Aroom is 96 ft long, 18 ft wide, and 27 ft high.
what is the diagonal distance (ft) from one of the lower corners to the
opposite upper corner? write the diagonal vector as a sum of components,
and calculate the vector magnitude from the components.
as a second method, use the ti-89 norm function and the vector to
calculate the diagonal-vector magnitude.

the norm of the distance is |d|=97.95 ft

the vector of the distance is d=96i+18j+27k

Step-by-step explanation:

As per the attached image, the distance from the origin of the x y & z axis is where the vector starts and it ends at the opposite side of the room.

Calculating the norm as the square root of the sum of each side of the rooms squared & calculating the vector as each side of the room multiplied by the i, j & k axis, the results are as mentioned above.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204