The two linear equations in two variable is:
12 x + 3 y = 40
7 x - 4 y = 38
(a) For a system of equations in two Variable
a x + by = c
p x + q y = r
It will have unique solution , when
As, you can see that in the two equation Provided above
So, we can say the system of equation given here has unique solution.
(b). If point (2.5, -3.4) satisfies both the equations, then it will be solution of the system of equation, otherwise not.
1. 12 x+3 y=40
2. 7 x-4 y=38
Substituting , x= 2.5 , and y= -3.4 in equation (1) and (2),
L.H.S of Equation (1)= 1 2 × 2.5 + 3 × (-3.4)
= 30 -10.20
= 19.80≠ R.H.S that is 40.
Similarly, L H S of equation (2)= 7 × (2.5) - 4 × (-3.4)
= 17.5 +13.6
= 31.1≠R HS that is 38
So, you can Write with 100 % confidence that point (2.5, -3.4) is not a solution of this system of the equation.
Solve this as you would an equation that does not involve trig. Don't let the trig scare you. If you had to solve 2x+8=0, the first thing you would do is factor out the common 2. In our equation, we have a common cos theta. I'm going to use beta as my angle. When we factor out beta, here's what we have.
. The Zero Product Property tells us that at least one of those factors has to equal zero. So we set them both equal to zero and solve. Let's get the equations first, then we will need our unit circle. First equation set to equal zero is
. On our unit circle, cos is the value inside the parenthesis that is in the x position within our coordinate. Look at all those coordinates as you go around the unit circle once (once around is equivalent to 2pi). You will find that the the cos is 0 at
. The next equation is
. Move the 1 over by subtraction and divide by 2 to get
. Same as before, go around the unit circle one time and look to see where the coordinate in the y place is -1/2. Sin corresponds to the y coordinate. You will find that sin is -1/2 at
. And there you go! Trig is so much fun!!!
Answer:
Step-by-step explanation:
A. Two measurements(AandB)are taken on the same round.\oIs there a difference in the measurement of the muzzle velocity between device A and device B at the α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
B. Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. Interpret your results. The confidence interval is (__,__)?
Answer:
Open chart in StatCrunch --- Stat --- T Stats --- Paired --- Enter values: Sample 1 = A, Sample 2 = B --- Click on Confidence Interval… and enter Level which is my #%. --- Compute
Step-by-step explanation:
are you sure you wrote the problem here correctly ?
because the distance will be 40km after less than half an hour just by the first car driving. way before the second car even starts.
to be precise, it would be after 60 minutes × 40 / 90
(= how many minutes of an hour are needed to reach 40km while going 90km/h) :
60 × 40 / 90 = 60 × 4 / 9 = 20 × 4 / 3 = 80/3 = 26.67 minutes.
but maybe the question was about 400km distance between the two cars.
so, the first car goes 90km/h for 2 hours.
at that moment it will be 2×90=180km ahead.
that would mean that 220km are still missing for the 400km assumption.
with each hour driving the first car makes 20km more than the second car.
to build up 220km that way would require
220/20 = 11 hours.
plus the 2 original head start hours this would make 13 hours as overall answer.
A) d = r - 5 where t is the full price
<span>b) p = ( r - 5 ) * 1.05 </span>
<span>c) p = (15.5-5)*1.05 = 10.5 * 1.05 = $ 11.02</span>
