A boat travels at 15 km/hr in still water. In travelling 45 km downstream from town A to town Bit completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?

Answers

Answer 1

Answer: Let the speed of river be x km/hr down stream.

Time = Distance / speed

Since river flows downstream, speed of boat down stream = Speed of boat + speed of river = (15 + x).

Since river flows downstream, speed of boat upstream = Speed of boat - speed of river = (15 - x).

Time Upstream - Time Downstream = 75 minutes

Time Upstream = 45 / (15 - x)

Time Downstream = 45 / (15 + x)

75 minutes = 75/60 = 5/4 hours

Time Upstream - Time Downstream = 75 minutes = 5/4 hours

45 / (15 - x) - 45 / (15 + x) = 5/4 Divide both sides by 45

1 / (15 - x) - 1 / (15 + x) = (5/4)*(1/45)

1 / (15 - x) - 1 / (15 + x) = 1/36

((15 + x) - (15 -x)) / (15-x)(15+x) = 1/36

(15 +x - 15 +x) / (15-x)(15+x) = 1/36

2x / (15-x)(15+x) = 1/36

(15-x)(15+x) = 2x*36

(15-x)(15+x) = 72x

225 - x² = 72x

0 = x² + 72x -225

x² + 72x -225 = 0 This is a quadratic function, use a calculator that can solve the function, by inputting the function.

x = 3, or -75. Since we are solving for speed, we can not have negative values.

x = 3 is the only valid solution.

Speed of the river = 3 km/hr downstream.

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What is the opposite and reciprocal of –1.8?Ο -1.8, 9/5

Ο 1.8, -5/9

Ο 1.8, 8.1

Ο 1.8, 5/9

Answers

Given a number "x" its opposite is "-x"
Given a number "x" its reciprocal is "-1/x"

-1.8
opposite=-(-1.8)=1.8
reciprocal=1/(-1.8)=-1/1.8=-0.5555....=-5/9

Answer: 1.8 , -5/9

The opposite number would be the same distance from zero on the number line in the opposite direction... -1.8 is 1.8 units from zero in the negative direction, so the opposite would be...

1.8 (in the positive direction)

The reciprocal refers to a fraction with the numerator and denominator flipped into the opposite position, so we need to convert to a fraction and then flip it.

-1.8 = -1 8/10 = -18/10 = -9/5 ... now flip it for the reciprocal

-9/5 turns into -5/9

So your answer is 1.8, -5/9

Jackyn thinks that negative 1/2 is greater than 1/4 because it is farther from zero on the number line. Is her thinking correct ? Explain

Answers

I think Jackyn is correct because 1/2 is half, which means it is .50. So 1/4 would be much smaller than .50 except if it was 2/4. The bigger the number is in negative, the smaller the number.

where G is a constant and M is the mass of the earth. Calculate the work done by the force of gravity on a particle of mass m as it moves radially from 7500 km to 9400 km from the center of the earth.

Answers

Answer:

$-2.0213* 10^(-7)GMm\text{ J}$

Step-by-step explanation:

Since, the force of gravity is,

$F = -(GMm)/(r^2)$

Where,

G = gravitational constant,

M = mass of earth,

m = mass of the particle,

r = distance of particle from centre of the earth,

∵ 7500 km = $7.5* 10^6$ meters

9400 km = $9.4* 10^6$ meters

Thus, work done by the force of gravity,

$W=\int_(7.5* 10^6)^(9.4* 10^6)F. dr$

$=-\int_(7.5* 10^6)^(9.4* 10^6)(GMm)/(r^2)dr$

$=GMm[(1)/(r)]_(7.5* 10^6)^(9.4* 10^6)$

$=GMm((1)/(9.4* 10^6)-(1)/(7.5* 10^6))$

$=GMm((7.5-9.4)/(9.4* 10^6))$

$=-GMm((1.9)/(9.4* 10^6))$

$\approx -2.0213* 10^(-7)GMm\text{ J}$

Where,

$G = 6.67408* 10^(-11) \text{ }m^3 kg^(-1) s^(-2)$

$M=5.972* 10^24 \text{ kg}$

8x^2+4x
FACTOR AND SHOW STEP BY STEOP PLEASE

Answers

Step-by-step explanation:

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The perimeter of a rectangle is 50 yards. The width is 1 more than one-half of the length. What are the dimensions of the rectangle?

Answers

Answer:

The length of the rectangle is 16 yards

The width of the rectangle is 9 yards

Step-by-step explanation:

The given parameters are;

The perimeter of the rectangle = 50 yards

The width, W of the rectangle = 1 + Length, L/2

Therefore we have;

W = 1 + L/2

2 × W + 2 × L = 50

2 × (1 + L/2) + 2 × L = 50

2 + L + 2·L = 50

3·L = 50 - 2 = 48

L = 48/3 = 16

The length, L = 16 yards

The width, W = 1 + L/2 = 1 + 16/2 = 1 + 8 = 9

The width, W = 9 yards.

Recall, $\pi$ is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, $\pi$ =c/d. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?

Answers

Though $\pi$ = $(c)/(d)$ , it is an approximate value. As we get an approximate value and not a fixed one, there is no contradiction. Mathematically,
$(c)/(d)$ = $(2 \pi r)/(2r)$ = $\pi$ .
Hence, no contradiction.

Yes, it is true that π = c / d . However, note here that c or the circumference is known by the equation c = 2πr. In finding the circumference, we take value of pi approximately, and hence there is no contradiction. However, even if the circumference is accurate, it will be an irrational number. Recall that an irrational number operated in any way results again into an irrational number.

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