Answer: The length of the arc is 1.57 centimeters
Step-by-step explanation: If the diameter has been given as 4 centimeters, then the radius would be diameter divided by 2, and that equals 2.
With the radius now known as 2, we can calculate the length of the arc as follows;
Length of an arc = (Ω/360) x 2πr
Where Ω is the angle subtended by the radio and r is the radius.
Length of an arc = (45/360) x 2 x 3.14 x 2
Length of an arc = (1/8) x 12.56
Length of an arc = 1.57
Therefore, the length of the arc is 1.57 centimeters
Answer:
Zeroes of this function are -3 and 9.
Step-by-step explanation:
Using quadratic formula we have:
(-6 +- 
) / 2(-1)
= -3, 9
If
<em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² - 5<em>x</em> + 9
then
<em>f '(x)</em> = 3<em>ax </em>² + 2<em>bx</em> - 5
Given that <em>f</em> (-1) = 12 and <em>f</em> '(-1) = 3, we get the system of equations
-<em>a</em> + <em>b</em> + 5 + 9 = 12
3<em>a</em> - 2<em>b</em> - 5 = 3
or
-<em>a</em> + <em>b</em> = -2
3<em>a</em> - 2<em>b</em> = 8
Multiply through the first equation by 2 and add it to the second one to eliminate <em>b</em> and solve for <em>a</em> :
2(-<em>a</em> + <em>b</em>) + (3<em>a</em> - 2<em>b</em>) = 2(-2) + 8
-2<em>a</em> + 2<em>b</em> + 3<em>a</em> - 2<em>b</em> = -4 + 8
<em>a</em> = 4
Substitute this into the first equation above to solve for <em>b</em> :
-4 + <em>b</em> = -2
<em>b</em> = 2
40^2 - 32^2=576
square root of 576 will be 24 so 24 is y
Start with point-slope form, where 
is the slope and 
is a known point on the line.
Substitute in the known values.
Distribute the 
to the 
.
Add 
to both sides.
