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Norma-Jean [14]
3 years ago
5

In triangle MPN, angle P is a right angle. If cos N= 3/5 which of the following statements is true

Mathematics
1 answer:
Bezzdna [24]3 years ago
3 0

Answer: Sin N = \frac{4}{5}

Step-by-step explanation:

Since we have given that

In triangle MPN, ∠P=90°

\cos N=\frac{3}{5}

As we know the formula for "Trigonometric Ratios":

\cos N=\frac{Base}{Hypotenuse}=\frac{3}{5}

By Pythagorus theorem , we get

H^2=B^2+P^2\\\\5^2=3^2+P^2\\\\25=9+P^2\\\\25-9=P^2\\\\16=P^2\\\\P=\sqrt{16}\\\\P=4\ units

So, we get,

\sin N=\frac{Perpendicular}{Hypotenuse}=\frac{4}{5}

Hence, Sin N = \frac{4}{5}

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Calculate the sum of the multiples of 4 from 0 to 1000
allochka39001 [22]

Answer:

sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

Step-by-step explanation:

This problem can be solved using concept of arithmetic progression.

The sum of n term terms in arithmetic progression is given by

sum = (2a+(n-1)d)n/2

where

a is the first term

d is the common difference of arithmetic progression

_____________________________________________________

in the problem

series is multiple of 4 starting from 4 ending at 1000

so series will look like

series: 0,4,8,12,16..................1000

a is first term so

here a is 0

lets find d the common difference

common difference is given by nth term - (n-1)th term

lets take nth term as 8

so (n-1)th term = 4

Thus,

d = 8-4 = 4

d  can also be seen 4 intuitively as series is multiple of four.

_____________________________________________

let calculate value of n

we have last term as 1000

Nth term can be described

Nth term = 0+(n-1)d

1000 =   (n-1)4

=> 1000 = 4n -4

=> 1000 + 4= 4n

=> n = 1004/4 = 251

_____________________________________

now we have

n = 1000

a = 0

d = 4

so we can calculate sum of the series by using formula given above

sum = (2a+(n-1)d)n/2

       = (2*0 + (251-1)4)251/2

       = (250*4)251/2

     = 1000*251/2 = 500*251 = 125,500

Thus, sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

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3 years ago
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elena-14-01-66 [18.8K]
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3 years ago
Read 2 more answers
What is the sum in simplest form? 5 3/4 + 2 1/2 A) 7 4/6 B) 7 2/3 C) 8 1/4
alina1380 [7]

Answer:

Step-by-step explanation:

5 3/4 + 2 1/2

Add the whole numbers first

5 + 2

Add the fractions next

3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 and 1/4

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