8to 10 questions its super hard i need in 8 and 9 i need choose 2 of the 3 questions but i dont know how to answer and i need put the figures and formulas too : (

a) The angle shown as 45.5 deg in the figure should read 45.8 deg.

tan 45.5 deg = y/175

y = 175 ft * tan 45.8 deg = 180 ft

tan 34.4 deg = z/175

z = 175 ft * tan 34.4 deg = 120 ft

y - z = 180 ft - 120 ft = 60 ft

The height of Pres. Washington's face is 60 ft.

b)

Area of 1/8 of a 12" pizza: 1/8 * pi * (12/2 ")^2 = 14.1 in.^2

Area of 1/6 of a 10" pizza: 1/6 * pi * (10/2 ")^2 = 13.1 in.^2

The slice of the 12" pizza is larger.

c)

A bearing of 27 deg is 90 - 27 = 63 deg counterclockwise from due East.

A bearing of 117 deg is 117 - 90 = 27 deg clockwise from due East.

The two bearing directions make a 90 deg angle between them.

55 km/h for 2 hours = 110 km

60 km/h for 1.5 hours = 90 km

The two amounts traveled are 110 km and 90 km at 90 deg from each other. They form the legs of a right triangle. The distance traveled from the starting point is the hypotenuse of the right triangle formed by the the two distances traveled.

(90 km)^2 + (110 km)^2 = d^2

d = 142 km

The distance traveled is 142 km.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

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step-by-step explanation: