Let
x = first odd integer
x + 2 = second odd integer
x + 4 = third odd integer
x + 6 = fourth odd integer
x + (x + 2) + (x + 4) + (x + 6) = -200
4x = -200 - 2 - 4 - 6
4x = -212
x = -53
Therefore, the four consecutive integers are -53, -51, -49, -47.
<span>The base of an exponential function can only be a positive number: it is TRUE
Proof
for all value of x, e^x always positive</span>
Answer:
p ≥ -10
Step-by-step explanation:
Divide both sides by-9:
When dividing or multiplying by a negative number, always flip the inequality sign:
-9p/-9 > = 90/-9
Cancel out the negatives:
9p/9 > = 90/-9
Simplify the fraction:
p > = 90/-9
Simplify the signs:
p > = -90/9
Find the greatest common factor of the numerator and denominator:
p >= -10 · 9/ 1 · 9
Factor out and cancel the greatest common factor:
p > = -10
Answer:
C = 5.
Step-by-step explanation:
First, you need to remember that:
For the function:
h(x) = Sinh(k*x)
We have:
h'(x) = k*Cosh(k*x)
and for the Cosh function:
g(x) = Cosh(k*x)
g'(x) = k*Cosh(k*x).
Now let's go to our problem:
We have f(x) = A*cosh(C*x) + B*Sinh(C*x)
We want to find the value of C such that:
f''(x) = 25*f(x)
So let's derive f(x):
f'(x) = A*C*Sinh(C*x) + B*C*Cosh(C*x)
and again:
f''(x) = A*C*C*Cosh(C*x) + B*C*C*Sinh(C*x)
f''(x) = C^2*(A*cosh(C*x) + B*Sinh(C*x)) = C^2*f(x)
And we wanted to get:
f''(x) = 25*f(x) = C^2*f(x)
then:
25 = C^2
√25 = C
And because we know that C > 0, we take the positive solution of the square root, then:
C = 5