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Karolina [17]
3 years ago
12

Given f(x)=3x^2+9x+k and the remainder when f(x) is divided by x+1 is -14, then what is the value of k?

Mathematics
1 answer:
MAXImum [283]3 years ago
6 0

Answer:

The value of k is -8.

Step-by-step explanation:

Given;

f(x) = 3x² + 9x + k

factor of the function = x + 1

remainder of the function = -14

let x + 1 = 0

x = -1

f(-1) = 3(-1)² + 9(-1) + k = -14

3(-1)² + 9(-1) + k = -14

3 - 9 + k = -14

-6 + k = -14

k = -14 + 6

k = -8

Therefore, the value of k is -8.

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A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat
konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles                    

First, we need to find b:    

a^{2} + b^{2} = h^{2}   (1)    

b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})

2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:  

0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}

\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h  

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

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