If a 50 kg object is at a location 25,600 km from Earth’s center, what is the gravitational force exerted by the object on Earth? In what direction does that force act?

Answer:

[See Below]

Step-by-step explanation:

✦ Formula = √area

  ✧ √484 = 22

✦ Check: 22 x 22 = 484

So the side length is 22.

~Hope this helps Mate. If you need anything feel free to message me.

The graph of the equation y = \(2^{x}\) - 5 is obtained by shifting the graph of

y =\(2^{x}\)  downside by 5 units.

To find a graph of equation y = \(2^{x}\) - 5, we can start with the reference of the parent function y = \(2^{x}\) and also apply the necessary transformations.  Initiating with the graph of the parent function y =\(2^{x}\) - 5.

This is an exponential function that passes through the point( 0, 1) and has a positive pitch. Apply the transformation -5 units over. This means we shift the entire graph over by 5 units. The point( 0, 1) will now come( 0,-4).thus, the graph of the equation y =  \(2^{x}\)- 5 is attained by shifting the graph of y =  \(2^{x}\) downcast by 5 units. The factual shape of the graph will act as that of the parent exponential function, but it'll be shifted over by 5 units.

Learn more about transformations;

https://brainly.com/question/30469223

#SPJ4

The correct question is given below-

Graph the equation shown below by transforming the given graph of the parent function. y= \(2^{x}\) obtain  y=\(2^{x}\)-5.

The probability for a data point is less than is 0.8413.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

The mean(μ)=4

Standard deviation(σ)=1

(P<5)

From the figure, standard normal distribution curve probability which we have to find P<5

It is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

P(x=4)=x-μ/σ

=4-4/1=0

P(x=4)=50%

P(x<5)=P(x=4)+P(x=1)

=50%+34.13%

=0.8413

P(x<5)=0.8413

Therefore, the probability a data point is less than 5 is 0.8413.

For such more questions about Probability

https://brainly.com/question/30034780

#SPJ4

Answer:

well, took me some time but I did answer all of em

Answer:

5. The Answer is 45.

6. 75

7. 110

8. 30

9. 12

10. 4

11. 5

12. 9

13. 60

14. 60

Step-by-step explanation:

When you solve it out, you know that vertical angles are congruent. So the top angle is 42. Then you need to find out the angle adjacent to the 87. This is a supplementary angle. Supplementary angles add up to 180. So, 180 - 87 = x. This comes out to 93. Then you just need to find ?. All angles in a triangle add up to 180. So 180 - 93 -42 = 45. ? = 45

For this one we know that the angles in a triangle add up to 180. So, 180 - 35 - 70 = 75. Vertical angles are congruent so ? is also equal to 75.

For this one, we know supplementary angles add up to 180. We use this for every angle. 180 - 145 = 35. 180 - 105 = 75. Angles in a triangle add up to 180 so, 180 - 75 - 35 = 70. We know the other angle in the triangle, we now need to find the angle that is supplementary. We know they add up to 180 so, 180 - 70 = 110. ? = 110

We know 2 of the angles, 90 and 60. We can solve for the third angle. 180 - 90 - 60 = 30. Vertical angles are congruent so ? also equals 30.

We now 2 angles. 60 and 70. We can find the third angle. 180 - 60 -70 = 50. We now need to solve for x. We can subtract 14 from 50 then divide it by 3. We get 12. X is = 12.

We know 2 angles. 65 and 90. This means the third angle is 25. We need to solve for x so 25 - 1 = 24. Then divide that by 6. We get 4. X = 4.

We know 2 angles. 70 and 70. This means the third angle is 40. We can divide that by 8 to find x. X = 5.

We know 2 angles. 70 and 90. This means the third angle is 20. We can subtract 2 to get 18. Then divide by 2. We get 9. X = 9.

We first need to find the last angle in the first triangle. 180 - 85 - 50. The third angle is 45. We now know 2 angles in the second triangle. We can now solve for ?. 180 - 75 - 45. ? = 60

We first need to find the last angle in the first triangle. 180 - 70 - 70. 40 is the last angle. We now have 180 - 40 - 80. It comes out to 60. ? = 60.

Answer:

figure is missing mate

20 : 7 is already the simplest term and  there is no need to further simplify.

