given 685x^2 - 58x-976=0, if "m" and "n" two solutions of the equation, Then what is the value of 137m+137n

12.33

Step-by-step explanation:

To obtain the value of 137m + 137n, let us calculate the value of m and n.

NOTE: m and n are the solutions to the equation: 685x² – 58x – 976 = 0

Thus, we can obtain the solutions to equation by doing the following:

685x² – 58x – 976 = 0

a = 685

b = – 58

c = – 976

Using formula method:

x = – b ± √(b² – 4ac) ÷ 2a

x = – (–58) ± √(–58² – 4×685×–976) ÷ 2 × 685

= 58 ± √(3364 – – 2674240) ÷ 1370

= 58 ± √(3364 + 2674240) ÷ 1370

= 58 ± √(2677604) ÷ 1370

= 58 ± 1636.3386 / 1370

= (58 + 1636.3386) / 1370 or (58

– 1636.3386) / 1370

= 1694.3386 / 1370 or – 1578.3386/1370

x = 1.24 or –1.15

Thus,

m = 1.24

n = –1.15

Finally, we can obtain the value of

137m + 137n as shown below:

137m + 137n

m = 1.24

n = –1.15

= (137 × 1.24) + (137 × – 1.15)

= 169.88 + (– 157.55)

= 169.88 – 157.55

= 12.33

Thus, the value of 137m + 137n is 12.33

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the correct option is b

step-by-step explanation: