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Rufina [12.5K]
3 years ago
15

\times \sqrt{75} " alt=" \sqrt{27} \times \sqrt{75} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Harman [31]3 years ago
5 0

Answer:

44.95

Step-by-step explanation:

\sqrt{27}  \times  \sqrt{75  }  \\  = 5.19 \times 8.66 \\ 44.9454

Two decimal places = 44.95

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Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60
TEA [102]

Answer: the rate at which the distance between the boats is​ increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

6 0
3 years ago
The slope of the line is
Nataliya [291]

ANSWER:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

HOPE THIS HELP

3 0
3 years ago
What are the roots of the equation?
Mariana [72]

Answer:

3x2

Step-by-step explanation:

because it is

4 0
3 years ago
The path followed by a roller coaster as it climbs up and descends down from a peak can be modeled by a quadratic function, wher
Romashka [77]

Answer:

y = -0.1x^2 + 250 ft

Step-by-step explanation:

Because this quadratic equation would have the curve-down form of:

y = -ax^2 + b

where a and b are positive coefficient.

If we let the peak (250 ft) of the curve be at x = 0. Then

y = -a0^2 + b = 250

b = 250

Also at the begins and ends, thats where y = 0, the 2 points are separated by 100 ft. So let the begin at -50 ft and the end at 50ft. We have

-a(\pm 50)^2 + 250 = 0

-a2500 = -250

a = 250/2500 = 0.1

Therefore, the model quadratic equation of our path would be

y = -0.1x^2 + 250 ft

8 0
3 years ago
Plz answer these questions without putting links and files
kotykmax [81]

Answer:

11/8 and 21/16

Step-by-step explanation:

3 x 1 = 3

4 x 2= 8

3/8+3/4(convert to eighth's)

3/8+6/8=11/8

1 1/8 = 9/8

9 x 1 = 9

8 x 2 = 16

9/16+3/4(convert to sixteenth's)

9/16+12/16

21/16

---

hope it helps

8 0
3 years ago
Read 2 more answers
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