Using sum and difference identities from trigonometric identities shows that; Asin(ωt)cos(φ) +Acos(ωt)sin(φ) = Asin(ωt + φ)
<h3>How to prove Trigonometric Identities?</h3>
We know from sum and difference identities that;
sin (α + β) = sin(α)cos(β) + cos(α)sin(β)
sin (α - β) = sin(α)cos(β) - cos(α)sin(β)
c₂ = Acos(φ)
c₁ = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
c₁² + c₂² =
(Asin(φ))² + (Acos(φ))²
= A²(sin(φ)² +cos(φ)²)
= A² * 1
= A²
Using common factor as shown in the trigonometric identity above for Asin(ωt)cos(φ) +Acos(ωt)sin(φ) gives us; Asin(ωt + φ)
Complete Question is;
y(t) = distance of weight from equilibrium position
ω = Angular Frequency (measured in radians per second)
A = Amplitude
φ = Phase shift
c₂ = Acos(φ)
c₁ = Asin(φ)
Use the information above and the trigonometric identities to prove that
Asin(ωt + φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
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Based on the financial data (information) provided in the table (see attachment) and assuming a total fixed cost (TFC) of $5, the business firm's: B. economic profit is equal to $16, .
<h3>What is an economic profit?</h3>
An economic profit can be defined as a measure of the difference between the total revenue that a business firm (economic entity) has received from the sales of its products (outputs) and the opportunity costs of its inputs.
This ultimately implies that, an economic profit is equal to the total revenue minus total cost. Thus, it typically involves subtracting the total cost of a product from the total revenue that a business firm (economic entity) receives through it sales.
Based on the financial data (information) provided in the table (see attachment), we can infer and logically deduce that business firm's economic profit is equal to $16, assuming a total fixed cost (TFC) of $5.
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The missing reason in the congruency proof given the parameters is; Definition of a perpendicular bisector.
<h3>How to prove congruency theorems?</h3>
We are given;
Triangle QPT is similar to triangle QRT.
SP ≅ SR
Now, According to perpendicular bisector definition, we know that perpendicular bisector is a line or a segment that is perpendicular to a segment and passes through the midpoint of the segment. This means that any point on the perpendicular bisector is equidistant from the endpoints of the line segment.
Thus, we can say that PT ≅ RT and the missing reason is definition of a perpendicular bisector.
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Confidentiality is a virtue which states that you need to secure information by limiting computer access to authorized personnel only.
Keeping confidential data is crucial especially if your business deals with very important information about a person and his security.
Trust is built between a company and a client. The client trusts the company to keep his information secure and confidential from outside parties. Once the confidentiality of the company is compromised, the business will suffer because clients will no longer trust the company to keep their data secure.<span />
Yes, they should. The art will be good
