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Stella [2.4K]
4 years ago
5

Use synthetic division to divide (x3 + x2 – 40x – 4) ÷ (x – 6).   

Mathematics
1 answer:
Nastasia [14]4 years ago
8 0
6  |  1   1   -40   -4
.   |       6    42   12
- - - - - - - - - - - - - -
.   |  1   7      2     8

\dfrac{x^3+x^2-40x-4}{x-6}=x^2+7x+2\text{ R }8

6   |   3   -9   -56   8
.    |        18   54   -12
- - - - - - - - - - - - - - -
.    |   3    9     -2   -4

\dfrac{3y^3-9y^2-56y+8}{y-6}=3y^2+9y-2\text{ R }-4
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3 years ago
Based on the graph below, how would you describe the curve?
victus00 [196]

D. is the correct answer

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liubo4ka [24]

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3 years ago
Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 − y2)
slamgirl [31]
<span>The answers to this problem are:<span>(<span>±5</span></span>√3/8,±5/8)<span>Here is the solution:
Step 1: <span><span><span>x2</span>+<span>y2</span>=<span>2516</span>[2]</span><span><span>x2</span>+<span>y2</span>=<span>2516</span>[2]</span></span>

Step 2: Substitute:<span> 
</span><span><span>8<span><span>(<span>25/16</span>)^</span>2</span>=25(<span>x^2</span>−<span>y^2</span>)
</span><span>8<span><span>(<span>25/16</span>)^</span>2</span>=25(<span>x^2</span>−<span>y^2</span>)</span></span>
</span><span>x^2</span>−<span>y^2</span>=<span>25/32</span><span>.

Add [2] and [3]:<span> 
</span><span>2<span>x^2</span>=<span>75/32
</span><span>x^2</span>=<span>75/74</span></span>
<span>x=±5</span></span>√3/8<span>
Substitute into [2]:<span> 
</span><span><span>75/64</span>+<span>y^2</span>=<span>50/32
</span><span>y^2</span>=<span>25/64</span></span>
<span>y=±<span>5/8</span></span>

</span>
</span>
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The scientific notation is 5.09 x 10^5
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