GRADE 9 MATH:
1 answer:
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Step-by-step explanation:
Volume of a sphere is
plug in 70 ft for the radius to get 1,436,755 cubic ft then divide that by 4 since the prompt describes a quarter sphere, giving you a tank volume of 359,189 cubic ft.
Volume of a cylinder is
from the second prompt we know the tanks are identical since they are said to be congruent which means the hight and radius are the same. Plug in 120 f for h and 35 ft for r to get the volume of a cylinder and then divide that by 2 to get the volume of a single tank. the volume of both tanks would be
To show tank model is a sixth of the original so you divide the radius by 6 and perform the same calculation as in the first portion of the problem ro get the volume a quarter sphere
To get the percentage of the model relative to the original you divide the models volume by the full scale volume
which is less than 1% of the full scale volume.
Remember pemdas
simpliify pathentsees, exponents then multiply divide add subtract
some exponential laws
![(xyz)^m=[(x)^m][(y)^m][(z)^m]](https://tex.z-dn.net/?f=%28xyz%29%5Em%3D%5B%28x%29%5Em%5D%5B%28y%29%5Em%5D%5B%28z%29%5Em%5D)
we have
(-5m^2q)^2(-3m^3q)
do each seperately
(-5m^2q)^2=
[(-5)^2][(m^2)^2][(q)^2]=
[25][m^4][q^2]=
25m^4q^2
second part
(-3m^3q)^3=
[(-3)^3][(m^3)^3][(q)^3]=
[-27][m^9][q^3]=
-27m^9q^3
so we multiply them together
(25m^4q^2)(-27m^9q^3)=
(25)(m^4)(q^2)(-27)(m^9)(q^3)=
(25)(-27)(m^4)(m^9)(q^2)(q^3)=
(-675)(m^13)(q^5)=
-675m^13q^5
answer is first one
simpliify pathentsees, exponents then multiply divide add subtract
some exponential laws
we have
(-5m^2q)^2(-3m^3q)
do each seperately
(-5m^2q)^2=
[(-5)^2][(m^2)^2][(q)^2]=
[25][m^4][q^2]=
25m^4q^2
second part
(-3m^3q)^3=
[(-3)^3][(m^3)^3][(q)^3]=
[-27][m^9][q^3]=
-27m^9q^3
so we multiply them together
(25m^4q^2)(-27m^9q^3)=
(25)(m^4)(q^2)(-27)(m^9)(q^3)=
(25)(-27)(m^4)(m^9)(q^2)(q^3)=
(-675)(m^13)(q^5)=
-675m^13q^5
answer is first one