4 sin^2 θ + 13cos^2 θ = 7
sin^2 θ = 1 - cos^ θ
4 - 4cos^2 θ + 13cos^2 θ = 7
9cos^2 θ = 3
cos^2 θ = 1/3
cos θ = # (1/3) # - square root
Square root of (1/3) has +1/3 and -1/3 as values of cos
Find the key angle by doing the cos inverse of #1/3
K.A = cos^-1 #(1/3) = 0.955
θ lies in all 4 quadrants
The values of θ are:
θ = 0.955, 2.186, 4.096, 7.23
Ignore 0.955, 2.186, 4.096, 7.23 as they are out of range pi/2 = 1.571
The the value of θ = 0.955 = 0.96 (to 2 d.p) radian
Hope it helped!
its A. because the exponent which in this case is 3, is multiplied 3 times. so 9 is multiplied 9 times
The equation to calculate the average rate of change is: y/x
y = f(x2) - f(x1)x = x2 - x1
x1: 1 (The smaller x value. It can be any number)x2: 2 (The larger x value. It also can be any number)f(x1): The value when you plug x1 into the function.f(x2): The value when you plug x2 into the function.
If we know this, the variables for this problem are assuming the function is 10(5.5)^x:
x2: 2x1: 1f(x2): 10(5.5)^(2) = 302.5f(x1): 10(5.5)^(1)= 55
This means:y = 302.5 - 55 = 247.5x = 2 - 1 = 1
Remember: the equation for avg rate of change is y/x
So, our average rate of change for the function on the interval [1,2] is 247.5 (y/x = 247.5/1)
<span>1. Find the magnitude and direction angle of the vector.
2. Find the component form of the vector given its magnitude and the angle it makes with the positive x-axis.
<span>3. Find the component form of the sum of two vectors with the given direction angles.</span></span>
Answer:
- Height = <u>9</u><u> </u>cm which means <u>Option </u><u>C </u>is the answer
Step-by-step explanation:
In the question we are given ,
- Volume of cylinder = <u>2</u><u>2</u><u>5</u><u>π</u><u> </u><u>cm³</u>
- Radius of cylinder = <u>5 cm</u>
And , we have to find the <u>height</u><u> of</u><u> </u><u>cylinder</u><u> </u>.
We know that ,

Our solution starts from here :

<u>Step </u><u>1</u><u> </u><u>:</u> Cancelling π with π :

<u>Step </u><u>2</u><u> </u><u>:</u> Substituting value of radius which is 5 cm in the formula :


<u>Step </u><u>3 </u><u>:</u> Transposing 25 to right hand side :

<u>Step </u><u>4</u><u> </u><u>:</u> Cancelling 225 by 25 :

- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>height</u><u> </u><u>of </u><u>cylinder</u><u> is</u><u> </u><u>9</u><u> </u><u>cm</u>
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<u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>