There are two numbers whose difference is 1 and the sum of their squares is 61. What are the numbers?

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

For what values of the variable x is the expression square root of 7x+14+ square root of 7-x a real number?