I believe Infiniti because x is bigger then one and there are many many numbers bigger then one.
Answer: The range is
The way to get this answer isn't completely obvious. What I did first was graph the function using GeoGebra allowing k to be a parameter. With k as a sliding parameter, the graph was able to be slid up and down the screen. The basic shape of the curve is a distorted W shape. The lowest point being the local minimum. Which is where the lower endpoint of the range would be.
Using the derivative, we can get
y = x^4 + 8x^3 + k
dy/dx = 4x^3 + 24x^2
set dy/dx equal to zero and solve for x
dy/dx = 0
4x^3 + 24x^2 = 0
4x^2(x + 6) = 0
4x^2 = 0 or x+6 = 0
x = 0 or x = -6
It turns out that x = 0 is a saddle point so we can ignore this value. Only x = -6 is where the local min is at. Plug this back into the original function
y = x^4+8x^3+k
y = (-6)^4+8(-6)^3+k
y = -432+k
y = k - 432
So when the input is x = -6, the output is k - 432 for some value k
In other words, the smallest y can get is k - 432. Otherwise it will be larger than this value
So that's why the range is
Note: if this calculus approach doesn't make much sense, then you can try various k values and use a calculator to find the lowest point. Making a table of k values with the corresponding lowest point would hopefully point you in the right direction.
Answer: 7^18/7^9, (7^3)^3 & 7^4 * 7 ^ 5.
The second, third & last options are the answers
These equations equal 40,353,607 btw
<em>Answer:</em>
<h3>
<em>B'=</em><em>(</em><em>1</em><em>6</em><em>,</em><em>1</em><em>4</em><em>)</em></h3>
<em>It </em><em>is </em><em>clear </em><em>from </em><em>the </em><em>co-ordinates</em><em> </em><em>of </em><em>the </em><em>square </em><em>that </em><em>CD </em><em>is </em><em>parallel </em><em>to </em><em>X </em><em>axis </em><em>and </em><em>BC </em><em>is </em><em>parallel </em><em>to </em><em>y-axis.</em><em> </em><em>So,</em><em>X=</em><em>8</em><em>,</em><em>y=</em><em>7</em>
<em>so </em><em>the </em><em>co-ordinates</em><em> </em><em>of </em><em>B=</em><em>(</em><em>8</em><em>,</em><em>7</em><em>)</em>
<em>Now </em><em>after </em><em>dilation</em><em> </em><em>of </em><em>factor </em><em>2</em><em>,</em><em> </em><em>all </em><em>coordinates</em><em> </em><em>will </em><em>be </em><em>multiplied</em><em> </em><em>by</em><em> </em><em>2</em><em>.</em>
<em>So </em><em>B'=</em><em>(</em><em>1</em><em>6</em><em>,</em><em>1</em><em>4</em><em>)</em>
<em>hope </em><em>it</em><em> helps</em>
To make 70% she has completed 7 out of 10 shots. for her to get 75% she would need 3 out of 4 each time.