The base of a pyramid is a square with side lengths of 5 centimeters. the slant height of each lateral face of the pyramid is 6 centimeters. what is the surface area of the pyramid?

85 cm²

Step-by-step explanation:

The base is a square with side length 5 cm.  The area of this base is

A = s² = (5 cm)² = 25 cm².

If the slant height of each lateral face of the pyramid is 6 cm, then we can find the area of each such face using the area-of-a-triangle formula,

A = (1/2)(base)(height), which here is

A = (1/2)(5 cm)(6 cm) = 15 cm² per lateral side.

The total area of these sides is 4(15 cm²) = 60 cm².

Then the total surface area of the pyramid is A = 60 cm² +  25 cm²  = 85 cm².

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

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: