MP=18-3.8x, MN=7.74, and NP=1.9x determine the value of x and MP

Part 1) x=1.8

Part 2) MP=11.16 units

Step-by-step explanation:

step 1

Find the value of x

In this problem we have that

MP=MN+NP

we have

MP=18-3.8x

MN=7.74

NP=1.9x

substitute the values and solve for x

18-3.8x=7.74+1.9x

Group terms

3.8x+1.9x=18-7.74

Combine like terms

5.7x=10.26

x=10.26/5.7

x=1.8

step 2

Find the value of MP

MP=18-3.8x

substitute the value of x

MP=18-3.8 (1.8) = 11.16 units

x = 1.8, MP = 11.16

Step-by-step explanation:

Given the functions below;

MP=18-3.8x, MN=7.74, and NP=1.9x

Adding vectorially, MP+PN = MN ... (1)

Given NP = 1.9x, therefore, PN = - 1.9x since PN = - NP

Substituting the value of the given vector functions in equation 1 will give;

18-3.8x-1.9x = 7.74

18-5.7x = 7.74

-5.7x = 7.74-18

-5.7x = - 10.26

x = - 10.26/-5.7

x = 1.8

To get MP, since MP = 18-3.8x

Substituting the value of x = 1.8 into the vector function MP;

MP = 18-3.8 (1.8)

MP = 18-6.84

MP = 11.16

Therefore, x = 1.8, MP = 11.16