Trigonometric Ratios
A right triangle is defined as a triangle that has one interior angle with a measure of 90°.
The trigonometric ratios are defined as relationships between sides and angles on right triangles.
To better explain the required ratio, we'll include the following image that contains the given triangle, as described in the question:
The cosine of the angle T (shown in the figure) is defined as:
The secant of an angle is the reciprocal of the cosine, thus:
The adjacent side to angle T is 77 and the hypotenuse is 85, thus:
Answer:
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
Step-by-step explanation:
f(x) = sin (tan^-1 (ln(x)))
u substitution
d/du (sin u) * du /dx
cos (u) * du/dx
Let u =(tan^-1 (ln(x))) du/dx =d/dx (tan^-1 (ln(x)))
v substitution
Let v = ln x dv/dx = 1/x
d/dv (tan ^-1 v) dv/dx
1/( v^2+1) * dv/dx
=1/(ln^2x +1) * 1/x
Substituting this back in for du/dx
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
We know that cos (tan^-1 (a)) = 1/ sqrt(1+a^2)
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
40,023,032 in word form:
forty million, twenty-three thousand, thirty-two
Answer:
Step-by-step explanation:
12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 =
= 429,981,696
An easy way to think of this is that there are 12 is being multiplied by itselg 8 times (there are 8 12s). Similar to how squared numbers work...
Hope this helps! If you need further explanation, let me know!
- profparis
9514 1404 393
Answer:
p(x) = x^3 +x^2 -82x +80
Step-by-step explanation:
If a polynomial function has a zero at x=a, then (x -a) is a factor. Your list of zeros means the factors are ...
p(x) = (x -8)(x +10)(x -1) . . . . . . . . factored form
When this is multiplied out, it becomes ...
p(x) = x^3 +x^2 -82x +80 . . . . . . standard form
_____
The factored form can be multiplied out using the distributive property.
= ((x(x +10) -8(x +10))(x -1)
= (x^2 +10x -8x -80)(x -1)
= (x^2 +2x -80)x -(x^2 +2x -80)
= x^3 +2x^2 -80x -x^2 -2x +80
= x^3 +x^2 -82x +80
