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3 years ago

A line segment has the endpoints P(-7, 6) and Q(-3, 9). Find the coordinates of its

Mathematics

1 answer:

Svet_ta [14]3 years ago

8 0

Answer:

$MP= (-5,7.5 )$

Step-by-step explanation:

$MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )$

$MP= (\frac{-7+-3}{2} )(\frac{6+9}{2} )$ -7+-3= -10 6+9=15

$MP= (\frac{-10}{2} )(\frac{15}{2} )$ -10/2=-5 15/2=7.5

$MP= (-5,7.5)$

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HELPPPPPPPPPPPPPPPPPPPPP

Tpy6a [65]

Answer:

Step-by-step explanation:

its a rational number because it isn't 0 and the others are incorrect i think

7 0

3 years ago

Read 2 more answers

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0

3 years ago

Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital am

zheka24 [161]

SOLUTION

We have been given the equation of the decay as

$\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}$

So we are looking for the time

Plugging the values into the equation, we have

$\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}$

Taking Ln of both sides, we have

$\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}$

Hence the answer is 4308 to the nearest year

8 0

1 year ago

Let f(x) represent a function.

STatiana [176]

Answer:

For $f(x+\frac{5}{4})$ , $f(x)$ is translated $\frac{5}{4}$ units left.

For $f(x)-\frac{5}{4}$ , $f(x)$ is translated $\frac{5}{4}$ units down.

Step-by-step explanation:

The transformation of $f(x)\rightarrow f(x+C)$ means that the graph shift to left by C units if C is positive number and shifts to right by C units if C is a negative number.

The transformation of $f(x)\rightarrow f(x)+C$ means that the graph shifts up by C units if C is positive number and shifts down by C units if C is a negative number.

Here, in the transformation of $f(x)\rightarrow f(x+\frac{5}{4}),C = \frac{5}{4}>0$ , so, the function translates left by $\frac{5}{4}$ units.

Similarly, in the transformation of $f(x)\rightarrow f(x)-\frac{5}{4},C = -\frac{5}{4}$ , so, the function translates down by $\frac{5}{4}$ units.

3 0

3 years ago

8.4 gallons of gas for $23.94. Which equation can be used to determine the price of each gallon of gas?

mojhsa [17]

Here is the equation: (gas=g)

8.5g= 23.94

All you need to do is the inverse of multiplication on the other side. (division)

23.94/8.5= 2.81647.....

g= 2.82 (rounded to the hundredths place)

I hope this helps!
~kaikers

6 0

4 years ago