A skate board ramp is built on an incline so that it rests on a porch that is 1.3m high. The bottom of the ramp is placed 2.5m from the porch. What is the angle that the ramp forms with the ground?

θ = 27.47°

Step-by-step explanation:

This problem can be represented as a right-angled triangle, as shown in the diagram below.

To find θ, we apply the tangent part of the trigonometric ratios SOHCAHTOA:

tanθ =

In the diagram, opposite = 1.3 m and adjacent = 2.5 m

Hence:

tanθ =

tanθ = 0.52

θ =

θ = 27.47°

The ramp forms 27.47° with the ground.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."