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3 years ago

If f(-3) = -8, then f(x)= 3x +

Mathematics

1 answer:

Nataly_w [17]3 years ago

7 0

Answer:

f(x)= 3x + 1

Step-by-step explanation:

Let's set the unknown variable as b, since it's a linear equation.

Using the point given (-3, -8), we can find b by plugging in the known numbers and solving.

-8 = -3 (3) + b

-8 = -9 + b

b = 1

If you want, you can check it by forming the complete equation and plugging in -3.

f(x)= 3x + 1

f(-3) = -9 + 1

f(-3) = -8 = -8

I hope this helped!

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A plane flies 452 miles north and then 767 miles west. What is the magnitude and direction of the plane's resultant vector?

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Answer:

The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.

Step-by-step explanation:

• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:

$\boxed{a^2 = b^2 + c^2}$

where:

a ⇒ hypotenuse (= resultant vector = ? mi)

b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).

Using the formula:

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⇒ resultant = 890.3 mi

• To find the direction, we can find the angle (labeled x in diagram) that the resultant makes with the north direction:

$tan (x) =\frac{767}{452}$

⇒ $x = tan^{-1} (\frac{767}{452} )$

⇒ $x = \bf{59.5 \textdegree}$

∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .

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