Pic from the problem
1 answer:
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Shown in the graph
<h2>Explanation:</h2>Using graph tools we can graph the function:
which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:
Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it ) will be:
This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:
By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:
Cubic function: brainly.com/question/13773618#
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<h2>Answer:</h2>
0 - 17i
<h2>Step-by-step explanation:</h2>Given expression;
i⁸⁰ + i³⁸ - i17
To express the expression in the form a+bi;
<em>i. Rewrite the expression such that it contains terms in i²</em>
(i²)⁴⁰ + (i²)¹⁹ - i17
<em>ii. Solve the result from (i) above using the identity i² = -1</em>
We know that the square root of -1 is i. i.e
<em>Squaring both sides gives</em>
<em>=> </em><em />
=> -1 = i²
Therefore,
i² = -1
<em>Substitute i² = -1 in step (i) above</em>
(-1)⁴⁰ + (-1)¹⁹ - i17
<em>(iii) Solve the result in (ii)</em>
We know that the when a negative number is raised to the power of an even number, the result is a positive number. If it is raised to the power of an odd number, the result is a negative number. Therefore,
(-1)⁴⁰ + (-1)¹⁹ - i17 becomes
1 + (-1) - i17
0 - i17
<em>(iv) Write the result from (iii) in the form a+bi</em>
0 - 17i