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Mathematics

1 answer:

andrew11 [14]3 years ago

3 0

The point-slope form of the equation for a line can be written as

... y = m(x -h) +k . . . . . . . for a line with slope m through point (h, k)

Your function gives

... f'(h) = m

... f(h) = k

a) The tangent line is then

... y = 5(x -2) +3

b) The normal line will have a slope that is the negative reciprocal of that of the tangent line.

... y = (-1/5)(x -2) +3

_____

You asked for "an equation." That's what is provided above. Each can be rearranged to whatever form you like.

In standard form, the tangent line's equation is 5x -y = 7. The normal line's equation is x +5y = 17.

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The lifeguard of the beach resort is on his post which is 4 m high. A boy in the pool is 9 meters away from him. Find the angle

Dovator [93]

$\large \underline{ \mathbb{QUESTION:}}$

The lifeguard of the beach resort is on his post which is 4 m high. A boy in the pool is 9 meters away from him. Find the angle of depression from the lifeguard to the boy.

$\large\underline{ \mathbb{ANSWER \: \& \: SOLUTION:}}$

$\large \tt{ tan \: x \: = \: \frac{opposite}{adjacent} }$

$\large \tt{tan \: x \: = \: \frac{4}{9}}$

$\large \tt{ \: \: \: \: \: \: \: \: x \: = \: tan ^{ - 1} \: (0.444)}$

$\large \tt {\: \: \: \: \: \: \: \: x \: = \: 23.96 ^{o} }$

$\:\:\:\:\:\:\:\: \large \boxed{\tt{\red{ x \: = \: 24 ^{o} }}}$

Therefore the angle of depression from the lifeguard to the boy is 24°.

8 0

2 years ago

Help finding the x & y intercept

nasty-shy [4]

The x-intercept will be the value of x when y=0. The solutions to (x+1)(x+2)=0 are -1 and -2 since we can substitute them in to have one of the values in parentheses equal to zero, so our x-intercepts are (-1, 0) and (-2, 0). The y-intercept is the value of y when x=0, or (0+1)(0+2)=2. Therefore, the y-intercept is (0, 2).

3 0

3 years ago

Situation:

omeli [17]

The half life of the substance is 6.92 days.

Half life can be defined as the time required to reduce the concentration to half of its initial value.

Here the equation given is

$\rm N = N_o e^{-kt}$