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3 years ago

Expand the following using either the Binomial Theorem You must show

1 answer:

n200080 [17]3 years ago

4 0

<h2><u><em>Answer:</em></u></h2><h2><em>A Pascal triangle is the triangular way of expanding a binomial. So the best way in expanding that function is thru Binomial Theorem and the expanded for of it is 8x^3+48x^2+98x+64 </em></h2><h2><em></em></h2><h2><u><em>Step-by-step explanation:</em></u></h2><h2><em>Before even trying to put this into the binomial form, we must figure out the coefficients. If we go by the Pascal's Triangles way we should end up with: </em></h2><h2><em> </em></h2><h2><em> 1 </em></h2><h2><em> </em></h2><h2><em> 1 1 </em></h2><h2><em> </em></h2><h2><em> 1 2 1 </em></h2><h2><em> </em></h2><h2><em>1 3 3 1 </em></h2><h2><em> </em></h2><h2><em>Going by the last level (which is the third level) we get 3C0:1, 3C1:3, 3C2:3, 3C3:1. </em></h2><h2><em> </em></h2><h2><em>Now with the equation: (a+b)^3 = 3C0a^3 + 3C1a^2 b + 3C2a b^2 + 3C3b^3 we just plug in all the values and simplify </em></h2><h2><em> </em></h2><h2><em>(2x+4)^3 = 2x^3 + 3(2x)^2 (4) + 3(2x) (4)^2 + (4)^3 </em></h2><h2><em> </em></h2><h2><em>(2x+4)^3 = 8x^3 + (3)(4x^2)(4) + (3)(2x)(16) + 64 </em></h2><h2><em> </em></h2><h2><em>Then we finally end with: (2x+4)^3 = 8x^3 48x^2 + 96x +64 </em></h2>

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What is the vertex of f(x) = 3(x+2)^2 -1

inna [77]

Answer:

$The~vertex~of~parabola~f(x) = a(x-h)^2+k~is~(h,k).\\Given~equation~of~parabola~is:\\f(x) = 3(x+2)^2-1\\So,~ h =-2 ~and~k=-1\\Therefore,~(-2,-1)~is~the~vertex~of~parabola.$

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2 years ago

The unit of measure that would be best to estimate the height of a cat would be:

snow_tiger [21]

Well usually a cat isn’t that big, probably a foot in length BUT heightwise it’s best to measure in inches because the average cat isn’t a whole foot tall!

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3 years ago

Please show work<br>its due soon<br>i really need answers

Debora [2.8K]

Answer:

Step-by-step explanation:

from 5 to 20 its mutiplied by 4 and from 6 to 24 it mutiplied by 4, and last 10 ×4 is 40

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3 years ago

gerald has 30 dollars to spend on lunch this month. lunch cost him 1.50 each day. after 8 days how much money has he spent?

pentagon [3]

Answer:

18 dollars

Step-by-step explanation:

$1.50*8=$12

$30-$12=$18

3 0

3 years ago

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y)= e^xy; X

kotykmax [81]

Answer:

f(x,y) = $e^{xy}$ is maximum at x = 2 and y = 2 and f(2,2) = $e^{4}$

Step-by-step explanation:

Since f(x,y) = $e^{xy}$ and x³ + y³ = 16, Ф(x,y) = x³ + y³ - 16

df/dx = y $e^{xy}$ , df/dy = x $e^{xy}$ , dФ/dx = 3x² and dФ/dy = 3y²

From the method of Lagrange multipliers,

df/dx = λdΦ/dx and df/dy = λdΦ/dy

y $e^{xy}$ = 3λx² (1) and x $e^{xy}$ = 3λy² (2)

multiplying (1) by x and (2) by y, we have

xy $e^{xy}$ = 3λx³ (4) and xy $e^{xy}$ = 3λy³ (5)

So, 3λx³ = 3λy³

⇒ x = y

Substituting x = y into the constraint equation, we have

x³ + y³ = 16

x³ + x³ = 16

2x³ = 16

x³ = 16/2

x³ = 8

x = ∛8

x = 2 ⇒ y = 2, since x = y

So, f(x,y) = f(2,2) = $e^{2 X2}$ = $e^{4}$

We need to determine if this is a maximum or minimum point by considering other points that fit into the constraint equation.

Since x³ + y³ = 16 when x = 0, y is maximum when y = 0, x = maximum

So, 0³ + y³ = 16

y³ = 16

y = ∛16

Also, when y = 0, x = maximum

So, x³ + 0³ = 16

x³ = 16

x = ∛16

and f(0,∛16) = $e^{0X\sqrt[3]{16} } = e^{0} = 1$ .

Also, f(∛16, 0) = $e^{\sqrt[3]{16}X0 } = e^{0} = 1$ .

Since f(0,∛16) = f(∛16, 0) = 1 < f(2,2) = $e^{4}$

f(2,2) is a maximum point

8 0

3 years ago