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kozerog [31]
3 years ago
14

Let P (n) be the statement that 12 + 22 + · · · + n2 = n(n + 1)(2n + 1)/6 for the positive integer n. a) What is the statement P

(1)? b) Show that P (1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis

Mathematics
1 answer:
andriy [413]3 years ago
4 0

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

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Solve for the variable using Trig ratio.
SIZIF [17.4K]

Answer:

x = 3.86

a = 5.86

Step-by-step explanation:

From the triangles attached,

By applying cosine rule in triangle 1,

cos(50)° = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

cos(50)° = \frac{x}{6}

x = 6cos(50)°

x = 3.86

Now we apply sine rule in the second triangle,

sin(23)° = \frac{\text{Opposite side}}{\text{Hypotenuse}}

sin(23)° = \frac{a}{15}

a = 15sin(23)°

a = 5.86

5 0
3 years ago
What is the rate of change between (-3.7, 1.4) and (-3.5,1)?
Anarel [89]

Answer:

-2

Step-by-step explanation:

the rate of change or slope (M) is -2

Hope this helps:P

6 0
3 years ago
Which absolute value function has a graph that is wider than the parent function, f(x) = |x|, and is translated to the right 2 u
RoseWind [281]

Transformation involves changing the form of a function.

The absolute value function is f(x)=0.3|x -2|

The parent function of the absolute value function is:

f(x)=|x|

When the function is translated 2 units to the right, the new function is:

f(x)=|x -2|

From the function to be wider than the absolute function, the function must be stretched by a factor less than 1.

The possible function from the list of given options is f(x)=0.3|x -2|

Read more about function transformation at:

brainly.com/question/1548871

6 0
3 years ago
In a particular year, a total of 50,127 students studied in two of the most popular host countries when traveling abroad. If 838
Arlecino [84]

Answer:

In the most popular abroad country: 29,255 students

In the second-most one: 20,872 students

Step-by-step explanation:

Let's write the situation in an equation to help us solve this. X represents the amount of students in the second most popular country. So we know that in total, there's 50,127 students so let's make an equation that equals this. ???????=50,127. As we know, the most popular country has 8383 more students than the second one so we can write it as x+8383 and for the second most popular country, we can write it as x. We know that both of the countries students combined equal 50,127 students so we have our equation. (x)+(x+8383)=50,127 students. After solving the equation, you get x=20, 872. As we know x=the amount of students in the second most popular country which means there's 20,872 students in the second one. Additionally, for the first most popular one, the equation for the amount of students in it is x+8383 so..... 20,872+8383=Total number of students in the most popular one which is 29,255 students.

7 0
3 years ago
I need help with 47-50
Genrish500 [490]
47.C
48.B
49.???
50.A
sorry doing something couldn't solve 49 right now

4 0
3 years ago
Read 2 more answers
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