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torisob [31]
3 years ago
11

An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airp

lane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind. Plane on outbound trip of 4 hours with 25 mph tailwind and return trip of 5 hours with 25 mph headwind Let r = the rate or speed of the airplane in still air. Let d = the distance
a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.
b. Solve the system of equations for the speed of the airplane in still air.
Mathematics
1 answer:
balu736 [363]3 years ago
6 0

Answer:

r  = 225 Mil/h     speed of the airplane in still air

Step-by-step explanation:

Then:

d  is traveled distance   and r  the speed of the airplane in still air

so the first equation is for a 4 hours trip

as  d = v*t

d  =  4 *  ( r  + 25)    (1)          the speed of tail wind  (25 mil/h)

Second equation the trip back in 5 hours

d  =  5  * ( r  - 25 )    (2)

So we got a system of two equation and two unknown variables  d  and

r

We solve it by subtitution

from equation (1)     d  =  4r  + 100

plugging in equation 2

4r  + 100  = 5r -  125    ⇒   -r  =  -225     ⇒    r  = 225 Mil/h

And distance is :

d  =  4*r  +  100         ⇒ d  =  4 * ( 225)  +  100

d  =  900 +   100

d  = 1000 miles

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If angle LMPis 11 degrees more than angle NMP and angle NML is 137 find each measure.
OLEGan [10]

Answer:

angle NMP = 63°

angle LMP = 74°

Step-by-step explanation:

Let angle NMP be x° . It's given that angle LMP is 11° more than angle NMP. So, angle LMP = x° + 11°

But angle NML = 137°.

So,

angle NMP + angle LMP = 137°

=> x° + x° + 11° = 137°

=> 2x° + 11° = 137°

=> 2x° = 137° - 11°

= 126°

=> x° = 126/2 = 63°

angle NMP = 63°

angle LMP = 63 + 11 = 74°

7 0
3 years ago
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Can a math god help me out?
Taya2010 [7]

Answer:

f(1)=70

f(n)=f(n-1)+6

Step-by-step explanation:

One is given the following function:

f(n)=64+6n

One is asked to evaluate the function for (f(1)), substitute (1) in place of (n), and simplify to evaluate:

f(1)=64+6(1)

f(1)=64+6

f(1)=70

A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:

a_n=a_(_n_-_1_)+d

Where (a_n) is the evaluator term (a_(_n_-_1_)) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,

a_n=a_(_n_-_1_)+d

a_n=a_(_n_-_1_)+6

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3 0
2 years ago
One angle in a triangle is 115 degrees. The other two angles are congruent. What is the measure of one of the missing angles?
kifflom [539]
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Hence,  the second and the third angles of the given triangle are 180-115/2= 65/2<span>

 (32 degrees and 30 minutes).</span>
7 0
3 years ago
Six less than two times a number is no more than 7
ziro4ka [17]

Answer:

n <=6.5

Step-by-step explanation:

Six less than two times a number is no more than 7

2n-6 <=7

Add 6 to each side

2n-6+6 <=7+6

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3 0
3 years ago
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I'm not sure exactly what it is but it would be a negitive 
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