<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
Answer:
369.7 mL of medication
Step-by-step explanation:
How many mL of medication are needed to last 10 days if the dose of medication is 2.5 tsp TID (three times a day)?
From the above question,
The dosage of the medication =
2.5 tsp 3 times a day
= 2.5 × 3 = 7.5 tsp per day.
Since
1 day = 7.5 tsp
10 days = x tsp
Cross Multiply
x = 10 × 7.5 tsp
x = 75 tsp of medication for 10 days.
Step 2
It is important to note that:
1 tsp = 4.929 mL
75 tsp = x mL
Cross Multiply
x = 75 × 4.929 mL
x = 369.669 mL of medication
Approximately = 369.7 mL of medication
Answer:
Multiply equation 
by 5 and 
by 4
Step-by-step explanation:
Given:
Equations are 
To find: constant by which each equation should be multiplied to eliminate the variable 
in the given system of equations
Solution:
Multiply equation (i) by 5 and (ii) by 4 to get the following equations:
On subtracting these equations, we get
So, the variable gets eliminated
The statements about the function that are true are
- The vertex of the function is at (–3,–16).
- The graph is increasing on the interval x > –3.
- The graph is positive only on the intervals where x < –7 and where x > 1.
<h3>How to interpret the graph?</h3>
The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
Read more about quadratic functions at
brainly.com/question/14933288
#SPJ1
Answer:
5, 2, 1, 3, 4, 6.
Step-by-step explanation:
Measure each feather in centimeters. Then order them from least to greatest.
