14. Given that 16x⁴+ - 4x³– 4b²x² + 7bx + 18 is divisible by 2x + b, (a) show that b³ - 7b² + 36 = 0,
(b) find the possible values of b.

(a) check the explanation

(b) the possible values of b is 6i or -29

Explanation:

Given function;

16x⁴ - 4x³– 4b²x² + 7bx + 18

(a)

factor of the given function = 2x + b

then, 2x + b = 0

x = -b/2

substitute the value of b into the given function;

16x⁴ - 4x³– 4b²x² + 7bx + 18

(b)

b³ - 7b² + 36 = 0

b²(b - 7) + 36 = 0

b²(b - 7) = -36

b² = -36                or b - 7 = -36

b = √(-36)             or  b = -36 + 7

b = √(-1) x √(36)   or  b = -29

b = 6i       or   -29              

hello!

let's go through all of these words' definitions.

u-shaped valley - where the valley curves down like a u shape

corrie - similar to the hole created at the top of a volcano when it erupts, it's almost like a dent in a mountain

pyramidal peak - a mountain where the peak is very sharp, such as the matterhorn.

arete - two valleys separated by a thin mountain range

i'm going to assume you know how to read a topographic map, but in case you don't, feel free to comment.

now, let's figure out which one's which:

a - seems to be a mountain range separating two valleys, with a mountain running from top center to bottom center and two valleys on either side. therefore, i'd consider this an arete.

b - it looks like a dent into the mountain, like what a corrie is.

c - looks to be a valley, with two steeper sides curving up around the bottom of the valley which has a river in it. i would consider this an u-shaped valley.

hope this !

could you attach a picture of the map?