Answer this or you officially lose your nnn

1) A

2) B, 6.0°

1.) The dot product of the vectors a and b is:

a . b = 30 (Fourth option)

2.) The angle between the vectors is:

ϴ = 6.0° (Second option)

Step-by-step explanation:

1.) a=<5,2> = <a1, a2> → a1=5, a2=2

b=<4,5> = <b1, b2> → b1=4, b2=5

The dot product of the vectors a and b is:

a . b = a1 b1 + a2 b2

a . b = (5)(4)+(2)(5)

a . b = 20 + 10

a . b = 30

2.) u=<2,-4> = <u1, u2> → u1=2, u2=-4

v=<3,-8> = <v1, v2> → v1=3, v2=-8

u . v = │u││v│cos ϴ     (1)

where:

u . v is the dot product of the vectors u and v

│u│is the module of vector u

│v│is the module of vector v

ϴ is the angle between the vectors u and v

The dot product of the vectors u and v is:

u . v = u1 v1 + u2 v2

u . v = (2)(3)+(-4)(-8)

u . v = 6 + 32

u . v = 38

│u│=sqrt( u1^2+u2^2)

│u│=sqrt[ (2)^2+(-4)^2 ]

│u│=sqrt(4+16)

│u│=sqrt(20)

│u│=sqrt(4*5)

│u│=sqrt(4) sqrt(5)

│u│= 2 sqrt(5)

│v│=sqrt( v1^2+v2^2)

│v│=sqrt[ (3)^2+(-8)^2 ]

│v│=sqrt(9+64)

│v│=sqrt(73)

Replacing the calculated values in equation (1):

(1) u . v = │u││v│cos ϴ

38 = 2 sqrt(5) sqrt(73) cos ϴ

38 = 2 sqrt(5*73) cos ϴ

38 = 2 sqrt(365) cos ϴ

Solving for cos ϴ: Dividing both sides of the equation by 2 sqrt(365):

38 / [2 sqrt(365)] = 2 sqrt(365) cos ϴ / [2 sqrt(365)]

19/sqrt(365) =cos ϴ

cos ϴ = 19/sqrt(365)

Solving for ϴ :

ϴ = cos^(-1) [19/sqrt(365)]

ϴ = cos^(-1) (19/19.10497317)

ϴ = cos^(-1) (0.994505453)

ϴ = 6.009005915°

Rounding to the nearest tenth of a degree:

ϴ = 6.0°

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,