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gulaghasi [49]
1 year ago
8

The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreas

ed by 1, the number obtained is 3/2. Find the fraction.
Mathematics
1 answer:
MA_775_DIABLO [31]1 year ago
3 0

Answer:\frac{13}{21}

Step-by-step explanation:

2( N+ 17) = 3 (N +7)

2N+ 34= ·3N+ 21

N= 13

D= N+8 = 13+8 = 21

Fraction is \frac{13}{21}

When Im using N is equal to numerator and D for denominator, in order to get the fraction we substitute and the results combine in the fraction like this  \frac{N}{D}

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The answer would be 10x+5y=100
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2 years ago
Find g−1(x) when g(x)=35x−9.
lana [24]

Answer: -(2x)/(5)-9

Step-by-step explanation:

4 0
3 years ago
Can someone explain step by step how to do this problem? Thanks! Calculus 2
Ganezh [65]

Answer:

  1.314 MJ

Step-by-step explanation:

As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.

There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.

The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.

<h3>Mass of water</h3>

The mass of the water being raised is the product of the volume of the cone and the density of water.

The cone volume is ...

  V = 1/3πr²h . . . . . . for radius 2 m and height 8 m

  V = 1/3π(2 m)²(8 m) = 32π/3 m³

The mass of water in the cone is then ...

  M = density × volume

  M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg

<h3>Center of mass</h3>

The center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.

<h3>Easy Way</h3>

The discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...

  W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J

<h3>Hard Way</h3>

As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.

  V(y) = (32π/3)(y/8)³

The differential volume at height y is the derivative of this:

  dV = π/16y²

The work done to raise this volume of water to a height of 10 m is ...

  (9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J

The total work done is the integral over all heights:

  \displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}

It takes about 1.31 MJ of work to empty the tank.

8 0
1 year ago
The sum of m and 10
GREYUIT [131]

Answer:

  1. m + 10
  2. c - 24
  3. 8 + 12
  4. (3×7) - 5
  5. (7 + a) × 6
  6. y ÷ (-5)
  7. (x - y) ÷ 3
  8. {(a + b)}^{2}  \div 3c
3 0
2 years ago
A high school senior applies for admission to college A and to college B. He estimates that the probability of his being admitte
Fiesta28 [93]

The probability that he will be rejected to at least one of the colleges is 0.51.

Given probability that he will admit in A is 0.7, probability that he will not be admit in B is 0.5, probability that atleast one of his applications got rejected is 0.6.

We have to find the probability that he will be rejected to at least one of the colleges.

Probability that he will admit in A =0.7

Probability that he will not admit in A=1-0.7=0.3

Probability that he will not admit in B =0.5

Probability that he will admit in B=1-0.5=0.5

Probability  that he will be rejected to at least one of the colleges=probability that he will admit in A* probability that he will not admit in B+ probability that he will admit in B* probability that he will not admit in A+ probability that he will not admit in A* probability that he will not admit in B

=0.7*0.5+0.5*0.3+0.5*0.3

=0.35+0.15+0.15

=0.51

Hence the probability that he will be rejected to at least one of the colleges is 0.51.

Learn more about probability at brainly.com/question/24756209

#SPJ4

4 0
2 years ago
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