Ratio can be defined as the given value divided by total value.

When presenting a ratio as an answer:

1. It has to be in the form of integer, it cannot be in the form of fraction or decimals

2. There should be of the equivalent units.

3. It must be in its simplest form

Convert the units in cm

Coloured Fabric = 70 mm

Coloured Fabric = 70 ÷ 10 cm

Coloured Fabric = 7 cm

Find the ratio of the Colour Fabric to White Fabric:

Coloured Fabric = 7 cm

White Fabric = 20 cm

Ratio of  White Fabric : Colour Fabric = 20 cm : 7 cm

Ratio of  White Fabric : Colour Fabric = 20 : 7

Therefore, 20 : 7 is already the simplest term and  there is no need to further simplify.

To learn more about Ratio from the given link.

https://brainly.com/question/13419413

#SPJ1

Using Euler'formula, the difference between maximum and minimum possible numbers of faces is 96.

A polyhedron is a 3D shape with flat faces, straight edges, and sharp vertices (corners). "polyhedron" meaning "many" and "polyhedron" meaning "area". Therefore, when many planes are joined, they form a polyhedron.

Because all faces are triangles. So on a triangular base with triangular faces on both sides that meet at the vertex.

Therefore, the minimum number of triangular faces of a regular polyhedron is = 4

Next, the double pyramid has "2n" triangular faces. where n is a natural number greater than 2 and 'n' represents the number of sides of the base of the pyramid.

A polyhedron having equal quadrilateral faces is known as regular hexahedron.

quadrilateral faced polyhedron with total sides 100 and vertices 6 , then using Euler's formula

F + V-E = 2

=> F + 6- 100= 2 => F = 96 maximum faces possible = 96

Now the difference between maximum and minimum number of faces = 100 - 4 = 96

So the difference between maximum and minimum faces is 96.

To learn more about Polyhedron, refer:

https://brainly.com/question/27231951

#SPJ4

The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

Learn more about behavior at https://brainly.com/question/22443880

#SPJ11

Answer:

Negative

Step-by-step explanation:

Answer:

I would say 4 units up, because point D is 4 units up for it's original position

The value c = 6.25 satisfies the condition f(c) = f_avg for the function f(x) = 1/sqrt(x) over the interval [4, 9].

To find the value c such that f(c) = f_avg for the function f(x) = 1/sqrt(x) over the interval [4,9], we first need to find the average value of the function over this interval.

The formula for the average value of a function f(x) over the interval [a,b] is given by:

f_avg = 1/(b-a) * ∫[a,b] f(x) dx

Substituting the values a = 4 and b = 9, and the function f(x) = 1/sqrt(x), we get:

f_avg = 1/(9-4) * ∫[4,9] 1/sqrt(x) dx
     = 2/5 * [2sqrt(9) - 2sqrt(4)]
     = 2/5 * 4
     = 8/5

So, the average value of f(x) over the interval [4,9] is 8/5.

To find the value c such that f(c) = f_avg, we set f(x) = f_avg and solve for x:

1/sqrt(x) = 8/5

Solving for x, we get:

x = (5/8)^2
 = 0.390625

Therefore, the value c such that f(c) = f_avg for the function f(x) = 1/sqrt(x) over the interval [4,9] is approximately 0.390625.

To find the value c such that f(c) = f_avg for the function f(x) = 1/sqrt(x) over the interval [4, 9], first we need to calculate the average value (f_avg) of the function over this interval.

The formula to find the average value of a continuous function over an interval [a, b] is:

f_avg = (1 / (b - a)) * ∫[a, b] f(x) dx

For f(x) = 1/sqrt(x) over the interval [4, 9]:

f_avg = (1 / (9 - 4)) * ∫[4, 9] (1/sqrt(x)) dx

Calculate the integral:

∫(1/sqrt(x)) dx = 2 * sqrt(x)

Now, evaluate the integral over the interval [4, 9]:

2 * (sqrt(9) - sqrt(4)) = 2 * (3 - 2) = 2

Now, calculate f_avg:

f_avg = (1 / 5) * 2 = 2/5

Now we want to find c such that f(c) = f_avg:

f(c) = 1/sqrt(c) = 2/5

Solve for c:

c = (1 / (2/5))^2 = 6.25

Visit here to learn more about Integral:

brainly.com/question/30094386

#SPJ11

Answer:

