Answer:
<u>x² - 22x + y² - 6y + 121 = 0</u>
Step-by-step explanation:
<u>General Form of Equation</u>
<u>Solving</u>
- (x - 11)² + (y - 3)² = (3)²
- x² - 22x + 121 + y² - 6y + 9 = 9
- <u>x² - 22x + y² - 6y + 121 = 0</u>
The given quadratic describes a parabola that opens upward. Its one absolute extreme is a minimum that is found at x = -3/2. The value of the function there is
(-3/2 +3)(-3/2) -1 = -13/4
The one relative extreme is a minimum at
(-1.5, -3.25).
_____
For the parabola described by ax² +bx +c, the vertex (extreme) is found where
x = -b/(2a)
Here, that is x=-3/(2·1) = -3/2.
Answer:
y= -3/5x + 2
Step-by-step explanation:
Answer:
9) x=58
10) r=4
11) m=4
12) p=3
13) x=6
14) x=-3
15) s=400
Step-by-step explanation:
9) x+2/5=12
x5 x5
x+2=60
-2 -2
x=58
10) 7r + 14 - 3r =30
-14 -14
<u>7r-3r</u>=16
4r=16
÷4 ÷4
r=4
11)
m+2=6
-2 -2
m=4
÷
÷
m=4
12) <u>2</u>(5p+9)=48
10p+18=48
-18 -18
10p=30
÷10 ÷10
p=3
13) <u>5</u>(2x-8)=20
10x-40=20
+40 +40
10x=60
÷10 ÷10
x=6
14)<u>6</u>(3-2x)=54
18-12x=54
-18 -18
-12x=36
÷-12 ÷-12
x=-3
15)
-
=40
x5 x5
2s-
=200
x2 x2
<u>2s-1s</u>=400
1s=400
÷1 ÷1
s=400
Split up the interval [2, 5] into

equally spaced subintervals, then consider the value of

at the right endpoint of each subinterval.
The length of the interval is

, so the length of each subinterval would be

. This means the first rectangle's height would be taken to be

when

, so that the height is

, and its base would have length

. So the area under

over the first subinterval is

.
Continuing in this fashion, the area under

over the

th subinterval is approximated by

, and so the Riemann approximation to the definite integral is

and its value is given exactly by taking

. So the answer is D (and the value of the integral is exactly 39).