+4+3x=−3x−3+3xx+4=−3Step 3: Subtract 4 from both sides.x+4−4=−3−4x=−7Answer:x=−7

3 0

2 years ago

The coefficient of x³ in the expansion of (3 +bx )⁵ is −720. Find the value of the constant b.​

The coefficient of x³ in the expansion of (3 +bx )⁵ is −720. Find the value of the constant b.