Let's evaluate 3x + 4 when x=5

1 answer:

6 0

It is simple
Step 1) substitute x = 5 into the equation
3x +4
3(5) + 4 gives you 3 times 5 + 4
The answer is 15 + 4 which is 19

Now substitute a and b into the equation 3(a) + 4(b) when the a = 6 and b = 5
Hereby 3(6) + 4(5)
3 * 6 = 18 and 4* 5 = 20
18 + 20 = 38
The answer is 38

Now finally
Substitute a and b Into the equation
3(3) + 4(6)
9+ 24 = 33

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F(x) = lnx/x

My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) Deduce:
 $e^{x} \geq x^{e}, x > 0$

Soln: Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.

3 0

3 years ago

What is the mode of the following numbers?

shtirl [24]

The mode of this is 8,10, and 5

7 0

2 years ago

Kirstin knows that the initial fee for adopting a dog from the animal shelter is $75. This fee needs to be considered when calcu

irina [24]

Answer:

The function is represented by $C(d) = 75\,USD + r\cdot d$ .

Step-by-step explanation:

In this case, we must observe that total cost of the dog ( $C(d)$ ) is the sum of two components: i) Fixed cost ( $C_{f}$ ) - Adoption fee, ii) Variable cost ( $C_{v}$ ) - Daily cost of feeding the dog, both measured in US dollars.