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Step2247 [10]
3 years ago
9

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1)

= −3, g '(3) = 2, then find h '(1) if h(x) = the quotient of f of x and g of x.
Mathematics
1 answer:
belka [17]3 years ago
3 0

Answer:

h'(1)=0

Step-by-step explanation:

We use the definition of the derivative of a quotient:

If h(x)=\frac{f(x)}{g(x)}, then:

h'(x)=\frac{f'(x)*g(x)-f(x)*g'(x)}{(g(x))^2}

Since in our case we want the derivative of h(x) at the point x = 1, which is indicated by: h'(1), we need to evaluate the previous expression at x = 1, that is:

h'(1)=\frac{f'(1)*g(1)-f(1)*g'(1)}{(g(1))^2}

which, by replacing with the given numerical values:

f(1) =4\\g(1)=3\\f'(1)=-4\\g'(1)=-3

becomes:

h'(1)=\frac{f'(1)*g(1)-f(1)*g'(1)}{(g(1))^2}=\\=\frac{-4*3-4*(-3)}{(3)^2}=\frac{-12+12}{9} =\frac{0}{9} =0

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Answer: 1256cm

Step-by-step explanation:

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3 years ago
2: A bag contains 5 black counters, 4 blue counters, and
drek231 [11]

Answer:

The probability that the counter  was blue is \mathbf{\frac{2}{5}}

Step-by-step explanation:

Number of black Counters = 5

Number of blue Counters = 4

Number of white Counters = 1

We need to write down the probability that the counter  was blue.​

First find Total Counters

Total Counters = Number of black Counters + Number of blue Counters + Number of white Counters

Total Counters = 5+4+1

Total Counters = 10

Now, we need to find probability that the counter taken was blue

The formula used is:

Probability= \frac{Number\:of\:favourable\:outcomes}{Total\:outcomes}

There are 4 blue counters in the back, so Favourable outcomes = 4

Probability= \frac{Number\:of\:favourable\:outcomes}{Total\:outcomes}\\Probability= \frac{4}{10}\\Probability= \frac{2}{5}

The probability that the counter  was blue is \mathbf{\frac{2}{5}}

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Mark records his science scores in each monthly assessment over a period of 5 months. In the first assessment he scores 76%. In
Trava [24]

This is the complete question:

Mark records his science scores in each monthly assessment over a period of 5 months. In the first assessment he scores 76%. In the second assessment he scores 73%. After that, his scores keep increasing by 2% in every assessment.  Assume that x represents the number of assessments since he starts recording and y represents the scores in each assessment, which of the following describes the situation?

a. a relation only b.

b. neither a function nor a relation

c. a function only

d. both a relation and a function

Answer:

  • <u><em>d. both a relation and a function</em></u>

Step-by-step explanation:

<em>A relation</em> is any statement, either verbal or mathematical, that connects, interrelates or associates, two or more elements (objects, persons, variables).

The text describes a situation where the scores in the assesments are related to the number of statements since Mark starts recording, hence this is a relation.

<h2>Is this relation a function or not?</h2>

In order for a relation be a function, the association has to be unambiguos. This means that for a given input only one output can exist. If an input can have two or more outputs, then you can not determine which is the output for that input. This is what defines whether a relation is a function or not.

In the situation described in the text, x is the input, i.e. the number of assessments since Mark starts recording the scores. Definetely, the number of assessment is not repeated: there is only one first assessment, only one second assessment, only one third assessment, ... the number of assessment cannot not get repeated. Of course, if the input is not repeated, there is only one output associated to the input (each assessment has just one associated score)  and the relation is a function.

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2 years ago
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