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defon
3 years ago
15

Find the exact values of the following, giving your answer as fractions

Mathematics
1 answer:
frosja888 [35]3 years ago
4 0
\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad 
a^n\implies \cfrac{1}{a^{-n}}
\\\\
-------------------------------\\\\
3^{-2}\implies \cfrac{1}{3^2}\implies \cfrac{1}{9}
\\\\\\
4^{-3}\implies \cfrac{1}{4^3}\implies \cfrac{1}{64}
\\\\\\
2^{-6}\implies \cfrac{1}{2^6}\implies \cfrac{1}{64}
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Determine the graph of the polar equation r =6/2-2cos theta<br> (picture provided)
vredina [299]

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

r=\frac{3}{1-cos(theta)}

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at  x = -3. Choice D fits this criteria

5 0
3 years ago
Graph the functions and approximate an x-value in which the exponential function exceeds the polynomial function. y = 4x y = 7x2
nordsb [41]

Answer:

The Exponential function is

y=4^x

And the polynomial function is

y=7 x^2 +4 x -2

And, we have to find the value of x for which, exponential function exceeds the polynomial function which can be written as

4^x> 7 x^2 +4 x -2

1. When , x= -1

LHS

4^{-1}=\frac{1}{4}=0.25

RHS

=7*(-1)^2 +4 *(-1)-2\\\\=7-4-2=1

2. When , x=0

L HS

 4^0=1

RHS

7*0+4*0-2= -2

3. When ,x= 0.5

L HS

 4^{0.5}=2

RHS

=7*0.25 +4*0.5 -2\\\\= 1.75+2-2\\\\=1.75

4. When , x=2

LHS

 4^{2}=16

RHS

=7*4^2+4*4-2\\\\=112+16-2\\\\=126

The Minimum value for which  exponential function exceeds the polynomial function is , x= 0.5

But,there is other value for which  exponential function exceeds the polynomial function is , x=2.

5 0
3 years ago
Im so confused on this please help if you can..​
Archy [21]

It's been a while since I have done these kind of questions, but I would say a 180 transformation would be my best answer. Hope this helps a bit!

4 0
3 years ago
nick is baking fudge. what is the minimum amount of plastic wrap needed to cover this piece of fudge?
Setler [38]

Answer:

4 inches

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Oliver has music lessons on Monday, Wednesday, and Friday. Each lesson is 3/4 of an hour. Oliver says he will have lessons for 3
sergey [27]
Automatically we know that he is wrong  because even if we round it to make it a friendly number (lets say 1)  it will still not equal 3 1/2
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That is why he is wrong :) hope this helped
5 0
3 years ago
Read 2 more answers
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