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2 years ago

The functions r and s are defined as follows.

Mathematics

1 answer:

irina1246 [14]2 years ago

8 0

Answer:

r(s(-2)) = -2

Step-by-step explanation:

We are given these following functions:

$r(x) = -2x + 2$

$s(x) = x^2 - 2$

Find the value of r(s (-2)).

First we find the composition of r and s functions. It is:

$r(s(x)) = r(x^2-2) = -2(x^2-2) + 2 = -2x^2 + 6$

At x = -2

$r(s(-2)) = -2(-2)^2 + 6 = -8 + 6 = -2$

r(s(-2)) = -2

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Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa

sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

8 0

2 years ago

I had two oranges, Bernice took two, how many do I have left?

Tpy6a [65]

Answer:

0 Oranges

Step-by-step explanation:

If you had 2 oranges at the start, then your no good friend Bernice took 2 of them, you don't have any oranges left, so get back at him and steal his bannanas! That'll teach him!

6 0

2 years ago

And engineer in blueprint calls for a 10.5 foot clearance from some pipes to the wall the pipes are currently 8.25 feet from the

tatuchka [14]

Answer:222

Step-by-step explanation:

add it

7 0

2 years ago

Solve 2x = 3.<br> Round to the nearest ten-thousandth.

levacccp [35]

divide by 2 on both sides.

3/2

x=1.5

7 0

2 years ago

Read 2 more answers

At most, how many unique roots will a third-degree polynomial function have?

beks73 [17]

The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.

In fact, if you use complex number, then a polynomial with degree n has exactly n roots.

So, in particular, a third-degree polynomial can have at most 3 roots.

In fact, in general, if the polynomial $p(x)$ has solutions $x_1,\ x_2,\ldots x_n$ , then you can factor it as

$p(x) = (x-x_1)(x-x_2)\ldots (x-x_n)$

So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as

$p(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)$

But this is a fourth-degree polynomial.

7 0

3 years ago