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WARRIOR [948]
3 years ago
13

For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. A circl

e with a radius 7 cm long is centered at Angle A's vertex, and Angle A subtends an arc length of 9.8 cm along this circle. The subtended arc is how many times as long as the circle's radius
Mathematics
1 answer:
lyudmila [28]3 years ago
3 0

9514 1404 393

Answer:

  1.4

Step-by-step explanation:

We want to find the multiplier n such that ...

  arc length = n × radius

  n = arc length / radius = (9.8 cm)/(7 cm)

  n = 1.4

The subtended arc is 1.4 times as long as the circle's radius.

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3 years ago
Find the vertex for the parabola given by the function ƒ(x) = −3x^2 − 6x.
telo118 [61]

Answer:

B) (−1, 3)  

Step-by-step explanation:

The standard form of a quadratic function is  

y = ax² + bx + c

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

In your equation, ƒ(x) = −3x² − 6x

a = -3; b = -6; c = 0

Calculate h

h = -(-6)/2(-3)]

h = 6/(-6)

h = -1

Calculate k

k = -3(-1)² -6(-1)

k = -3 + 6

k = 3

So, h = -1, k = 3, a = -3

The vertex form of the equation is  f(x) = -3(x + 1)² + 3.

The vertex is at (-1, 3).

The figure below shows the graph of ƒ(x) = −3x² − 6x  with the vertex

at (-1, 3).

4 0
3 years ago
There are 5 times more boys than girls total number of students is 2814
DiKsa [7]

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8 0
4 years ago
If a is the average (arithmetic mean) of 6m and 10, b is the average of 4m and 4, and c is the average of 14m and 16, what is th
Paha777 [63]

Answer:

6m+7.5

Step-by-step explanation:

the arithmetic mean is the average of two numbers

it is given that a is average of 6m and 10

so a=\frac{6m+10}{2}

b is the average of 4m and 4

so b=\frac{4m+4}{2}

c is the average of 14m and 16

so c=\frac{14m+16}{2}

now the average of a ,b and c is given by

average=\frac{a+b+c}{3}=\frac{\frac{6m+10}{2}+\frac{4m+4}{2}+\frac{14m+16}{2}}{3}=6m+7.5

4 0
3 years ago
I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing
ss7ja [257]
X = E/W dimension 
<span>y = N/S dimension </span>

<span>4x + 4x + 2y + 2y = 64 </span>
<span>8x + 4y = 64 </span>
<span>4y = 64 - 8x </span>
<span>y = 16 - 2x </span>

<span>Area = xy = x(16 - 2x) = 16x - 2x^2 </span>

<span>Maximum of y = ax^2 + bx + c is when x = -b / 2a </span>

<span>so x = -16 / -4 = 4 </span>
5 0
3 years ago
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