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KiRa [710]
3 years ago
13

2 (n)- 2n - 2; Find p(9)

Mathematics
2 answers:
nadya68 [22]3 years ago
6 0

Answer:

P(9)=16

Step-by-step explanation:

P(n)=2n-2\\\\P(9)=2(9)-2\\\\P(9)=18-2\\\\P(9)=16

Rzqust [24]3 years ago
5 0
P(9)=16
p(n)=2n-2
P(9)=2(9)-2
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Evaluate Dx / ^ 9-8x - x2^
Solnce55 [7]
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
4 0
3 years ago
ok its the walls of a room are repesentations of what basic element of geomotery A.point B.line C.plane D.ray please answer!
Reil [10]

Answer:

i think its C)

Step-by-step explanation:

4 0
2 years ago
Given that<br> a = 2,5= 2 and C = -1<br> work out<br> 2b – 3ac
poizon [28]

Step-by-step explanation:

2b-3ac

=2×2-3×2×(-1)

= 4+6

=10

6 0
3 years ago
There are (4^9)5 ⋅ 4^0 books at the library. What is the total number of books at the library? 4^9 - 4^45 - 4^46 - 1
maria [59]
Exponent rules : (a^m)^n = a^(mn) and a^0 = 1

(4^9)^5 * 4^0 =
4^45 * 1 =
4^45 <==
7 0
3 years ago
Write an equation of a line in slope intercept form that passes through the given points:
GarryVolchara [31]

Answer:

The answer is y= -1/3x-5

Step-by-step explanation:

(9, -8) and (-6, -3)

m= y²-y¹/x²-x1

m= (-3)-(-8)/(-6)-9

m= 5/-15

m=-1/3

y=mx+b

y=-1/3x+b

-3=-1/3(-6)+b

-3=2+b

-2 -2

-5=b

The answer is y=-1/3x-5

3 0
3 years ago
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