The base of an open rectangular box is of length (2x+5) cm and width x cm. The area of this base is 58cm^2. The height of the open box is (x-2) cm.
a) show that 2x^2+5x-58=0
b) solve the equation in the question above, giving your answer to 2 decimal places
c) calculate the volume of the box, stating units of you answer

B)

C) volume =   .

Step-by-step explanation:

Here we have , The base of an open rectangular box is of length (2x+5) cm and width x cm. The area of this base is 58cm^2. The height of the open box is (x-2) cm. We need to find the following :

a) show that 2x^2+5x-58=0

We know that area of rectangle =

⇒

Putting values according to question we get :

⇒

⇒

⇒  

b) solve the equation in the question above, giving your answer to 2 decimal places

Solving this equation :

⇒  

By quadratic formula

⇒

⇒

⇒

⇒    { Since side can't be negative ! }

⇒

c) calculate the volume of the box, stating units of you answer

Since x = 4.28 , other sides are

We know that volume is given by :

⇒

⇒

⇒

Therefore , volume =   .

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet