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1 year ago

Find the equation of a line passing through a point (3,5) and perpendicular to the line joining the points (3, 7) and (7, -1)

Mathematics

1 answer:

eduard1 year ago

7 0

Step-by-step explanation:

we start first by finding the gradient of the line

change in y/change in x

7-(-1)/3-7=8/-4

=-2

then for perpendicular lines m1m2=-1

therefore to find the gradient of that line

-2m2=-1

therefore m2=2

so therefore

y-5/x-3=2

so y-5=2x-6

y-2x=-1

in the form y= mx +c

then y=2x-1

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1 year ago

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3 years ago

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3 years ago

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8 0

2 years ago

PLEASE HELP NEED THIS ANSWERED CORRECTLY

Helen [10]

f(3) = 1.9

Solution:

Given function:

$$f(x)=\frac{14}{7+2 e^{-0.6 x}}$

To find f(3):

Substitute x = 3 in the given function.

$$f(3)=\frac{14}{7+2 e^{-0.6 (3)}}$

$$f(3)=\frac{14}{7+2 e^{-1.8}}$

Let us first simplify $2e^{-1.8}$ .

Apply exponent rule: $a^{-b}=\frac{1}{a^{b}}$

$2e^{-1.8}=2\frac{1}{e^{1.8}}$

The value of $e^{1.8}=6.04964$ . (using calculator)

$$\frac{2}{e^{1.8}}=\frac{2}{6.04964}=0.33059$

$2e^{-1.8}=0.33059$

Substitute this value in f(3).

$$f(3)=\frac{14}{7+0.33059}$

$$f(3)=\frac{14}{7.33059}$

$$f(3)=1.90980$

f(3) = 1.9

Hence the value of f(3) is 1.9.

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2 years ago