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3 years ago

How to solve this (b) ???

Mathematics

1 answer:

vladimir1956 [14]3 years ago

5 0

(b). → Simplify: [{5^(x-+1) + 5^x}/{6×5^x}]

= [{5^(x+1+x)}/{6×5^x}]

= [{5^(2x+1)}/{6×5^x}]

= [{5^(2x+1-x)}/6]

= [{5^(x+1)}/6]Ans.

(c). 4a³b²

= 4(3)³(-2)²

Since, a = 3 and b = -2.

so,

= 4(3*3*3)(-2*-2)

= 4(27)(4)

= 108(4)

= 432Ans.

also read similar questions: simplify 6/x-6+3x/x+5-1/(x-6)(x+5)..

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Fiona wants 6 red, 3 green and 3 yellow buttons on her dress. All buttons must be placed along a straight vertical line with no

elixir [45]

The appropriate method to use in solving the given question is permutation. Then, the numbers of ways to arrange the buttons is 1320 ways.

In the given question, the order of arrangement is important, so that the number of ways that Fiona could order the buttons can be determined by permutation method.

i.e $_{n}$ $P_{r}$ = $\frac{n!}{(n - r)!}$

Red 6

Green 3

Yellow 3

Total 12

Since no two neighbouring buttons of the same colour is allowed, then 3 buttons would be arranged at a time.

Thus, n = 12 and r = 3;

$_{12}$ $P_{3}$ = $\frac{12!}{(12 - 3)!}$

= $\frac{12!}{9!}$

= $\frac{12*11*10*9!}{9!}$

= 12 x 11 x 10

$_{12}$ $P_{3}$ = 1320

Therefore the buttons can be arranged in 1320 ways without two neighbors having the same colour.

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3 0

3 years ago

Read 2 more answers

If -xy+ 1 + x^2 = 2y then find the equations of all tangent lines to the curve y= -2

Black_prince [1.1K]

Answer:

(see attached workings)

y = -4x + 2

y = (4/5)x + 2/5

Step-by-step explanation:

Rewrite the function to make y the subject.
Find the x values of the points when y=-2 by substituting y=-2 into the rewritten function
Differentiate the function
Input the found values of x into the differentiated function to find the gradients of the tangents to the curve at y=-2
Use the equation of a straight line and the points where y=-2 and the found gradients to find the equation of the tangent lines.

See attached for complete step-by-step.