MATHEMATICS HIGH SCHOOL

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 1

Answer:

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,

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

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

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How do you solve (2z-3)(4z-7)=0

Answers

The key to this is to realize that if EITHER quantity in parentheses is zero,
then the whole left side is zero, and the equation is true.

First quantity: (2z-3). If this is zero, then the whole equation is true.

   2z - 3 = 0
Add 3 to each side: 2z    = 3
Divide each side by 2: z = 3/2 or 1.5

Second quantity: (4z-7). If this is zero, then the whole equation is true.

   4z - 7 = 0
Add 7 to each side: 4z    = 7
Divide each side by 4: z = 7/4 or 1.75

So the original equation has two solutions:

   z = 1.5
and
   z = 1.75 .

There are two values of z in this question. (2z - 3)
-3 / 2 = -1.5
-1.5 x -1 = 1.5

(4z - 7)
-7 / 4 = -1.75
-1.75 x -1 = 1.75

z = 1.5 or 1.75

What is the volume of a cylinder using pi or 3.14 which the height being 8 and the width being 2

Answers

Answer:

The volume of the cylinder is 25.12

Step-by-step explanation:

The width is the diameter in the circle of the base

radius = half of diameter

r = 2/2 = 1

To calculate the volume of a cylinder we have to use the following formula:

v = volume

h = height = 8

π = 3.14

r = radius = 1

v = (π * r²) * h

we replace the unknowns with the values we know

v = (3.14 * (1)²) * 8

v = (3.14 * 1) * 8

v =3.14 * 8

v = 25.12

The volume of the cylinder is 25.12

The farmer's market has a total of 98 tents. the ratio of food tents to retail tents is 9:5.

a. Write a system of linear equations that represent this situation.

b. How many food tents are at the market?

c. How many retail tents are at the market?

Answers

Answer:

Let x represents the food tents and y represents the retail rents.

As per the given statement: The farmer's market has a total of 98 tents.

⇒ $x + y = 98$ ......[1]

Also, it is given that the ratio of food tents to retails tents is 9 : 5.

⇒ $(x)/(y) = (9)/(5)$

By cross multiply, we have;

5x = 9y

Divide both sides by 5 we get;

$x = (9)/(5)y$

Substitute this value x in equation [1] to solve for y;

$(9)/(5)y + y = 98$

Combine like terms;

$(14)/(5)y = 98$

Multiply both sides by $(5)/(14)$ we get;

$y =98 * (5)/(14) = 7 * 5 = 35$

Substitute the value of y= 35 in $x = (9)/(5)y$ to solve for x;

$x = (9)/(5) * 35 = 9 * 7 = 63$

(a)

System of linear equation that represents situation is:

$x + y = 98$

$x = (9)/(5)y$

(b)

As x represents the food tents.

Therefore, 63 food tents are at the market.

(c)

y= 35 retail tents are at the market.

F+r=98
5f=9r
F is food tents, r is retail tents.
Plug in f=9/5r to the top to get 14/5r=98. Then 2/5r=14. So r=35 and f=9/5*35=63.

to multiply a number by 12, Carter likes to multiply the number by 10 and then multiply it by 2 and add the product. Write an expression with parenthesis how carter would solve 12×16

Answers

Since carter multiplies by 10 and then by 2 and adds the two, here we have been given 16 * 12

Step 1: Carter would first multiply the number by 10. This would be = 16*10

Step 2: Carter would multiply the number by 2. This would be = 16*2

Step 3: He would add the two. This would be = (16*10) + (16*2)

Carter's solution would be:

=16*12

=(16*10) + (16*2)

= 160 + 32

= 192

In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.

Answers

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

$\sin \angle P=\frac{\text{Opposite leg}}{\text{Hypotenuse}}=(MN)/(MP)\n \nMN=MP\sin \angle P\n \nMN=4\sin 21^(\circ)\approx 1.43\ cm$

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

$\cos \angle M=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}=(MH)/(MN)\n \nMH=MN\cos \angle M$

In the right triangle, two acute angles are always complementary, so

$m\angle M=90^(\circ)-m\angle P=90^(\circ)-21^(\circ)=69^(\circ)$

Thus,

$MH=1.43\cos 69^(\circ)\approx 0.51\ cm$

PLEASE ANSWER ASPAA The x-intercept of the equation 2y – x = -6 is: 3. -3. 6. None of these choices are correct.

Answers

Answer:

x = 6

Step-by-step explanation:

The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:

2(0) - x = -6

0 - x = -6

-x = -6

x = 6

Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.

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