Answer:
(0, 1).
Method 1 (Substitution):
Substituting our two y's, we get the following:
Thus, the only set of solutions is (0, 1). A quick sketch (either by hand or on Desmos) can confirm this.
Method 2 (Elimination):
We have two equations. We'll let the top one be equation 1 and the bottom one be equation 2. Eliminating as many variables as we can, we subtract (2) from (1) to get:
0 = 3x => x = 0.
So the only set of solutions is (0, 1).
Method 3 (Gaussian elimination):
We can place this in an augmented matrix and row reduce.
![\left[\begin{array}{cccc}1&5&1 & 1\\1&2&1 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%261%20%26%201%5C%5C1%262%261%20%26%201%5Cend%7Barray%7D%5Cright%5D)
Row reducing this gives us:
![\left[\begin{array}{cccc}1&5&1 & 1\\0&3&0 & 0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%261%20%26%201%5C%5C0%263%260%20%26%200%5Cend%7Barray%7D%5Cright%5D)
This tells us that the only solution for x is x = 0 (since we read this as "3x = 0") and thus, the only solution we get is (0, 1).
This is the concept of trajectories;
We are required to calculate the time taken for the base ball whose distant to reach the maximum height has been modeled by h=-16t^2+64t+4.2 took to hit the ground. Here we proceed as follows;
At the time when the base ball hits the ground the height,h=0
Thus;
-16t^2+64t+4.2=0
this is a quadratic equation, to solve the quadratic equation we use the formula;
t=[-b+/- sqrt(b^2-4ac)]/(2a)
where;
a=-16,b=64, c=4.2
thus substituting the values in our formula we get:
t=[-64+/-sqrt(64^2-4*(-16)*4.2)]/(-16*2)
t=[-64+/- sqrt(4364.8)]/(-32)
t=[-64+/-66.1]/(-32)
t=4.1 or-0.1
thus the we take the positive value t=4.1 and we conclude that the time taken for the ball to hit the ground was 4.1 seconds
Answer:
gain = 0
% = 0
Step-by-step explanation:
<em><u>Profit</u></em>
He sells one for a profit of 25% That means he sells one of them for 100% + 25% = 125%
₹1500 * 125/100 = ₹187500/100 = ₹1875
<em><u>Loss</u></em>
Here he sells it for 25% less than the selling price he wanted.
100% - 25% = 75%
₹1500 * 75/100 = ₹112500/100 = ₹1125
<em><u>Discussion</u></em>
He should make ₹1500 + ₹1500 = ₹3000 without either profit or loss.
What he actually accomplishes is ₹1125 + ₹1875 = ₹3000
So he has a net gain (loss) of 0.
The % is 0
Answer:
√3681
Step-by-step explanation:
D= √(30+30)^2+(19-10)^2
D= √60^2+9^2
D= √3600+81
D= 3681
There is only one solution.
y = x+2
x = -1
Substitute x = -1 in y = x+2
y=-1+2
y = 1
We only get the single value of y and x so It's clear that there's only one solution.
