Answer:
Step-by-step explanation:
<u>Equation of a Circle</u>
A circle of radius r and centered on the point (h,k) can be expressed by the equation
We are given the equation of a circle as
Note we have corrected it by adding the square to the y. Simplify by 3
Complete squares and rearrange:
We can see that, if r=4, then
Or, equivalently
There are two solutions for 
:
Keeping the positive solution, as required:
A, F, and G.
The others have breaks in the range or don’t include all real numbers.
Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
Answer:
Step-by-step explanation:
From the given information, it is clear that the shape of ant form is rectangular prism.
Let us write formula for volume of rectangular prism (ant form)
V = l x w x h
Use the formula to write an equation.
Plug V = 375, w = 2.5 and l = 15
375 = 15 x 2.5 x h
375 = 37.5 x h
Divide both sides of the equation by 37.5
375/37.5 = (37.5 x h)/37.5
10 = h
Hence, the height of the form is 10 inches.
You can apply the Pythagorean theorem:
a^2 + b^2 = c^2
c is the longest side of the triangle
2.2^2 + 4.2^2 = 6.7^2
4.84 + 17.64 = 44.89
22.48 =/= 44.89
That is not a right triangle
