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mars1129 [50]
3 years ago
6

Calculate the magnitude of the gravitational field of the moon at the location of Earth, in meters per square second.

Mathematics
1 answer:
givi [52]3 years ago
7 0

Answer:

Step-by-step explanation:

We need to find magnitude of acceleration due to gravity on earth surface due to moon

g_{m}=\frac{GM}{R^2}

where M=mass of moon

R=distance between moon and earth

G=gravitational constant

G=6.673\times 10^{-11}\ N-m^2/kg^2

M=7.35\times 10^{22}\ kg

R=3.84\times 10^8\ m

a_m=\frac{6.673\times 10^{-11}\times 7.35\times 10^{22}}{(3.84\times 10^8)^2}

a_m=3.33\times 10^{-5}\ m/s^2

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Solve the following using Substitution method<br> 2x – 5y = -13<br><br> 3x + 4y = 15
Digiron [165]

\huge \boxed{\mathfrak{Question} \downarrow}

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\left. \begin{array}  { l  }  { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.

  • To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

2x-5y=-13, \: 3x+4y=15

  • Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

2x-5y=-13

  • Add 5y to both sides of the equation.

2x=5y-13

  • Divide both sides by 2.

x=\frac{1}{2}\left(5y-13\right)  \\

  • Multiply \frac{1}{2}\\ times 5y - 13.

x=\frac{5}{2}y-\frac{13}{2}  \\

  • Substitute \frac{5y-13}{2}\\ for x in the other equation, 3x + 4y = 15.

3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15  \\

  • Multiply 3 times \frac{5y-13}{2}\\.

\frac{15}{2}y-\frac{39}{2}+4y=15  \\

  • Add \frac{15y}{2} \\ to 4y.

\frac{23}{2}y-\frac{39}{2}=15  \\

  • Add \frac{39}{2}\\ to both sides of the equation.

\frac{23}{2}y=\frac{69}{2}  \\

  • Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

\large \underline{ \underline{ \sf \: y=3 }}

  • Substitute 3 for y in x=\frac{5}{2}y-\frac{13}{2}\\. Because the resulting equation contains only one variable, you can solve for x directly.

x=\frac{5}{2}\times 3-\frac{13}{2}  \\

  • Multiply 5/2 times 3.

x=\frac{15-13}{2}  \\

  • Add -\frac{13}{2}\\ to \frac{15}{2}\\ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

\large\underline{ \underline{ \sf \: x=1 }}

  • The system is now solved. The value of x & y will be 1 & 3 respectively.

\huge\boxed{  \boxed{\bf \: x=1, \: y=3 }}

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The sum of 11.6 and 4.1 by rounding each number to the nearest whole.
Karo-lina-s [1.5K]
11.6 rounded to the nearest whole is 12 and 4.1 rounded to the nearest whole is 4 (rule is if the decimal [or number in general] is 4 or lower, the whole stays the same and if the number is 5 or higher, the whole goes up by one). 12+4=16
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gregori [183]

Answer:

\large\boxed{-8\sqrt9=-24}

Step-by-step explanation:

\sqrt{a}=b\iff b^2=a\\\\\sqrt9=3\ \text{because}\ 3^2=9\\\\-8\sqrt9=-8(3)=-24

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WARRIOR [948]

Answer:

a) only extreme values are used in its calculation.

Step-by-step explanation:

In a data set, the range is given by the subtraction of it's highest value by it's lowest value.

The disadvantage is that it gives a high weight to extreme values, not focusing on central values. So the correct answer is given by option a

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marshall27 [118]

Answer:

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Step-by-step explanation:

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