Answer: 1) 5040 and 2) 165
Step-by-step explanation:
1) Here total number of letters = 10
The number of permutations that can be formed using 4 letters at a time
= P (10, 4)
=
=
=
=
= 10 × 9 × 8 × 7
= 5040
2) Here the total number of machine = 11
The different combinations of machines can Geoff choose from to use
=
=
=
=
= 11 × 5 × 3
= 165
<em>(Check the attached image).</em>
<h2>Step-by-step explanation:</h2><h3>1. Identify the given information.</h3>a. We have the slope of the line, 1/4.
b. We also have a point of said line, because when the question states "y-intercept 5..." it's telling us that the lines touches the y intercept on the value y= 5, and this only happens when x= 0. Hence, a given point is (0, 5).
• Formula for constructing linear equations.
Formula: ; where m is the slope of the function; x1 is the x value of a point the function passes through, and y1 is the y value of a point the function passes through.
<em>(Check the attached image).</em>
Applying the differentiation rule, it can be obtained that:
,
and
.
The exponential function exists a mathematical function designated by f(x)=\exp or e^{x}. Unless otherwise determined, the term generally directs to the positive-valued function of a real variable, although it can be extended to complex numerals or generalized to other mathematical objects like matrices or Lie algebras.
In mathematics, the derivative of a function of a real variable estimates the sensitivity to change of the function value affecting a change in its statement. Derivatives exist as a fundamental tool of calculus.
.
Given that .
So, differentiating with respect to
, we get:
.
So, using the above formula , we get:
.
Now, substituting in
and
, we obtain:
and
.
Therefore, applying the differentiation rule, we get:
,
and
.
To know about the differentiation rule, refer:
#SPJ9