The correct answer is B) 9 m.
The measure of the sector of circle R is 32π/9 m. The measure of the central angle is 80°. This means that the sector is 80/360 = 2/9 of the circle. The area of a circle is given by A=πr², so the area of the sector is A=2/9πr². To verify this, 2/9π(4²) = 2/9π(16) = 32π/9.
Using this same formula for circle S, we will work backward to find the radius:
18π = 2/9πr²
Multiply both sides by 9:
18*9π = 2πr²
162π = 2πr²
Divide both sides by 2π:
162π/2π = 2πr²/2π
81 = r²
Take the square root of both sides:
√81 = √r²
9 = r
Answer:
Fourth and fifth ones are right
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
(a)
(b)
(c)
Step-by-step explanation:
We are required to construct 3 linear equations starting with the given solution z = 1/3.
<u>Equation 1</u>
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Multiply both sides by 9
Rewrite 3 as 5-2
9z=5-2
Add 2 to both sides
Our first equation is:
<u>Equation 2</u>
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Multiply both sides by 21
Rewrite 7 as 11-4
21z=11-4
Subtract 11 from both sides
Our second equation is:
<u>Equation 3</u>
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Multiply both sides by 6
Rewrite 6z as 4z+2z
4z+2z=2
Subtract 2z from both sides
Our third equation is:
Answer:
B) The maximum y-value of f(x) approaches 2
C) g(x) has the largest possible y-value
Step-by-step explanation:
f(x)=-5^x+2
f(x) is an exponential function.
Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞
Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→
Lim x→ -∞ f(x) = 2
Then the maximun y-value of f(x) approaches 2
g(x)=-5x^2+2
g(x) is a quadratic function. The graph is a parabola
g(x)=ax^2+bx+c
a=-5<0, the parabola opens downward and has a maximum value at
x=-b/(2a)
b=0
c=2
x=-0/2(-5)
x=0/10
x=0
The maximum value is at x=0:
g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2
The maximum value of g(x) is 2
