CPhill

What's the question???

log_x 8 = 1/3      this says that

x^(1/3)  = 8      cube both sides

x = 8^3   =  512

logx+log(x+21)=2

Rewrite the left side as

log [ x * (x + 21)]  = 2       and 2 can be written as log 100......so we have....

log [x ( x + 21) ]  = log 100      we can forget the logs and solve this:

x ( x + 21)   = 100    simplify

x^2 + 21x  = 100

x^2 + 21x - 100  = 0  factor as

(x + 25) ( x - 4)  = 0

Setting each factor to 0, x = -25  or x = 4

Reject -25 since it makes the logs negative

x= 4 is the soultion

6) An airplane is flying in the direction 15° North of East at 550 mph. A wind is blowing in the direction 15° South of East at 45 mph.

    a)  Find the component form of the velocity of the airplane and the wind.

    b)  Find the actual speed ("ground speed") and direction of the airplane.

The components of the velocity of the plane are   <550cos15, 550sin15>

The components of the wind velocity  are  < 45cos345, 45 sin345 >

The x components of the resultant  = 550cos15 + 45cos345  = about  574.726

The y components of the resultant  = 550sin15 + 45sin345  = about 130.7

So...the resultant ground speed = sqrt[ 574.726^2 + 130.7^2]  = about 589.4 mph

4)  A plane leaves the airport on a bearing 45° traveling at 400 mph. The wind is blowing at a bearing of 135° at a speed of 40 mph. What is the actual velocity of the plane?

The vector of the plane's path of  travel and the wind vector are at right angles to each other......the resultant [the actual velocity] is give by :

sqrt [400^2 + 40^2]  = about 402 mph

Here's a pic :

3.    The bearing of the boat  is  [90 + 45]°  = 135°

Here's a pic :

1.  The distance from port can be found using the Law of Cosines

d^2 =  7.5^2 + 4.1^2  - 2(7.5)(4.1)cos(118)

d = sqrt [7.5^2 + 4.1^2  - 2(7.5)(4.1)cos(118)] = about 10.096 miles

It's bearing [ from port]    is given by :

(90 - arctan[6.62/ 7.62 ] ) °  =  [ 90 - 41]°  = about 49°

Here's a pic :

15 stations * 15.4 seeds per station  = 231 seeds.....however......geno's answer makes more sense, because we can't actually have "15.4" seeds

Real Numbers

Rational Numbers

Integers