To find where on the hill the canonball lands
So 0.15x = 2 + 0.12x - 0.002x^2
Taking the LHS expression to the right and rearranging we have -0.002x^2 + 0.12x -
0.15x + 2 = 0.
So we have -0.002x^2 - 0.03x + 2 = 0
I'll multiply through by -1 so we have
0.002x^2 + 0.03x -2 = 0.
This is a quadratic eqn with two solutions x1 = 25 and x2 = -40 since x cannot be negative x = 25. The second solution y = 0.15 * 25 = 3.75
Answer:
31
Step-by-step explanation:
First type of clay required 3 cups of flour per batch
She made 5 batches
5 * 3 = 15
So she used 15 cups of flour for the first type of clay
Second kind of clay required 4 cups of flour per batches
She made 4 batches
4 * 4 = 16
So she used 16 cups of flour for the second type of clay
we now add the total number of cups of flour used for each type of clay
16 + 15 = 31
She used a total of 31 cups of flour
Answer:
V = a²b³ + acb² units³
Step-by-step explanation:
The volume of a rectangular prism is given by :
V = l×b×h
Here, l = b² units
b = aunits
h = ab+c units
So, the volume of the prism is given by :
V = b² × a × (ab+c)
= ab²(ab+c)
= a²b³ + acb²
Hence, the required volume is a²b³ + acb² units³.
Answer:
84
Step-by-step explanation:
Let the first digit = x
Let the second digit =y
x + y = 12
x + 4 = 3*y
===========
From the second equation, we learn that x = 3y - 4
Put that into the first equation.
3y - 4 + y = 12 Combine the left side
4y - 4 = 12 Add 4 to both sides
4y = 16 Divide by 4
4y/4 = 16/4
y = 4
=================
x + 4 = 12
x + 4 - 4 = 12-4
x = 8
So the number is 84
Answer:
y²/324 -x²/36 = 1
Step-by-step explanation:
Where (0, ±b) are the ends of the transverse axis and y = ±(b/a)x describes the asymptotes, the equation of the hyperbola can be written as ...
y²/b² -x²/a² = 1
<h3>Application</h3>
Here, we have transverse axis endpoints of (0, ±18) and asymptotes of y = ±3x, so we can conclude ...
b = 18
b/a = 3 ⇒ a = 18/3 = 6
The equation of the hyperbola in standard form is ...
y²/324 -x²/36 = 1
