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.
X²+2x+3=(x²+2x+1)+2=(x+1)²+2
the graph of x²+2x+3 has a vertex at (-1,2), a symmetry line x=-1, go through the y axis at (0, 3), opening upward above y=2
Answer:
3 weeks
Step-by-step explanation:
Two puppies from the same litter are named Bruno Puppy Weight and Jasper. Their weights during the first weeks are plotted on the coordinate grid. At which age did Bruno and Jasper weigh the same?
Solution:
We can see that Bruno and Jasper weight is represented by a straight line. Let y represent the weight of the puppies in ounce and x represent the age in weeks.
For Bruno:
The line passes through (1, 10) and (5, 16), hence the equation of the line is:
For Jasper:
The line passes through (0, 12) and (3, 13), hence the equation of the line is:
To find the age at which both puppies weighed the same, we have to solve equation 1 and 2 simultaneously. Subtract equation 1 from 2:
-1.167x + 3.5 = 0
1.167x = 3.5
x = 3
Put x = 3 in equation (2)
y = (1/3)(3) + 12 = 13
The solution is (3, 13)
Therefore both Jasper and Bruno weigh the same weight of 13 ounce at 3 weeks of age
Answer:
7.
∠M=51°
8.∠ABC=125°
Step-by-step explanation:
when we extend one line of a triangle ,the external angle is equal to the sum of two opposite internal angles.
7.
151-2y=84+6y+3
151-2y=87+6y
151-87=6y+2y
64=8y
y=64/8=8
∠M=6y+3=6×8+3=48+3=51°
8.
20x-15=90+5x
20x-5x=90+15
15x=105
x=105/15=7
∠ABC=20x-15=20×7-15=140-15=125°
Answer:
Step-by-step explanation:
first athlete =28.65
second athlete=24.25
the first athlete jump - second athlete jump
28.65-24.25
= 4.40
the first athlete long jump then the second athlete
