Answer:
Step-by-step explanation:
The vertical displacement function is 
, where 
is measured in meters and 
in seconds. Ball hits the ground when 
. That is:
Whose roots can be found by using the General Formula for Second-Order Polynomials:
Solutions of this polynomial are:
Only the first root is physically consistent.
So when you're solving for x here and distribute 8 on the right side, it would look like this:
Now in order to solve for x, we know we have to get all the x's on one side of the equal sign. Let's get all our x's to the left side. Since the right side has a positive 8x, you need to subtract 8x on the right. But whatever you do to one side you must do to the other. So since we are subtracting 8x on the right, we need to do that on the left.
But we can't! Since both sides will cancel out to zero before x can be solved.
Therefore the answer is 0.
Hope that helps!
We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ =
π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.
R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14
a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³
b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂
</span>Vₐ = 3 × <span>
π r³
</span>Vₐ = 3 ×
3.14<span> (6.5 cm)³</span>
Vₐ = 3,449.3 cm³
c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V =
×100
V =
×100
V = 0.6666 ×100
V = 66.66%
Answer: $169
Step-by-step explanation: The expression 25 + 18 x 8 represents the amount she will pay if she participates for 8 months.
Multiply 18 x 8 to find the cost for 8 months. $18 x 8 = $144.
Now add $25 to $144, which equals $169
Congruent triangles are all the same. Given that the faces of a triangular pyramid are congruent then all its faces are the same. It is also good to note that this pyramid has 4 faces. Given that the surface area of the pyramid is 372m^2, the area of one face will be:
area=(total area)/(number of faces)
=372/4
=93 m^2
