Answer:
1. I have simplified the first question:
2. I have found the parabola properties:
Hello :
<span>note :
an equation of the
circle Center at the w(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : </span><span>x²+y²-16x+6y+53=0
(</span>x²-16x) +( y²+6y ) +53 = 0
(x² -2(8)x +8² - 8²) +(y² +2(3)x -3²+3² ) +53=0
(x² -2(8)x +8²) - 8² +(y² +2(3)x +3²)-3² +53=0
(x-8)² +( y+3)² = 20
the center is : w(8,-3) and ridus : r = <span>√20</span>
The equation would be 30+3m=162 then you solve the problem.
Answer:
y (plane speed) 400 miles/hr
x (wind speed) 40 miles/hr
Step-by-step explanation:
going into the wind make the plane flew 5,5 hours to get 1980 miles, implies the real travel speed was
1980 / 5,5 = 360 miles/hours, and at the same time is the result of:
speed plane (y) in direction A to B plus wind speed (x) in direction B to A. Notice opposites direction speed, so we have:
y + (-x) = 360 (1)
The return fly took 4,5 hours so 1980/4,5 = 440 miles/ hours as the result
Y + x = 440 (2)
We have a two equation with two variables system, It could be solved for any of the procedures. We will use the substitution method.
From equation (1) y + (-x) = 360 y - x = 360 y = 360 + x (1)
In the second equation
y + x = 440 then we replace y for its value as function of x
(360 + x ) + x = 440
Solving for x 360 + 2x = 440 or 2x = 440 – 360
x (440 - 360)/2
x = 40 miles/hr
X (wind speed ) = 40 miles/hr
And replacing the value of x in eq. (1) y = 360 + 40 = 400
Y (plane speed) = 400 miles /hr
. Let me do my best.
<span>$187,500 is cost of house. </span>
<span>20%, or $37,500 is the down payment. </span>
<span>The loan amount would be $187,500 - $37,500 = $150,000. </span>
<span>If we assume the annual rate of the loan is 4.65% </span>
<span>Then the monthly rate would be 4.65%/12 = 0.3875% </span>
<span>If the loan is $150,000, the interest is 0.3875% </span>
<span>The interst for the first month is $150,000 * 0.3875% = $581.25. </span>
<span>You stated that their payment is $1,575. </span>
<span>So the amount that pays off the loan is $1,575 - $581.25 = $993.75. </span>
<span>At the end of the month, they owe $150,000 - $993.75 = $149,006.25 </span>
<span>For the second month, the amount of the payment that goes towards interst is </span>
<span>$149,006.25 * 0.3875% = $577.40. and the amount that goes towards the loan is $997.60. </span>
<span>At the end of the second month they owe $148,008.65. </span>
<span>Regarding realized income, we recommend a monthly loan payment not to exceed 28% of the monthly income. So if a payment of $1,575 is 28% of Gross, then the math is : $1,575 = 0.28*Gross. </span>
<span>Gross = $5,625 monthly. </span>
<span>About $67,500 annually. </span>
<span>About $33.75 an hour.</span>