Answer:
y(x) = 7e^(5x)
Step-by-step explanation:
The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that
dy/dx = 5y
Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)
Using the above stated law now, we can relate to our equation, saying that
y(x) = y(0) e^(5x)
The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have
y(x) = 7e^(5x)
And that is our needed equation of the curve
Answer:
12.5%
Step-by-step explanation:
There are two types of spinners here and the outcome of them is independent. That means
P(odd number,C) = P(odd number) * P(C)
There are two odd numbers out of four numbers in the first spinner. The chance of odd number will be:
P(odd) = 2/(2+2)= 1/2= 50%
There are four letters and the desired outcome is C. The chance for C will be:
P(C)= 1/4= 25%
Then the chance will be:
P(odd number,C) = P(odd number) * P(C)
P(odd number,C) =50% * 25% = 12.5%
Answer:
ummmmm I guess I could add the dimensions in the text.
Step-by-step explanation:
The picture is a black screen.
Answer:
Real values of x where x < -1
Step-by-step explanation:
Above the x-axis, the function is positive.
The function is decreasing when the gradient is negative.
The function has a positive
coefficient, therefore the vertex is a local minimum;
This means the gradients are negative before the vertex and positive after it;
To meet the conditions therefore, the function must be before the vertex and above the x-axis;
This will be anywhere before the x-intercept at x = -1;
Hence it is when x < -1.
Answer:
~q→~p
Step-by-step explanation:
The contrapositive of a statement is formed by negating the hypothesis and conclusion of a statement and switching them (the hypothesis becomes the conclusion and vice versa).
With this definition we can conclude that the contrapositive of p→q would be ~q→~p
