Taking
gives
, so that the integral becomes
When
, we have
and from here we can substitute
to proceed from here.
Quick note: When we set
, we are implicitly enforcing
just so that the substitution can be undone later via
. But note that over this domain, we automatically guarantee that
, so the absolute value bars can be dropped immediately.
Answer:
(x + 9)(x4)
Step-by-step explanation:
So, the possible side
lengths of the quilt are (x + 9) and (x + 4) units.
9514 1404 393
Answer:
- ornament area = 379.8 cm²
- paint needed: 114 bottles
Step-by-step explanation:
The surface area of one cone with slant height s and radius r is ...
SA = πr² +πrs = πr(r+s)
For the cone that is half an ornament, the surface area is ...
SA = (3.14)(4.2 cm)(4.2 cm + 10.2 cm) = 189.9072 cm²
The area of one ornament is the area of two cones:
one ornament area = 2×189.9072 cm² ≈ 379.8 cm²
60 ornaments will be 120 cones, so will have a total surface area of ...
total area = 120(189.9072 cm²) = 22,788.864 cm²
__
If one bottle of paint will cover 201 cm², then the number of bottles of paint required is ...
(22788.864 cm²)/(201 cm²/bottle) ≈ 113.4 bottles
Answer:
About 131.95 (you may have to round up)
Step-by-step explanation:
Volume of a cone = pi(r^2)(h/3)
= pi(3^2)(14/3)
= pi(9)(4 & 4/5)
= pi(43.2)
If your teacher wants an exact number, you have to multiply 43.2 y whatever your teacher says to shorten pi to, usually 3.14. The about 131.95 is from 43.2*3.14 I think.
if you drop the radius to less than that, then the Area will also drop to less than 1 unit, in this case it happens to be a decimeter
