Answer:
x = and y =
Step-by-step explanation:
Applying the trigonometric functions to the given triangle;
i. To determine the value of x;
Sin θ =
Sin 45 =
x = 16 * Sin 45
= 16 *
x =
ii. To determine the value of y;
Cos θ =
Cos 45 =
y = 16 * Cos 45
= 16 *
y =
Thus, x = and y =
dP/dt = 1000 * 9^t is the bacteria population's growth rate.where:P(t) is the population at time t, andP(0) = 6000.
The population after one hour would be:
P(1) = P(0) + <Integral of dP/dt from 0 to 1>
P(1) = P(0) + [ 1000 * 9^1 / ln(9) - 1000 * 9^0 / ln(9) ]
P(1) = 6000 + 3641 = 9461 would be the answer
Answer:
The solution to the system of equations are;
x = -4/3
y = 5/3
Step-by-step explanation:
To find the Solution, we would carry the Operation simultaneously.
4x + 2 = -2y .........(i)
6y - 18 = 6x ..........(ii)
First let's rearrange the equations, to make the journey smoother
2y + 4x = -2 ...........(iii)
6y - 6x = 18 ...........(iv)
Let's Multiply equation (III) by 3 so as to have a uniform spot to begin elimination.
3.2y + 3.4x = -2 . 3
6y + 12x = -6............... (v)
Let's subtract equation (v) from equation (iv)
= 0y - 18x = 24
-18x = 24
x = - 24 / 18
x = -4/3
Let's substitute (x = -4/3) in equation (ii), so that we can solve for the value of y:
6y - 18 = 6x
6y - 18 = 6 (-4/3)
6y - 18 = -8
6y = -8 + 18
6y = 10.
y = 10 / 6
y = 5/3
The solution to the system of equations are;
x = -4/3
y = 5/3
Answer:
<em>C. y = 3x + 13.</em>
Step-by-step explanation:
The point slope form of a line is
y - y1 = m(x - x1) where m = the slope, and (x1, y1) is a point on the line.
So, substituting:
y - 1 = 3(x - -4)
y - 1 = 3(x + 4)
y = 3x + 12 + 1
y = 3x + 13.