Answer:
D). 659.73 in^3.
Step-by-step explanation:
The volume of a cone = 1/3 π r^2 h
The volume of the large cone = 1/3 π 6^2 * 20 in^3.
The plane passes through the midpoint of the cone so the height of the small cone = 10 in
and the radius of this cone is 1/2 * 6 = 3 in.
The volume of the small cone = 1/3 π 3^2 * 10 in^3.
So the volume of the blue section
= 1/3 π 6^2 * 20 - 1/3 π 3^2 * 10
= 659.73 in^3.
Answer:
The inequality is;
p≤ 10.53
where 10.53 is the highest value she can spend on other stationery
Step-by-step explanation:
Here, we want to write an inequality
The amount she has to spend is 33
This means she can spend less than or equal to this amount
she has spent 22.47 and still has p to spend
Mathematically;
p + 22.47 ≤ 33
p ≤ 33-22.47
p ≤ 10.53
Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
Answer:
x = 35
Step-by-step explanation:
