Answer:
We should attempt synthetic division to find when
x
3
−
k
x
2
+
2
k
x
−
15
x
−
3
has a remainder of
0
, which would signify that it is a factor of the polynomial.
The synthetic substitution would be set up as:
3
−
∣
∣
∣
1
−
k
2
k
−
15
−−−
−−−
−−−
−−−
−−−
|
0
Treating the synthetic division like any other synthetic division problem, we see that
3
−
∣
∣
∣
1
−
k
2
k
−
15
−−−
−−−
3
−−−−−−−−
−
3
k
+
9
−−−−−−−−
−
3
k
+
27
−−−−−−−−−
1
−
k
+
3
−
k
+
9
|
0
If the remainder equals
0
, then we know that
−
3
k
+
27
+
(
−
15
)
=
0
Solve this to see that
k
=
4
.
Thus,
(
x
−
3
)
is a factor of
x
3
−
4
x
2
+
8
x
−
15
.
We can calculate the length of AB using the Pythagorean Theorem, where:
So, replacing PA by 34 and PB by 16 and solving for AB, we get:
Then, AC = AB + BC, But AB = BC, so:
AC = 2*AB
Replacing AB by 30, we get:
AC = 2*30 = 60
Answer: AC=60
5).
and
6).
The volume of a sphere is
(4/3) (pi) (radius)³ .
In #5, the 'pi' is already there next to the answer window.
You just have to come up with the (4/3)(radius³).
Remember that the radius = 1/2 of the diameter.
7). The volume of a cylinder is
(pi) (radius²) (height) .
Divide the juice in the container by the volume of one can,
to get the number of cans he can fill.
8). The volume of a cone is
(1/3) (pi) (radius of the round bottom)² (height) .
He starts with a small cone, he then adds clay to it to make it higher.
The question is: How much clay does he ADD to the short one,
to make the bigger one ?
Use the formula to find the volume of the short one.
Use the formula again to find the volume of the bigger one.
Then SUBTRACT the smaller volume from the bigger volume.
THAT's how much clay he has to ADD.
Notice that the new built-up cone has the same radius
but more height than the first cone.
_______________________________________
Don't worry if you don't understand this.
The answer will be this number:
(1/3) (pi) (radius²) (height of the big one minus height of the small one).
Answer:
a. or c.
Step-by-step explanation:
.18 21/5 27
18 10/ 5 12
Answer:he will use 45 minutes to burn 540 calories . he spend a total of 50 minutes ie including 5 minutes of rest.
Step-by-step explanation: 1 minute burns 12 calories
Therefore 540÷12 = 45 minutes plus 5 minutes of rest = 50 minutes.
