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Nata [24]
3 years ago
5

Solve, for 0 ≤ θ < 360 , the equation sin2 θ = 1 + cos θ

Mathematics
1 answer:
marshall27 [118]3 years ago
3 0

Answer:

θ = 90°, 180°, or 270°

Step-by-step explanation:

sin²θ = 1 + cos θ

Use Pythagorean identity.

1 − cos²θ = 1 + cos θ

Move everything to one side and simplify.

0 = cos²θ + cos θ

Factor.

0 = cos θ (cos θ + 1)

Solve.

cos θ = 0 or -1

θ = 90°, 180°, or 270°

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Michael got a loan for the Playstation 5. His loan was $600. At a 3.75% interest rate he had to pay $7.50 in interest. How long
Semmy [17]

Answer:

4 mo.

Step-by-step explanation:

I = PRT      P = 600    R = .0375    I = 7.50

7.50 = 600(.0375)T

7.5 = 22.5T

T = 7.5/22.5 = 1/3 yr = 4 mo.

6 0
2 years ago
A motor vehicle has a maximum efficiency of 39 mpg at a cruising speed of 40 mph. The efficiency drops at a rate of 0.1 mpg/mph
svp [43]

Answer:

38 mpg

Step-by-step explanation:

Initial efficiency = 39 mpg

Initial speed = 40 mph

Final speed = 50 mph

The efficiency drop  between 40 mph and 50 mph is given by:

E_d = 0.1 \frac{mpg}{mph}*\Delta V

The total efficiency drop from 40 to 50 mph is:

E_d = 0.1 \frac{mpg}{mph}*(50-40)mph\\E_d = 1\ mpg

Therefore, the efficiency at 50 mph is:

E_{50} = E_{40} -E_d\\E_{50} = 39 -1\\E_{50} = 38\ mpg

5 0
3 years ago
Consider the sequence 3, -9, 27, -81, .. Find the 14th term of the sequence.
bagirrra123 [75]

Answer:

let 'a' be the first term, 'd' be the common difference between all the terms of the sequence

Step-by-step explanation:

therefore, a = 3,

and, d = -9 -3

          = -12

hence the 14th term would be,

=> a + 13d

=> 3 + 13( -12 )

=> 3 - 156

=> - 153

5 0
3 years ago
Read 2 more answers
What is the LCM of x^2+5 and x^2+10x+25?
avanturin [10]

Answer:

(x+5)²(x²+5)

Step-by-step explanation:

Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25

On factorising we have:

x²+5x+5x+25

= x(x+5) +5(x+5

= (x+5)(x+5)

= (x+5)²

The LCM can be calculated as thus

| x²+5, (x+5)²

x+5| x²+5, (x+5)

x+5| x²+5, 1

x²+5| 1, 1

The factors of both equation are x+5 × x+5 × x²+5

The LCM will be the product of the three functions i.e

(x+5)²(x²+5)

This hives the required expression.

5 0
3 years ago
The income statement of Carla Vista Co for the month of July shows net income of 2300 based on service revenue 6500, salaries an
Blizzard [7]

Answer:

-500

Step-by-step explanation:

2300-6500-2500--1100--600-150-250-+600

3 0
2 years ago
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