1. to calculate the height of a tree, marie measures the angle of elevation from a point a to be 34º. she then walks 10 feet directly toward the tree, and finds the angle of elevation from the new point b to be 41°. what is the height of the tree?

h ≈ 30.10  ft

Step-by-step explanation:

Marie measures the angle of elevation from a point A to a tree as 34° . She works 10 ft directly towards the tree and discovered the new angle of elevation is 41°. The height of the tree can be computed below.

let

a = distance from point B to the tree

h = height of the tree

The right angle triangle formed from point B,  we can use tan to find the height of the tree.

tan 41°  = opposite /adjacent

tan 41° = h/a

cross multiply

h = a tan 41°

The right angle formed from point A

tan 34° = opposite/adjacent

tan 34° = h/(a + 10)

(a + 10)tan 34° = h

Therefore,

a tan 41° = (a + 10)tan 34°

0.8692867378

a =  0.6745085168(a + 10)

0.8692867378a = 0.6745085168a + 6.7450851684

collect like terms

0.8692867378a - 0.6745085168a = 6.7450851684

0.194778221a = 6.7450851684

a = 6.7450851684/0.194778221

a = 34. 629565532  ft

height of the tree can be find with

h = a tan 41°

h = 34. 629565532 × 0.8692867378

h =  30.103022053  ft

h = 30.10 ft

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?