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3 years ago

What is the slope of the line passing through the points (6, 7) and (1, 5)?

Mathematics

2 answers:

Nookie1986 [14]3 years ago

7 0

Answer: it’s a fraction and it’s 2/5

Step-by-step explanation:

pochemuha3 years ago

6 0

The slope is 2/5, 5-7 divided by 1-6=2/5

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Find the minimum and maximum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f

nata0808 [166]

Via Lagrange multipliers:

$L(x,y,\lambd)=x^2y+x+y+\lambda(xy-5)$
$L_x=2xy+1+\lambda y=0$
$L_y=x^2+1+\lambda x=0$
$L_\lambda=xy-5=0$

$\underbrace{10}_{2xy}+1+\lambda y=0\implies \lambda=-\dfrac{11}y$
$xy=5\implies y=\dfrac5x\implies\lambda=-\dfrac{11}5x$

$\impliesx^2+1+\left(-\dfrac{11}5x\right)x=0\implies x^2=\dfrac56\implies x=\pm\sqrt{\dfrac56}$
$xy=5\implies y=\pm\sqrt{30}$

At these points, we get local minima of $f\left(\pm\sqrt{\dfrac56},\pm\sqrt{30}\right)=\pm2\sqrt{30}$ .

- - -

Another way to do this is to make $f(x,y)$ a function independent of $y$ , which is made possible by the constraint.

$xy=5\implies y=\dfrac5x$
$\implies f(x,y)=f\left(x,\dfrac5x\right)=F(x)=6x+\dfrac5x$
$\implies F'(x)=6-\dfrac5{x^2}=0\implies x=\pm\sqrt{\dfrac56}$

and so on.

8 0

3 years ago

Help asap!! 15 points!!

adoni [48]

Answer:

a) y = -500x + 130,000

b)67,500 gallons remaining

c) 260 hours

Step-by-step explanation:

Since water is being removed at a rate of 500 gallons per hour, the slope would be a negative.

a) y = -500x + 130,000

For<u> part b</u> input 125 for x:

y = -500(125) + 130,000

y = 67,500

There are 67,500 gallons remaining

For part c we are solving for the x intercept

0 = -500x + 130,000

Subtract 130,000 from both sides

-130,000 = -500x

x = 260

It will take 260 hours for the pool to completely drain

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3 years ago

Determine the range of the following graph:

vivado [14]

Answer:

3,6 I think is the range.

4 0

3 years ago

Find the interest on $6,000 at 5% for 1 year. I will give brainiest if correct

tino4ka555 [31]

Answer:

$300

Step-by-step explanation:

I = prt

I = 6000(.05)(1)

I = 300

6 0

3 years ago

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Sb plz help not much a lot of points!!!!! Plz help

Tatiana [17]

Answer:

10 months

Step-by-step explanation:

22x+80=30x

subtract both sides by 30x

-8x+80=0

then subtract 80 from both sides

−8x=−80

divide both sides by -8

x=10

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3 years ago

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