Answer: 818.4
Step-by-step explanation:
Using the area of a sector formula, we get the area of the entire sector is
.
Using the formula
, we get the area of the triangle is
.
So, the area of the shaded sector is 
The function g is defined by:
g(x) = (4 + x) / (5 + 3x) ...(1)
Now, we need to find g(5n); that is, we make: x = 5n
Replacing this into equation (1):
g(5n) = (4 + 5n) / (5 + 3*(5n)) = (4 + 5n) / (5 + 15n)
So, the final answer is:
g(5n) = (4 + 5n) / (5 + 15n)
Answer:
The highest score is 94.
Step-by-step explanation:
Let the highest score be denoted by, <em>A</em>, the lowest score be, <em>B</em> and the middle score be <em>X</em>.
Then,
A + X + B = 87 × 3 = 261 ...(i)
X + B = 83.5 × 2 = 167 ...(ii)
⇒ B = 167 - X ...(iii)
A + X = 89 × 2 = 178 ...(iv)
⇒ A = 178 - X ...(v)
Substitute (iii) and (v) in (i) and solve for <em>X</em> as follows:
A + X + B = 261
178 - X + X + 167 - X = 261
345 - X = 261
X = 84
Substitute the value of <em>X</em> in (iii) and solve for B as follows:
B = 167 - X
= 167 - 84
= 83
Substitute the value of <em>X</em> in (v) and solve for A as follows:
A = 178 - X
= 178 - 84
= 94
Thus, the highest score is 94.
<h2>
Answer: slope = - 95</h2><h2>
</h2>
Step-by-step explanation:
The question gives us two points, (87, 91) and (88, -4), from which we can find the slope and later the equation of the line.
<u>
</u>
<u>Finding the Slope</u>
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (91 - (- 4)) ÷ (87 - 88)
= - 95
<em><u /></em>
<em><u /></em>
<em><u>Checking my answer:</u></em>
<em>Finding the Equation</em>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-4) = - 95 (x - 88)
y + 4 = - 95 (x - 88)
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>