Answer:
q=-1128/169
Step-by-step explanation:
x²n-14x+q=0 here a=1, b= -14, c=q
let the roots of the equation beα and β
then the sum of the roots= S= α+β= -b/a=-(-14)/1=14
α+β=14 ⇒β=14-α--------(i)
product of the roots=P= αβ= c/a= q/1=q------(ii)
since α-β=6--------(given)----(iiI)
put the values of β from equation i to equation iii
α-14α=6
-13α=6
α=-6/13
put the values of α and β in eq. (ii)
αβ=q=(-6/13)(14-(-6/13)
q=(-6/13)(182+6/13)
q=(-6/13)188/13
q=-1128/169
0.1 is the decimal equivalent.
the length of z is C. 15 cm
Answer:
Step-by-step explanation:
First we need to find their rate of speed.
r = d / t
For ant,
Convert millimeters to inches.
1 inch = 25.4 mm
18 mm = 0.7 inch
r = 0.7 / 5
r = 0.14 inches per second
For beetle,
r = 8 / 3
r = 2.7 inches per second
From the rates, you can tell that the beetle crosses the Garden first.
To know how long it takes for the ant to cross is by dividing the length by the rate.
1 yard = 36 inches
13 yards = 468 inches
468 ÷ 0.14 = 668.5 ≈ 669 seconds
In terms of minutes:
11 minutes and 15 seconds
The ant would cross the garden in 11 minutes and 15 seconds (or 669 seconds <em>up to you</em>).
Answer:

the rate of change of height when the water is 1 meter deep is 21 m/min
Step-by-step explanation:
First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).
As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

this can be substituted back in the volume equation

the rate of the water flowing in is:

The question is asking for the rate of change of height (m/min) hence that can be denoted as: 
Using the chainrule:

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h


reciprocating

plugging everything in the chain rule equation:



L = 12, and h = 1 (when the water is 1m deep)


the rate of change of height when the water is 1 meter deep is 21 m/min