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Lunna [17]
3 years ago
11

Write a quadratic function that is concave up with only one x-intercept at 32.

Mathematics
1 answer:
GuDViN [60]3 years ago
5 0
Here's one:
y=43x^2-43*32^2
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Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thu
cluponka [151]

Answer:

<em>Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.</em>

Step-by-step explanation:

Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.

Suppose, her speed in nice weather is  x mph.

As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: (x-18) mph

<u>We know that,</u>  Time = \frac{Distance}{Speed}

So, <u>the time of driving in clear weather</u> =\frac{50}{x} hours

and <u>the time of driving in thunderstorm</u> =\frac{16}{x-18} hours.

Given that, <u>the total time for the trip is 1.5 hours</u>. So, the equation will be......

\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0

Using zero-product property.........

x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12

<em>We need to ignore x=12 here, otherwise the speed in thunderstorm will become negative.</em>

So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph

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