Im on the verge of tears. set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies. who gains altitude more quickly, a pilot traveling 400 mph and rising at an angle of 30 degrees, or a pilot traveling 300 mph and rising at an angle of 40 degrees?

The pilot traveling 400 mph rising at an angle 30 degrees is going to gain more altitude faster

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Explanation:

Draw out the triangles as you see in the attached image below. We'll use the sine rule because we want to tie together the unknown height (h) which is the opposite side of the reference angle, to the known hypotenuse (the speed of the aircraft)

For the first plane,

sin(angle) = opposite/hypotenuse

sin(30) = h/400

h = 400*sin(30)

h = 200

so the first plane is gaining altitude at 200 mph (each hour, the plane is 200 miles higher up)

For the second plane

sin(angle) = opposite/hypotenuse

sin(40) = h/300

h = 300*sin(40)

h = 192.836282905961

h = 192.84

which is smaller than the previous result (200)

So we see that the first plane is rising faster

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240