Answer:
10cm/s²
Step-by-step explanation:
Acceleration is the change in velocity of an object with respect to time.
Given velocity v(x) to be x³-2x+6
Acceleration = ∆v/∆x
Differentiating the velocity function to get acceleration we have,
Acceleration = dv/dt = 3x²-2
Acceleration of the particle at x = 2 will give;
dv/dt @ x = 2 is 3(2)²-2
= 12-2 = 10cm/s²
Answer:
The value of f(z) is not constant in any neighbourhood of D. The proof is as explained in the explaination.
Step-by-step explanation:
Given
For any given function f(z), it is analytic and not constant throughout a domain D
To Prove
The function f(z) is non-constant constant in the neighbourhood lying in D.
Proof
1-Assume that the value of f(z) is analytic and has a constant throughout some neighbourhood in D which is ω₀
2-Now consider another function F₁(z) where
F₁(z)=f(z)-ω₀
3-As f(z) is analytic throughout D and F₁(z) is a difference of an analytic function and a constant so it is also an analytic function.
4-Assume that the value of F₁(z) is 0 throughout the domain D thus F₁(z)≡0 in domain D.
5-Replacing value of F₁(z) in the above gives:
F₁(z)≡0 in domain D
f(z)-ω₀≡0 in domain D
f(z)≡0+ω₀ in domain D
f(z)≡ω₀ in domain D
So this indicates that the value of f(z) for all values in domain D is a constant ω₀.
This contradicts with the initial given statement, where the value of f(z) is not constant thus the assumption is wrong and the value of f(z) is not constant in any neighbourhood of D.
Answer:
Use 49 ounces of the 14% allow and 41 ounces of the 23% alloy.
Step-by-step explanation:
Each ounce of the 14% copper contains 0.14 ounce of pure copper.
Each ounce of the 23% copper contains 0.23 ounce of pure copper.
Each ounce of the 18.1% copper contains 0.181 ounce of pure copper.
Use x ounces of the 14% and y ounces of the 23% to make 90 ounces of 18.1% alloy.
x+y = 90
y = 90-x
0.14x + 0.23y = 0.181·90
0.14x + 0.23(90-x) = 16.29
0.14x + 20.7 - 0.23x = 16.29
-0.09x + 20.7 = 16.29
4.41 = 0.09x
x = 49
y = 90-x = 41
Use 49 ounces of the 14% allow and 41 ounces of the 23% alloy.
Answer:
1.7 meters
Step-by-step explanation:
because an equilateral triangle has 3 sides and they are all the same you can just divide 5.1 by 3
5.1 / 3 = 1.7
it is 1.7 m
• x+1.793= 2.42
x-1.793= 2.42-1.793 FALSE
• 5.25x = 15.75
Solve for x, by dividing both sides of the equation by 5.25
x = 15.75/5.25
x = 3 TRUE
• The equation x = 2.4 *11.62 can be rewritten as x = 11.62 * 2.4. TRUE
• The solution to the equation x + 9.43 = 16.09 is x = 6.66.
x+9.43 = 16.09
Subtract 9.43 from both sides of the euqation:
x-9.43+9.43= 16.09-9.43
x = 6.66 TRUE
