Answer:
42.42in³
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cone
Step one
We know that the volume of a cone is
V= 1/3πr²h
Given data
Diameter d= 6 inches
Radius r= diameter/2= 6/2= 3 inches
Height h = 4.5 inches
Step two
Substituting our given data we have
Volume = 1/3*3.142*3²*4.5
V= 1/3*3.142*9*4.5
V= 127.251/3
V= 42.42in³
Answer:
305
Step-by-step explanation:
We are adding 3 each time
5+3 = 8
8+3 = 11
The formula for an arithmetic sequence is
an = a1+d(n-1) where a1 is the first term and d is the common difference
an = 5+3(n-1)
We want the 101 term
a101 = 5 +3(101-1)
= 5+3(100)
= 5+300
= 305
Solve by Factoring x^(2/3)-7x^(1/3)+10=0
x
2
3
−
7
x
1
3
+
10
=
0
x
2
3
-
7
x
1
3
+
10
=
0
Rewrite
x
2
3
x
2
3
as
(
x
1
3
)
2
(
x
1
3
)
2
.
(
x
1
3
)
2
−
7
x
1
3
+
10
=
0
(
x
1
3
)
2
-
7
x
1
3
+
10
=
0
Let
u
=
x
1
3
u
=
x
1
3
. Substitute
u
u
for all occurrences of
x
1
3
x
1
3
.
u
2
−
7
u
+
10
=
0
<h3>Answer:</h3>
301.6 cubic meters
<h3>Step-by-step explanation:</h3>
A cylinder is a shape with straight sides with circular or oval cross-sections. We know that the cylinder in the question must be a circular cylinder due to its radius description.
Volume Formula
A circular cylinder has a volume of 
. In this equation, V is the volume, r is the radius, and h is the height. The question tells us that r=4m and h=6m. So, we can plug these values into the formula.
Solving for Volume
To solve plug the values into the formula and rewrite the equation.
Next, apply the exponents.
Then, multiply the constants.
Finally, multiply the remaining terms. Remember to use the pi button on the calculator and not an estimation to get a more exact value.
Make sure your answer is rounded to the correct digit. This means that the volume must be 301.6 cubic meters.
So this one is a little tricky because in order to solve you need to combine like terms. The only problem is that two fractions don't have the same denominator.
This is what you do.
2/3 - 1/9
= (2*9) - (1*3) / 3*9
= 18 - 3 / 27
= 15/ 27
Simplify.
5/9 + y = 7/9
Now since you need to isolate the variable you have to subtract 5/9 from both sides. Since the denominator is the same you can just subtract the numerator.
So y = 2/9
I hope this helps love! :)
