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Lisa [10]
3 years ago
5

Solve the problem. six times Tim’s age is 54. His sisters age times three is also 54. How old are Tim an his sister Amy?

Mathematics
1 answer:
Semenov [28]3 years ago
6 0

If t is Tim's age, then 6t=54, so t=9.

If a is Amy's age, then 6a=54, so her age is also a=9.

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The height of a tennis ball tossed into the air is modeled by h(x) = 40x â€" 16x 2, where x is elapsed time in seconds. During w
egoroff_w [7]

The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.

Given that,

The height of a tennis ball tossed into the air is modeled by,

\rm h(x) = 40x - 16x^2

Where x is elapsed time in seconds.

We have to determine,

During what time interval will the tennis ball be at least 15 feet above the ground?

According to the question,

The height of a tennis ball tossed into the air is modeled by,

\rm h(x) = 40x - 16x^2

Where x is elapsed time in seconds.

Then,

When the tennis ball be at least 15 feet above the ground,

h(x) = 15

Substitute the value of h(x) in the equation,

\rm h(x) = 40x - 16x^2\\\\ 15 = 40x - 16x^2\\\\ 16x^2-40x+15=0

Factorize the equation for finding the time interval will the tennis ball be at least 15 feet above the ground is,

\rm 16x^2-40x+15= 0\\\\x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2-4 \times 16 \times 15}}{2 \times 16}\\\\x =  \dfrac{-(-40)\pm \sqrt{1600- 960}}{32}\\\\x =  \dfrac{40\pm \sqrt{640}}{32}\\\\x =  \dfrac{40 + 25.29}{32} \\\\x =  \dfrac{40 + 25.29}{32} \ and \ x =  \dfrac{40 - 25.29}{32}\\\\x = \dfrac{65.29}{32} \ and \ x = \dfrac{14.71}{32}\\\\x = 2.04 \ and \ x = 0.45

Hence, The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.

For more details about Inequality refer to the link given below.

brainly.com/question/17177510

7 0
3 years ago
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