An architect wants to draw a rectangle with a diagonal of 15 centimeters. The length of the rectangle is to be 6 centimeters more than twice the width. What dimensions should she make the rectangle

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

Step-by-step explanation:

Assume x be the width of the rectangle.

The length of the rectangle is to be 6 cm more than twice the width.

The length of the rectangle is= (2x+6) cm

Then the diagonal of the rectangle is

                                                              cm

According to the problem,

Squaring both sides

⇒5x²+45x-21x-189=0

⇒5x(x+9)-21(x+9)=0

⇒(x+9)(5x-21)=0

⇒x+9=0  or,   5x-21=0

⇒x= -9, 4.2

Since the width of a rectangle can not negative.

So, x=4.2 cm

The width of rectangle is = 4.2 cm

The length of the rectangle is =(2×4.2+6)

                                                  =14.4 cm

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.