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3 years ago

a line is perpendicular to y = 3/7x - 2 and intersects the point (3,3). What is the equation of this perpendicular line?

Mathematics

1 answer:

snow_lady [41]3 years ago

6 0

Answer:

y = -7/3x + 10

Step-by-step explanation:

Step 1: Find the slope of the perpendicular line

Do this by taking the negative inverse of the first line

m = -7/3

Step 2: Find b

y = mx + b

y = -7/3x + b

3 = -7/3(3) + b

3 = -7 + b

b = 10

You should get y = -7/3x + 10 as your final answer.

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Answer: (a) $e^3$

(b) $e^{10}$

(c) $\dfrac{1}{e^4}$

(d) $e^{4}$

Step-by-step explanation:

Properties of exponents :

1) $a^m\times a^n=a^{m+n}$

2) $\dfrac{a^m}{a^n}=a^{m-n}$

3) $(a^m)^n=a^{mn}$

4) $a^{-n}=\dfrac{1}{a^n}$

Now , we simplify the given expression using the above properties.

a) $(e^6)(e^{-3})$

$=e^{6+(-3)}$ [By property (1)]

$=e^{6-3}=e^3$ [∵ (+)(-)=(-)]

b) $(e^{-2})^{-5}$

$=e^{-2\times-5}$ [By property (3)]

$=e^{10}$ [∵ (-)(-)=(+)]

c) $(\dfrac{e^6}{e^2})^{-1}$

$=(e^{6-2})^{-1}$ [By property (2)]

$=(e^{4})^{-1}$

$=\dfrac{1}{e^4}$ [By property (4)]

d) $(e^3)^{\frac{4}{3}}$

$=e^{3\times\frac{4}{3}}$ [By property (3)]

$=e^{4}$

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3 years ago