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4 years ago

Two joggers are running toward each other. They start off being 5 miles apart. Joe, leaves at 7:00 AM and

Mathematics

1 answer:

saveliy_v [14]4 years ago

7 0

Answer: Hello mate!

the initial distance between Joe and Jack is 5 miles.

we know that Joe travels at 4 mph and jack travels at 5mph.

Now, let's define the 7:00 AM as our time zero, where the time is measured in hours.

We know that Joe starts running at t = 0h and Jack starts running at t = 0.5h

then the position equations are J1 for joe and J2 for Jack.

J1(t) = 4mph*t

J2(t) = 5mph*(t - 0.5h)

where the -0.5h appears because Jack starts 0.5h after.

If they run towards each other, then they will met when J1(t) + J2(t) = 5mi, wich means that between the two runned the 5 miles that separated them:

J1(t) + J2(t) = 4t + 5(t- 0.5) = 4t + 5t - 2.5 = 9t - 2.5 = 5

and now we want to isolate t

9t - 2.5 = 5

9t = 5 + 2.5 = 7.5

t = 7.5/9 = 0.8333.. hours

Then they well met 0.83 hours after the 7:00 Am

We also could write this in a more elegant way:

we know that one hour has 60 minutes, then a 0.83333.. of an hour has 0.83*60 = 50 minutes

Then they met at 7:50 AM

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Write the equation of the graphs below and explain

solniwko [45]

Answer:

y = 3√(x+3) -2

Step-by-step explanation:

The given points seem to match those of (half) a parabola that opens to the right. The parent function would be ...

x = y^2

or ...

y = √x . . . . . gives the upper half of the parabola only

It seems to have a vertical expansion by a factor of 3 and a translation of the vertex from (0, 0) to (-3, -2). The transformed function is then ...

y = 3√(x +3) -2

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We have transformed the parent function using ...

y = a·f(x-h) +k

where <em>a</em> is the vertical expansion factor, <em>h</em> is the horizontal translation, and <em>k</em> is the vertical translation.

5 0

4 years ago

The 3 × 3 matrix P satisfies the matrix equation P^2 = P.

riadik2000 [5.3K]

Answer: The answers are given below.

Step-by-step explanation: Given that a 3 × 3 matrix P satisfies the matrix equation P² = P.

We are to

(a) find the possibilities for the determinant of P.

(b) explain the reason behind there are no other possibilities.

(c) give an example of P, for each possible determinant.

(a) According to the given information, we have

$P^2=P\\\\\Rightarrow P^2-P=0\\\\\Rightarrow P(P-I)=0\\\\\Rightarrow P=0,~~~P=I.$

So, P can be either a zero matrix of order 3 or an identity matrix of order 3.

If P = 0, then det(P) = 0 and if P = I, then det(P) = 1.

Therefore the possible determinants of P are 0 and 1.

(b) There can be any other determinant other than 0 and 1, because if so, then the given equation P² = P will not be satisfied.

(c) If |P| = 0, then the matrix P can be can be of the form as follows:

$P=\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right] .$

If |P| = 1, the the matrix P can be of the form as follows :

$P=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] .$

Thus, all the parts are answered.

4 0

3 years ago

Resolver el siguiente sistema de ecuación:

snow_tiger [21]

Answer:

$x=-1\\y=4$

Step-by-step explanation:

$\frac{5x+2y}{3}=1$

$\frac{2x+y}{2}=1$

Vamos a utilizar el método de sustitución. Vamos a despejar la segunda ecuación por alguna de las variables. Elegiré la y porque esta sola.

$\frac{2x+y}{2}=1$

Vamos a empezar por eliminar ese 2 del denominador. Para hacer esto, multiplicamos por 2 ambos lados de la ecuación.

$2x+y=1*2$

$2x+y=2$

Como vamos a despejar la y, restamos 2x en ambos lados.

$y=2-2x$

Listo.

------------------------------------------------------------------------

Procedemos a reemplazar el valor de y en la primera ecuación.

$\frac{5x+2y}{3}=1$

$\frac{5x+2(2-2x)}{3}=1$

$\frac{5x+4-4x}{3} =1$

Procedemos a operar términos semejantes.

$\frac{x+4}{3} =1$

Nos deshacemos del 3 multiplicando.

$x+4=1*3\\x+4=3$

Restamos 4

$x=3-4\\x=-1$

-----------------------------------------------------------------------------

Una vez encontrado el valor de x, procedemos a reemplazar en cualquier ecuación para encontrar el valor de y. Usaré la segunda ecuación.

$\frac{2x+y}{2}=1$

$\frac{2(-1)+y}{2}=1$

Procedemos a resolver;

$\frac{-2+y}{2} =1$

Multiplicamos por 2.

$-2+y=1*2$

$-2+y=2$

Sumamos 2

$y=2+2\\y=4$

-------------------------------------------------------------------------------

Para comprobar que los valores son correctos, reemplazamos ambos valores en cualquier ecuación y el resultado debe ser igual.

Usaré la primera.

$\frac{5x+2y}{3} =1$

$\frac{5(-1)+2(4)}{3} =1$

Resolvemos;

$\frac{-5+8}{3} =1$

$\frac{3}{3}=1$

$1=1$

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4 years ago

Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint. The average

bagirrra123 [75]

The y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought. Therefore, option B is the correct answer.

Given that, Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint.

The average is (15 + 3x)/(3+x) per pint.

We need to find what quantity will be represented by the y-intercept of the graph.

<h3>How to find the y-intercept of the graph?</h3>

Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

Now, the graph of y=(15 + 3x)/(3+x)is given below.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (−5,0)

y-intercept(s): (0,5)

So, the y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought.

Therefore, option B is the correct answer.

To learn more about y-intercept visit:

brainly.com/question/14180189.

#SPJ1

7 0

1 year ago

What is the value of k? 11=−3k−22−8k

just olya [345]

11 = -3k - 22 - 8k....combine like terms on the right side
11 = -11k - 22 ...add 22 to both sides
11 + 22 = -11k
33 = -11k....divide both sides by -11
-33/11 = k
-3 = k <===

4 0

3 years ago

Read 2 more answers