9514 1404 393
Answer:
- -2.2(6) +1.8(4) . . . temperature change
- 42 °C
Step-by-step explanation:
At the end of the first 6 hours, the temperature change was ...
(-2.2 K/h)(6 h) = -13.2 K
The change in the next 4 hours was ...
(1.8 K/h)(4 h) = 7.2 K
Then the total change over the 10-hour period was ...
(-2.2)(6) +(1.8)(4) . . . . . expression for temperature change
This evaluates to -13.2 +7.2 = -6.
__
The final temperature is the sum of the initial temperature and the temperature change:
final temperature = 48 °C -6 °C = 42 °C
_____
<em>Additional comment</em>
When temperature is measured on the Celsius scale, a change of 1 degree is called a kelvin (K).
<h2>
Explanation:</h2>
In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.
So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.
So let's name the vertices as:
First pair of opposite sides:
<u>Slope:</u>
Second pair of opposite sides:
<u>Slope:</u>
So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:
So the diagonals measure the same, therefore this is a rectangle.
Answer:
Explanation:
We must write this equation in the form
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
Where
(
a
,
b
)
are the co ordinates of the center of the circle and the radius is
r
.
So the equation is
x
2
+
y
2
−
10
x
+
6
y
+
18
=
0
Complete the squares so add 25 on both sides of the equation
x
2
+
y
2
−
10
x
+
25
+
6
y
+
18
=
0
+
25
=
(
x
−
5
)
2
+
y
2
+
6
y
+
18
=
0
+
25
Now add 9 on both sides
(
x
−
5
)
2
+
y
2
+
6
y
+
18
+
9
=
0
+
25
+
9
=
(
x
−
5
)
2
+
(
y
+
3
)
2
+
18
=
0
+
25
+
9
This becomes
(
x
−
5
)
2
+
(
y
+
3
)
2
=
16
So we can see that the centre is
(
5
,
−
3
)
and the radius is
√
16
or 4
30% is 3/10. 260 times 3/10 is 780/10, or 78. She read 78 pages. 260 - 78 is 182 pages left.
