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2 years ago

9. Let f be a continuous function such that f(3) = 4 and f(5)=2. Let h(x)= f(x) + 2x. Explain why

Mathematics

1 answer:

GaryK [48]2 years ago

4 0

Since f(x) is continuous, so is h(x).

Also, since f (3) = 4 and f (5) = 2, we have

h (3) = f (3) + 2•3 = 4 + 6 = 10

h (5) = f (5) + 2•5 = 2 + 10 = 12

It follows from the intermediate value theorem that there is some t between 3 and 5 such that h(t) is between 10 and 12, and namely there is some t for which h(t) = 11.

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F/13 = 6.2 what is the value of f

nekit [7.7K]

Answer:

The value of f is 80.6.

Step-by-step explanation:

We are given the equation and asked to solve for f.

If we are given a fraction with a variable in the numerator, we can multiply both sides of the equation by the denominator to isolate it.

For example, if you look at this equation:

$\displaystyle\frac{a}{26}=17.9$

We can multiply both sides by 26 to get the a by itself so the equation can be solved.

$\displaystyle26\times\frac{a}{26}=17.9\times26\\\\a = 465.4$

Therefore, we can apply this same technique to the equation $\frac{f}{13}=6.2.$

$\displaystyle\frac{f}{13}=6.2\\\\13\times\frac{f}{13}=6.2\times13\\\\f = 80.6\ \text{or} \ \frac{403}{5}$

Therefore, the value of f is 80.6.

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3 years ago

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I need clean and clear answers please! Thank you

lina2011 [118]

Okay so we get: subtract m + 8 from 5m + 11

5m + 11 = 16 + m or 16m

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What is the surface area of an ice cream cone if the radius is 2 inches

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It goes 19 1 and 4ths to the area surface

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3 years ago

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Help ASAP!! i need help finding out the pattern of 3 and 4

melomori [17]

Answer:

See below.

Step-by-step explanation:

For 3, we have:

1, 3, 6, ___, 15, 21, _____, 36, _______

Let's try to determine the pattern. From 1 to 3, we added 2.

From 3 to 6, we added 3.

So, it seems that the fourth term would be to add 4, and then add 5. Let's try it:

6+4=10

10+5=15.

So, it seems we're correct. So, we will add 6, then 7, and then 8, etc. Therefore, our correct sequence would be:

1 (+2), 3 (+3), 6 (+4), 10 (+5), 15 (+6), 21 (+7), 28 (+8), 36 (+9), 45

For 4, we have:

100, _____, 64, ______, 36, 25, _______

Notice that these all are perfect squares. 10 squared is 100, 8 squared is 64, etc. Thus, we can rewrite this as:

10², _____, 8², ______, 6², 5², ______

Therefore, our blanks would be:

10², 9², 8², 7², 6², 5², 4².

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