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alisha [4.7K]
2 years ago
10

Identify the figure and denote it by its appropriate symbol

Mathematics
1 answer:
Gekata [30.6K]2 years ago
5 0
B: ray
Rays are a linear formation that start at a point and continue forever in a direction. The photo shows a point on one end, and an arrow on the other indicating that it starts at the point and continues forever past the arrow.
You might be interested in
<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B
riadik2000 [5.3K]

Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

where we assume |r| < 1. Multiplying on both sides by r gives

r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}

and subtracting this from S_n gives

(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}

As n → ∞, the exponential term will converge to 0, and the partial sums S_n will converge to

\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

We must have |r| < 1 since both sums converge, so

\dfrac{15}a = \dfrac1{1-r}

\dfrac{150}{a^2} = \dfrac1{1-r^2}

Solving for r by substitution, we have

\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)

\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}

Recalling the difference of squares identity, we have

\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15

It follows that

\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0
2 years ago
Use the sum and difference identities to find the exact values of the sine, cosine, and tangent of the angle. . 165 = 135 + 30
Serhud [2]
So lets get to the problem 

<span>165°= 135° +30° </span>

<span>To make it easier I'm going to write the same thing like this </span>
<span>165°= 90° + 45°+30° </span>

<span>Sin165° </span>
<span>= Sin ( 90° + 45°+30° ) </span>
<span>= Cos( 45°+30° )..... (∵ Sin(90 + θ)=cosθ </span>
<span>= Cos45°Cos30° - Sin45°Sin30° </span>

<span>Cos165° </span>
<span>= Cos ( 90° + 45°+30° ) </span>
<span>= -Sin( 45°+30° )..... (∵Cos(90 + θ)=-Sinθ </span>
<span>= Sin45°Cos30° + Cos45°Sin30° </span>


<span>Tan165° </span>
<span>= Tan ( 90° + 45°+30° ) </span>
<span>= -Cot( 45°+30° )..... (∵Cot(90 + θ)=-Tanθ </span>
<span>= -1/tan(45°+30°) </span>
<span>= -[1-tan45°.Tan30°]/[tan45°+Tan30°] </span>

<span>Substitute the above values with the following... These should be memorized </span>
<span>Sin 30° = 1/2 </span>
<span>Cos 30° =[Sqrt(3)]/2 </span>
<span>Tan 30° = 1/[Sqrt(3)] </span>
<span>Sin45°=Cos45°=1/[Sqrt(2)] </span>
<span>Tan 45° = 1</span>
4 0
3 years ago
Find missing angleeeeeeeeeeeeeeeeeeeeeeee​
dimulka [17.4K]

Answer:

C) 80

Step-by-step explanation:

triangles always add up to 180 degrees, so 80+20=100 the missing angle is 80 degrees

4 0
2 years ago
The measures of the angles of a triangle are shown in the figure below. Solve for x.
MissTica

Answer: X= 25 degrees

Step-by-step explanation:

A triangle is 180 degrees.

115+40=165

180-165=25 degrees

6 0
2 years ago
2. Bacterial Culture Problem: When you grow a
Galina-37 [17]

The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases

<h3>Find the area at times t = 0, t = 5, and t = 10.</h3>

The complete question is added as an attachment

The function is given as:

A(t) = 9 * (1.1)^t

Substitute t = 0, t = 5, and t = 10.

A(0) = 9 * (1.1)^0 = 9

A(5) = 9 * (1.1)^5 = 14.5

A(10) = 9 * (1.1)^10 = 23.3

The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases

<h3>Use the results of part a to find the radius of the culture at these three times</h3>

The area of a circle is

A = πr^2

Make r the subject

r = √(A/π)

So, we have:

r = √(9/π) =  1.7

r = √(14.5/π) =  2.1

r = √(23.3/π) =  2.7

The radius is changing at an increasing rate

<h3>Write an equation for the composite function R(A(t)).</h3>

In (b), we have:

r = √(A/π)

Express as a function

r(A(t)) = √(A/π)

Hence, the equation for the composite function is R(A(t)) = √(A/π)

<h3>The restriction for the function R * A</h3>

We have:

r(A(t)) = √(A/π)

A(t) = 9 * (1.1)^t

This gives

r(A(t)) = √(9 * (1.1)^t/π)

The radius is 30.

So, we have:

√(9 * (1.1)^t/π) = 30

Square both sides

(9 * (1.1)^t/π)= 900

Divide by 9

(1.1)^t/π= 100

Multiply by π

(1.1)^t= 314

Take the logarithms of both sides

t * log(1.1) = log(314)

Solve for t

t = 60

Hence, the restriction on the domain is 0 <= t <= 60

Read more about composite functions at:

brainly.com/question/13502804

#SPJ1

7 0
1 year ago
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