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pentagon [3]
3 years ago
15

Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)

Mathematics
1 answer:
asambeis [7]3 years ago
7 0

Answer:

(15°, 165°)

Step-by-step explanation:

Given the equation 6 sin2(x) = 3, we are to find the value of x that satisfies the equation in the interval  [0, 2π]

Given

6 sin2(x) = 3,

Divide both sides by 6

6 sin2(x)/6 = 3/6

sin2(x) = 1/2

2x = sin^-1(0.5)

2x = 30°

x = 30°/2

x = 15°

Since sin is positive in the second quadrant, x2 = 180-15

x = 165°

Hence the values within the interval are 15 and 165.

(15°, 165°)

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-8.0 is classified as?Select all that apply * Natural Number Whole Number Integer Rational Number
grigory [225]

Answer:

Integer and Rational Number

Step-by-step explanation:

Natural numbers are positive numbers starting at 1 and going onward.  Since -8.0 is not a positive number, it is not a natural number.

Whole numbers are natural numbers and 0 altogether.  -8 is not greater than zero or positive, so it is not a whole number.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.  -8.0 can also be written as -8/1, so it is a rational number and an integer, since every integer is a number over 1 and also a rational number.

7 0
3 years ago
1.Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg wereused in a procedure. Write an equation t
Sophie [7]

1)\text{   }N_t\text{ = 90\lparen}\frac{1}{2})^{\frac{t}{17.5}}

2) 5.625 mg will be left

Explanation:

1) Half-life = 17.5 days

initial amount of Arsenic-74 = 90 mg

To get the equation, we will use the equation of half-life:

\begin{gathered} N_t\text{ = N}_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}} \\ where\text{ N}_t\text{ = amount remaining} \\ N_0\text{ = initial amount} \\ t_{\frac{1}{2}\text{ }}\text{ = half-life} \end{gathered}N_t\text{ = 90\lparen}\frac{1}{2})^{\frac{t}{17.5}}

2) we need to find the remaining amount of Arsenic-74 after 70 days

t = 70

\begin{gathered} N_t=\text{ 90\lparen}\frac{1}{2})^{\frac{70}{17.5}} \\ N_t\text{ = 5.625 mg} \end{gathered}

So after 70 days, 5.625 mg will be left

4 0
1 year ago
The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square fee
Lunna [17]

Answer:

=13.73 ft²

Step-by-step explanation:

The diameter of the largest possible circle that can be cut out of  a square is equal to the length of the side of the square.

Therefore the diameter of the circle cut from a square of side 8ft =8ft

r=4ft

Area of the remaining board= Area of square- area of circle

=side²-πr²

=8²-π×4²

=64-16π

=13.73 ft²

6 0
3 years ago
Given: SY and TZ, transversal UX ∠YVW and _______ are alternate interior
Bond [772]

< yvw and < twv   are alternate interior angles


opposite sides of the transversal and inside are alternate interior angles

4 0
3 years ago
Read 2 more answers
What is the solution of -5x &gt; 25? <br> a. x &gt; -5 <br> b. x 5 <br> d. x &lt; 5
devlian [24]
The solution possible can be correct by dividing both sides by -5 ;Sooo x>-5.....
5 0
3 years ago
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