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balandron [24]
3 years ago
13

the amount of gasoline used by a car varies jointly as the distance travelled and the square root of the speed.Suppose a car use

d 25 liters on a 100 km trip at 100kph,about how many liters will it use on 1000 km trip at 64 kph?​
Mathematics
1 answer:
klemol [59]3 years ago
4 0

Answer:

200 litres

Step-by-step explanation:

let g be gasoline used, d the distance travelled and s the speed, then the equation relating the quantities is

g = kd\sqrt{s} ← k is the constant of variation

To find k use g = 25, d = 100 and s = 100, then

25 = k × 100 × \sqrt{100} = k × 100 × 10 = 1000k ( divide both sides by 1000 )

0.025 = k

g = 0.025d\sqrt{s} ← equation of variation

When d = 1000 and s = 64, then

g = 0.025 × 1000 × \sqrt{64} = 0.025 × 1000 × 8 = 200

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Two sides of a triangle are 8 m and 9 m in length and the angle between them is increasing at a rate of 0.06 rad/s. Find the rat
Lelechka [254]
<h2>Rate at which area is increasing is 1.08 m²/s.</h2>

Step-by-step explanation:

Area of triangle is with side a and b and angle C between them is given by

                             A = 0.5 ab SinC

Here we need to find how area changes with  a and b fixed and C is changing,

                       \frac{dA}{dt}=\frac{d}{dt}\left (0.5 absinC\right )\\\\\frac{dA}{dt}=0.5ab\frac{d}{dt}\left (sinC\right )\\\\\frac{dA}{dt}=0.5abcosC\frac{dC}{dt}

We have

                 a = 8 m

                 b = 9 m

                 C=\frac{\pi}{3}rad\\\\\frac{dC}{dt}=0.06rad/s

Substituting

                 \frac{dA}{dt}=0.5\times 8\times 9\times cos\left ( \frac{\pi}{3}\right )\times 0.06\\\\\frac{dA}{dt}=1.08m^2/s

Rate at which area is increasing is 1.08 m²/s.

4 0
3 years ago
3x + y = 5<br><br> 2x - 2y = -2
Vesnalui [34]

Answer:

Solving the system of equations:

x: 1

y: 2

Step-by-step explanation:

Plug it in to see if it is right, to make sure of course.  Better to be safe than sorry.

7 0
2 years ago
Read 2 more answers
Given z=4+3i evaluate z​
DerKrebs [107]

Answer:

5

Step-by-step explanation:

Assuming we want to evaluate |z|, given that, z=4+3i.

Then, by definition of modulus,

|x + yi|  =  \sqrt{ {x}^{2} +  {y}^{2}  }

|4+ 3i|  =  \sqrt{ {4}^{2} +  {3}^{2}  }

|4+ 3i|  =  \sqrt{ 16+  9 }  \\ |4+ 3i|  =  \sqrt{25 }  \\ |4+ 3i|  = 5

Therefore the modulus be of the given complex number is 5 units

5 0
3 years ago
Y=2x+5 y=3x−1 solve by subsitution
loris [4]

Answer:

(6,17)

Step-by-step explanation:

2x+5=3x-1

-3x        -3x

-x+5=-1

-5      -5

-x=-6

^divided by -1 on both sides

x=6

y=2x+5

y=(2)(6)+5

y=17

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2 years ago
Nicole has a 10 m ball of string. She cuts 6 lengths of 40 cm each, How much string does she use?​
amid [387]

answer is 760 m left

4 0
3 years ago
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