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3 years ago

Consider the quadratic equation 2x² + 72 + k = 0. Which value of k results in the equation having complex solutions?

Mathematics

1 answer:

postnew [5]3 years ago

5 0

Hi there!

$\large\boxed{k> 6.125}$

We can use discriminants to determine the value of k for which the equation would have complex solutions. (Those involving i)

If b² - 4ac < 0, then the equation will have complex solutions. Therefore:

Plug in the given values of b and a to solve:

7² - 4(2)(k) < 0

Simplify:

49 - 8k < 0

Solve the inequality:

49 < 8k

6.125 < k

k > 6.125. Anything greater than 6.125 would result in complex solutions.

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A fish was swimming LaTeX: 2\frac{1}{2}2 1 2 feet below the water's surface at 1:00 p.M. Three hours later, the fish was at a de

marin [14]

Answer:

$\frac{23}{4}$ feet

Step-by-step explanation:

The depth of the fish to the surface of water at 1:00 pm = 2 $\frac{1}{2}$ feet

= $\frac{5}{2}$ feet

The depth of the fish to its initial position at 4:00 pm = 3 $\frac{1}{4}$ feet

= $\frac{13}{4}$ feet

The position of the fish with respect to the water's surface at 4:00 pm = the depth of the fish to the surface of water at 1:00 pm + the depth of the fish to its initial position at 4:00 pm

= $\frac{5}{2}$ + $\frac{13}{4}$

= $\frac{10 + 13}{4}$

= $\frac{23}{4}$

The position of the fish with respect to the water's surface at 4:00 pm is $\frac{23}{4}$ feet.

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3 years ago

I need help finding perimeter of a rectangle with the side missing

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The perimeter of a rectangle is (2 lengths) plus (2 widths).

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3 years ago

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 6000 Fun Noodles per day d

Salsk061 [2.6K]

PART A:
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y-yo = m (x-xo)
First we look for the slope of the line:
m = (y2-y1) / (x2-x1)
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Then, we substitute any point in the generic equation:
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y = -1000x + 9000

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