Part 1:
180 = 5p+98 + 9p-2
180 = 14p + 96
84 = 14p
6 = p
part 2:
angle S will be the same as angle Q, so:
9p-2
9(6)-2
54-2
M
Answer: On the 29th day
Step-by-step explanation:
According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.
On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.
The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are
lilypads on the 30th, and
lilypads on the 29th. This can be deduced multiplying succesively by 2.
Answer: x^2 + y^2 -10y = 0
Step-by-step explanation:
Cartesian coordinates, also called the Rectangular coordinates, isdefined in terms of x and y. So, for the problem θ has to be eliminated or converted using basic foundations that are described by the unit circle and the right triangle trigonometry.
r= 10sin(θ)
Remember that:
x= r × cos(θ)
y= r × sin(θ)
r^2= x^2 + y^2
Multiply both sides of the equation by r. This will give:
r × r = 10r × sin(θ)
r^2 = 10r × sin(θ)
x^2 + y^2= 10r × sin(θ)
Because y= r × sin(θ), we can make a substitution. This will be:
x^2 + y^2= 10y
x^2 + y^2 -10y = 0
The above equation is the Rectangular coordinate equivalent to the given equation.
(9x^4-13x^3-x-7)+(7x^3-2x+1)=
9x^4-13x^3-x-7+7x^3-2x+1=
9x^4+(-13+7)x^3+(-1-2)x-7+1=
9x^4+(-6)x^3+(-3)x-6=
9x^4-6x^3-3x-6
Answer: Option <span>D.)9x^4−6x^3−3x−6</span>
Answer:
14.52 seconds.
Step-by-step explanation:
We have been given that the height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation
. We are asked to find the time, when the rocket will hit the ground.
We know that the rocket will hit the ground, when height will be 0. So to find the time when rocket will hit the ground, we will substitute
in our given equation as:

Let us solve for x using quadratic formula.








Upon rounding to nearest 100th of second, we will get:

Since time cannot be negative, therefore, the rocket will hit the ground after 14.52 seconds.