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Andre45 [30]
2 years ago
5

Please help

Mathematics
1 answer:
Firdavs [7]2 years ago
3 0

Answer:

(–10, –2), (6, 6)

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

<u><em>Verify each case</em></u>

case 1) (5, –4), (–2, 1)

substitute in the formula

m=\frac{1-(-4)}{-2-5}

m=\frac{1+4}{-2-5}

m=\frac{5}{-7}

m=-\frac{5}{7}  ----> the slope is negative

case 2) (6, –10), (2, 10)

substitute in the formula

m=\frac{10-(-10)}{2-6}

m=\frac{10+10}{2-6}

m=\frac{20}{-4}

m=-5  ----> the slope is negative

case 3) (–10, –2), (6, 6)

substitute in the formula

m=\frac{6-(-2)}{6-(-10)}

m=\frac{6+2}{6+10}

m=\frac{8}{16}

m=0.5  ----> the slope is positive

case 4) (5, –1), (–6, 6)

substitute in the formula

m=\frac{6-(-1)}{-6-5}

m=\frac{6+1}{-6-5}

m=\frac{7}{-11}

m=-\frac{7}{11}   ----> the slope is negative

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a dock is 5 feet above water. suppose you stand on the edge of the dock and pull a rope to a boat at a constant rate of 2 ft/s.
Firdavs [7]

Answer:

The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.

Step-by-step explanation:

The diagram of the situation described is shown in the attached image.

The distance of the boat to the dock along the water level at any time is x

The distance from the person on the dock to the boat at any time is y

The height of the dock is 5 ft.

These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.

According to Pythagoras' theorem

y² = x² + 5²

y² = x² + 25

(d/dt) y² = (d/dt) (x² + 5²)

2y (dy/dt) = 2x (dx/dt) + 0

2y (dy/dt) = 2x (dx/dt)

When the boat is 4 ft from dock, that is x = 4 ft,

The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s

The speed with which the boat is approaching the dock = (dx/dt)

Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock

When the boat is 4 ft from the dock, x = 4 ft.

And we can obtain y at that point.

y² = x² + 5²

y² = 4² + 5² = 16 + 25 = 41

y = 6.40 ft.

So, to the differential equation relation

2y (dy/dt) = 2x (dx/dt)

when x = 4 ft,

y = 6.40 ft

(dy/dt) = 2 ft/s

(dx/dt) = ?

2 × 6.40 × 2 = 2 × 4 × (dx/dt)

25.6 = 8 (dx/dt)

(dx/dt) = (25.6/8) = 3.20 ft/s.

Hope this Helps!!!

4 0
3 years ago
Given the function F(x)=3x+2 f(x)=8 find the following f(x)=8
sergiy2304 [10]
I believe the answer is 26. But I’m new to this I just learned this last week.
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3 years ago
Jacob mixes ⅓ cup of yellow paint for every ⅕ cup of blue paint to make green paint. How many cups of yellow paint are needed fo
Nana76 [90]

Answer:

\frac{5}{3} cups

Step-by-step explanation:

Jacob mixes \frac{1}{3} cup of yellow paint for every \frac{1}{5} cup of blue paint to make green paint.

The ratio of yellow paint to blue paint =  \frac{1}{3} : \frac{1}{5}

                                                              = 5:3

 \frac{1}{5} cup of blue paint =  \frac{1}{3} cup of yellow paint

 1 cup of blue paint =  \frac{1}{3} ÷ \frac{1}{5} cup of yellow paint

⇒ \frac{1}{3} ÷ \frac{1}{5}

⇒ \frac{5}{3}

Hence, For 1 cup of blue paint needed \frac{5}{3} cups of yellow paint.

8 0
3 years ago
5. When looking at a map, a student realizes that Birmingham is nearly due west of Atlanta, and Nashville is nearly due north of
leonid [27]

Answer: 250 mi

Step-by-step explanation:

Here we can think in a triangle rectangle:

The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.

And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.

Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.

Now we can apply the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse:

Then:

H = √(A^2 + B^2)

H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi

Then the estimated distance from Atlanta to Nashville is 250 mi

6 0
3 years ago
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Answer:

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Step-by-step explanation:

6 0
3 years ago
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