If cos θ -sin θ =1, find θ cos θ +sin θ?

Answers

Answer 1

Answer: $cos\theta-sin\theta=1\ \ \ \ |square\ both\ sides\n\n(cos\theta-sin\theta)^2=1\n\ncos^2\theta-2sin\theta cos\theta+sin^2\theta=1\n\n1-2sin\theta cos\theta=1\n\n-2sin\theta cos\theta=1-1\n\n-2sin\theta cos\theta=0\iff sin\theta=0\ or\ cos\theta=0\n\n\theta=k\pi\ or\ \theta=(\pi)/(2)+k\pi\ \ \ \ (k\in\mathbb{Z})$

$For\ \theta=k\pi\to cosk\pi-sink\pi=\pm1-0=\pm1\to conclusion:\theta=2k\pi\n\nFor\ \theta=(\pi)/(2)+k\pi\to cos((\pi)/(2)+k\pi)-sin((\pi)/(2)+k\pi)=0-(\pm1)=\mp1\to\n\to conclusion:\theta=(3\pi)/(2)+2k\pi\n\n============================\n\ncos\theta+sin\theta=(*)\n\nfor\ \theta=2k\pi\to(*)=1+0=1\n\nfor\ \theta=(3\pi)/(2)+2k\pi\to(*)=0-1=-1$

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Barry wants to take out a loan from his bank for $1000 to buy bicycle the interest rate on the loan from the bank is 9% he wants to pay the toll amount in three monthly payments what is the amount that vary with pay in interest rate loan

Answers

The required interestpaid by Barry is given as, $22.5.

Given that,
Barry wants to take out a loan from his bank for $1000 to buy a bicycle the interest rate on the loan from the bank is 9% he wants to pay the toll amount in three monthly payments what is the amount that varies with pay in interest rate loan is to be determined.

What is interest?

Simpleinterest is defined as the percentage of earnings on the lending for a period of time

Here,
Principal = 1000
Rate = 9%
Time = 3 / 12 = 0.25 years
So,
Interest = Principal × rate × time
interest = 1000 × 0.09 × 0.25
Interest = $22.5

Thus, the required interestpaid by Barry is given as, $22.5.

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Answer:

22.50

Step-by-step explanation:

formula I=prt

I=1000x0.09x.25

I=22.50

What is an expression which combines numbers and operations?

Answers

An expression that combines numbers and operations is a mathematical statement that represents a calculation or computation.

An expression can involve various arithmetic operations such as addition, subtraction, multiplication, division, exponentiation, and more.

Here are some examples of expressions:

Addition: 5 + 3

Subtraction: 10 - 2

Multiplication: 4 × 6

Division: 20 / 5

Exponentiation: 2³ (2 raised to the power of 3)

Combination: (5 + 3) × 2

In the last example, the expression combines addition and multiplication. Parentheses can be used to indicate the order of operations, ensuring that calculations are performed correctly according to mathematical conventions (e.g., multiplication before addition).

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An algebraic expression or mathematical expressions combines numbers and operations.

Solve the equation for y: w- 302 4y-12

Answers

the equation (y-3)^2 =4y-12

y = -7

Gannon had to cut aribbon into even pieces.
The ribbon was 3 feet
long. How many pieces
would he cut if they were
all 0.75 feet long?

Answers

He would be able to cut 4 pieces.

steps for patient medication decrease 25 mg per day for one week. Whats the change at end of the week?

Answers

The answer would be 25 mg minus the last day of the week

The change at the end of the week is 175

3x squared times 2x squared

Answers

When multiplying numbers with exponents, you only multiply the coefficients. The variable is then copied (this applies to numbers with similar variables), and the exponents are then added. This is shown below:

3x^2 * 2x^2 = 6x^4

The simplified form of the expression 3x² * 2x² is 6x⁴.

To simplify the expression 3x² * 2x², we need to multiply the coefficients and add the exponents of the variables.

Step 1: Multiply the coefficients (numbers in front of the variables):

3 * 2 = 6

Step 2: Add the exponents of the variables (x² * x² = x²⁺² = x⁴):

x² * x² = x²⁺² = x⁴

Step 3: Put the results together:

6x⁴

Therefore, the simplified form of the expression 3x² * 2x² is 6x⁴.

In summary, when multiplying two terms with the same variable (x) raised to a power (exponent), we multiply their coefficients (3 and 2, which results in 6) and add their exponents (2 and 2, which results in 4). The final answer is 6x⁴, where 6 is the coefficient and x⁴ represents the variable raised to the power of 4. This calculation follows the rules of multiplying terms with variables and exponents.

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