Answer:
Step-by-step explanation:
2 units squared.
Explanation:
You can go about this in two ways: Algebra and Integrals.
Algebra
y = 2x-6 is linear, thus if we take the value over the x interval [2,4] we can use geometry to calculate the area.
graph{2x-6 [-2.27, 7.73, -2.18, 2.82]}
You can see two triangles in the graph (you could also find this algebraically). Thus, you can calculate the area.
=
2
⋅
(
1
2
⋅
b
⋅
h
)
=
2
⋅
(
1
2
⋅
1
⋅
2
)
=
2
square units
Integrals
An integral gives the area under the curve. Remember though that if a function goes below the X axis, the integral is negative Thus you have to do two separate integrals based on the X intercept.
finding the X intercept (that is where y = 0)
2
x
−
6
=
0
x
=
3
when
y
=
0
When
x
<
3
, then y is negative. Thus, we have to find the negative integral from 2 to 3 and the positive integral from 3 to 4
=
−
∫
3
2
2
x
−
6
d
x
+
∫
4
3
2
x
−
6
d
x
=
−
[
x
2
−
6
x
]
3
2
+
[
x
2
−
6
x
]
4
3
=
−
[
9
−
18
−
4
+
12
]
+
[
16
−
24
−
9
+
18
]
=
−
[
−
1
]
+
[
1
]
=
2
units squared. And Tada, that is the same as the other answer!
Answer:
221 minutes
Step-by-step explanation:
His goal is 8 minutes or less for every mile during the marathon.
8 x 52 = 416
That gives him 416 total minutes to complete the marathon goal.
He already ran the first half in 195 minutes, so we do this to find the time for the other half:
416 - 195 = 221
He has 221 minutes in the second half of the marathon to meet his goal.
Answer:x=1, y=1
Step-by-step explanation:
2(1)-1=1
3(1)1-1=2
