All categories

3 years ago

Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter

Mathematics

2 answers:

prisoha [69]3 years ago

6 0

Phil has 24 more rocks thank petter does

Lilit [14]3 years ago

3 0

Phil have 24 more rocks than Peter

You might be interested in

Graph g(x)=−x 2 −6x−6

Nina [5.8K]

Here's the graph.

The vertex is at (-3, 3), and it goes through points (-2, 2), (-4, 2), (-1, -1), (-5, -1).

3 0

3 years ago

Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19

Katen [24]

$x''+4x'+53x=15$

has characteristic equation

$r^2+4r+53=0$

with roots at $r=-2\pm7i$ . Then the characteristic solution is

$x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)$

For the particular solution, consider the ansatz $x_p=a_0$ , whose first and second derivatives vanish. Substitute $x_p$ and its derivatives into the equation:

$53a_0=15\implies a_0=\dfrac{15}{53}$

Then the general solution to the equation is

$x=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)+\dfrac{15}{53}$

With $x(0)=8$ , we have

$8=C_1+\dfrac{15}{53}\implies C_1=\dfrac{409}{53}$

and with $x'(0)=-19$ ,

$-19=-2C_1+7C_2\implies C_2=-\dfrac{27}{53}$

Then the particular solution to the equation is

$\boxed{x(t)=\dfrac1{53}e^{-2t}(409cos(7t)-27\sin(7t)+15)}$

8 0

3 years ago

Calling a Math Genius!!! What is the incorrect Step?

Pie

When you divide something by 3/4, there's no way something can decrease, unless the number is a fraction below 3/4.

Since in Step 2, they divided 27 by 3/4, but ended up with 20 1/4, that means that they got step 2 wrong, because 27 / (3/4) is equal to 27 * 4/3 = 36

(This is because dividing by a fraction is the same thing as multiplying by the reciprocal of the fraction.)

So therefore they got Step 2 wrong.

3 0

3 years ago

A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize reven

Cerrena [4.2K]

Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y) = $100x-34x^2+5xy+50y+3xy-16y^2$