Mathematics: Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)

Find the tangent line equations for the given functions

yulimariu27

16.08.2021

${ \bf{f(x) = \tan x + 9 \sin x }}$

For gradient, differentiate f(x):

${ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}$

Substitute for x as π:

${ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}$

Gradient of tangent = -8

${ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi$

Equation of tangent:

${ \boxed{ \bf{y = - 8x + 8\pi}}}$

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ramirecinthi24

17.10.2020

Volume = 1659.84Surface area = 1205.36

Step-by-step explanation:

Volume for triangular prism = 1/2 * b * l * h

we are given the length and the height but not the base.

since it is a right triangle we can use the Pythagorean theorem a^2 + b^2 = c^2

13.3^2 + b^2 = 20.5^2

176.89 + b^2 = 420.25

b^2 = 243.36

b = $\sqrt{243.36}$ = 15.6

1/2 (15.6)(13.3)(16) = 1659.84

Front: 15.6 x 13.3 = 207.48

Back: 15.6 x 13.3 = 207.48

Left: 15.6 x 16 = 249.6

Right: 13.3 x 16 = 212.8

Bottom: 20.5 x 16 = 328

207.48 + 207.48 + 249.6 + 212.8 + 328 = 1205.36

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