Antonio wants to invest $7600 in a saving account. Determine the interest rate (simple interest) required for Antonio’s investment to double in value in 12 years.

Solution:

Given that,

Antonio wants to invest $7600 in a saving account

Antonio’s investment to double in value in 12 years

To find: Rate of interest

The total amount using simple interest is given as:

Where,

p is the principal

r is the rate of interest

t is the number of years

From given,

p = 7600

t = 12 years

r = ?

Antonio’s investment to double

Therefore,

A = 2(7600) = 15200

Substituting the values we get,

Thus interest rate required for Antonio’s investment to double in value in 12 years is 8.3 % per annum

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

answer: yard ramps with a level off platform are typically 36 feet long. truck, rather than at an angle, enabling access to those pallets at the very back of the truck. if you are using your yard ramp to convert a loading dock into a drive-in door, we even at 60 inches (5 feet) high and a 30 foot ramp, the slope of the ramp will be less

step-by-step explanation: