What is the equation in point-slope form for the line parallel to y=6x-3 that contains P(-9,7)

It’s timed please help

love history [14]

Answer:

4 is included in the domain

Step-by-step explanation:

6 0

3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

4 years ago

Rob owes Debra $36 and pays her 1/3 of what he owes. How much does he now owe?

wolverine [178]

Answer:

24

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

PLEASE HELP! 35 POINTS

nignag [31]

no solution, they are all the same line

4 0

3 years ago

A.Sum of integer and its additive inverse is ___________.B.Sum of -22 and -44 is ______________.C.-36 ÷ ( ___)=-9d._________ is

Ede4ka [16]

Answer:

A. 0

B. -66

C. 4

D. 998

E. -12

Step-by-step explanation:

A. By definition, the sum of anything and its additive inverse is zero.

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B. If you have trouble with sums, your calculator can help.

-22 + (-44) = -22 -44 = -66

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C. -36/x = -9 can be solved by multiplying by x and dividing by -9:

-36 = -9x

-36/-9 = x = 4

Since the product of the divisor and quotient is the dividend, dividing the dividend by either gives the other. Here, your dividend is -36 and your quotient is -9. To find the divisor, you can divide -36 by -9, as we did.

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D. The absolute value function changes the sign of negative numbers to positive:

|-998| = 998

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E. If you have trouble with sums, your calculator can help.

(−2)−[(−3)−(−7)−(−6)]

= -2 -(-3 +7 +6) = -2 -10 = -12

4 0

3 years ago