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pashok25 [27]
3 years ago
7

Find k so that the following function is continuous: f(x)={kx8x2if0≤x<5if5≤x.

Mathematics
1 answer:
tankabanditka [31]3 years ago
3 0

Check the one-sided limits:

\displaystyle \lim_{x\to5^-}f(x) = \lim_{x\to5}kx = 5k

\displaystyle \lim_{x\to5^+}f(x) = \lim_{x\to5}8x^2 = 200

If <em>f(x)</em> is to be continuous at <em>x</em> = 5, then these two limits should have the same value, which means

5<em>k</em> = 200

<em>k</em> = 200/5

<em>k</em> = 40

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Divide 180 in a ratio of 4:5:9
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A student incorrectly determined that the length of DE is 29 cm explaining that 12-7 = 5 and 36-7 = 29 explain what mistake the
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Answer:

The length of the hypotenuse ≈ 39.7 cm

Explanation:

Since the given triangle is a right-angled triangle, this means that we can apply the Pythagorean theorem.

The equation for Pythagorean calculation is:

(hypotenuse)² = (first leg)² + (second leg)²

In the given, we have:

first leg = 30 cm

second leg = 26 cm

Substitute with the givens in the above equation to get the hypotenuse as follows:

(hypotenuse)² = (30)² + (26)²

(hypotenuse)² = 1576

This means that:

either hypotenuse = √1576 = 39.69 ≈ 39.7 cm ..........> accepted

or hypotenuse = -√1576 = -39.69 ......> rejected as length can't be negative

Hope this helps :)

6 0
2 years ago
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