Answer:
-sqrt(3)/2
Step-by-step explanation:
Use double angle identity for sin(2x)
sin(2x)=2sin(x)cos(x)
We are given sin(x)=-1/2 so we already have so far that:
sin(2x)=2(-1/2)cos(x)
sin(2x)=-1*cos(x)
We just need to find cos(x).
x is in the fourth quadrant so cosine will be positive there
knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.
So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2
The <em>exponential</em> function y = 290 · 0.31ˣ reports a decay as its <em>growth</em> rate is less than 1 and greater than 0. Its <em>percentage</em> rate of decrease is equal to 69 %.
<h3>How to determine the behavior of an exponential function</h3>
<em>Exponential</em> functions are <em>trascendental</em> functions, these are, functions that cannot be described <em>algebraically</em>. The <em>simplest</em> form of <em>exponential</em> functions is shown below:
y = a · bˣ (1)
Where:
- a - Initial value
- b - Growth rate
- x - Independent variable.
- y - Dependent variable.
Please notice that this kind of <em>exponential</em> function reports a <em>growth</em> for b > 1 and <em>decay</em> for b < 1 and b > 0. According to the statement we have the function y = 290 · 0.31ˣ, then we conclude that the exponential function given reports a <em>decay</em>.
The <em>percentage</em> rate of decrease is determined by the following formula:
100 × (1-0.31) = 100 × 0.69 = 69 %
The <em>percentage</em> rate of decrease related to the <em>exponential</em> function is 69 %.
To learn more on exponential functions: brainly.com/question/11487261
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624 because thats why i used a caculater. your welcom,e
We are given parabola equation y=x^2-10x+30.
We need to convert it in vertex form y= a(x-h)^2+k.
We need to find the value of a, h and k to get the vertex form.
For the given equation y=x^2-10x+30, the coefficient of x^2 is 1.
Therefore, a=1.
Now, let us find values of h and k.
h = -b/2a.
h = -(-10)/2(1) = 5.
Plugging x=5 in given equation to get the value of k.
y= x^2-10x+30 => (5)^2 -10(5) +30 = 25 -50 +30 = 5.
Therefore, k =5.
Therefore, vertex (h,k) = (5,5).
<h3>So, the vertex form is </h3>
Answer and Step-by-step explanation:
First, find the total amount of marbles.
5 + 4 + 3 = 12
There are 12 marbles in total.
The probability of picking a red or blue marble would be 9 out of 12, since it is asking for either the red marble or the blue marble.
9/12 is the answer. (Simplifies down to 3/4)
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