519

Step-by-step explanation:

an = 8n - 1

a65 = 519

final answer is 519

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

the line isn't vertical because the y coordinate would have to be 0 in order for the line to be vertical

Answer:

y= -(1/2)x+1

Step-by-step explanation:

it is a vertical line so it also passes through (1,0) so slope (m)= -(1/2)

c=1

Answer:

50.6°

Step-by-step explanation:

complementary angles sum to 90° , that is

complementary angle + 39.4° = 90° ( subtract 39.4° from both sides )

complementary angle = 90° - 39.4° = 50.6°

Answer:

\(\sf x=2, \ x = -8\)

solving steps:

\(\hookrightarrow \sf log_4 x+log_4 (x+6)=2\)

\(\hookrightarrow \sf log_4 (x(x+6))=log_4 (16)\)

\(\hookrightarrow \sf log_4 (x^2+6x)=log_4 (16)\)

\(\hookrightarrow \sf x^2+6x=16\)

\(\hookrightarrow \sf x^2+6x-16=0\)

\(\hookrightarrow \sf x^2+8x-2x-16=0\)

\(\hookrightarrow \sf x(x+8)-2(x+8)=0\)

\(\hookrightarrow \sf (x-2)(x+8)=0\)

\(\hookrightarrow \sf x=2, \ x = -8\)

The solution of the logarithmic function is x = 2 and x = -8

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

log₄ x + log₄ ( x + 6 ) = 2

where 2 = log₄ ( 16 )

From the properties of logarithm , we get

log A + log B = log AB

log₄ x ( x + 6 ) = log₄ ( 16 )

On simplifying , we get

x ( x + 6 ) = 16

x² + 6x - 16 = 0

On factorizing , we get

x² - 2x + 8x - 16 = 0

x ( x - 2 ) + 8 ( x - 2 ) = 0

( x + 8 ) ( x - 2 ) = 0

Hence , the solution is x = -8 and x = 2

To learn more about logarithm click :

https://brainly.com/question/12049968

#SPJ7

Answer:

y=-35

Step-by-step explanation:

Steps

$\frac{y}{5}-=-7$

$\mathrm{Subtract\:}-\mathrm{\:from\:both\:sides}$

$\frac{y}{5}=-7$

$\mathrm{Simplify}$

$\frac{y}{5}=-7$

$\mathrm{Multiply\:both\:sides\:by\:}5$

$\frac{5y}{5}=5\left(-7\right)$

$\mathrm{Simplify}$

$y=-35$

Answer:

y = 35

Step-by-step explanation:

    multiply by -5 on both sides

    -5 and -5 cancel out

    -5 times -7 is 35

    y = 35

Answer:

Therefore, the unknown number is 5.

Step-by-step explanation:

We can translate "Eight times the difference of a number and six is negative eight" into an algebraic equation as given below,

8(x - 6)

= -8                (where x is the unknown number we are trying to find)

The expression "the difference of a number and six" means x - 6. So, "eight times the difference of a number and six" means 8(x - 6).

The equation states that the product of 8 and the difference of the number x and 6 is equal to -8.

To solve for x, we can simplify the equation,

8(x - 6) = -8

8x - 48 = -8

8x = 40

x = 5

Therefore, the unknown number is 5.

Answer:

What point C represents is that you can get 8 packs of paper clips for $34.50.

Hope this helps!

The rate of change of the area when the radius is 3 centimeters is 0 square centimeters per minute.

To calculate the rate of change of the area when the radius is 3 centimeters, we can use the formula for the area of a circle:

A = πr²

where A is the area and r is the radius.

First, let's differentiate both sides of the equation with respect to time (t), using the chain rule:

dA/dt = d/dt (πr²)

To obtain dA/dt, we need to know the rate of change of the radius (dr/dt) with respect to time.

Provided in the problem, the rate of change of the radius is 8 centimeters per minute.

So dr/dt = 8.

Now we can substitute the provided values into the equation:

dA/dt = d/dt (π(3)²)

      = d/dt (9π)

      = 0

Since the radius is constant at 3 centimeters (there is no change in the radius), the rate of change of the area (dA/dt) is 0.

To know more about rate of change refer here:

https://brainly.com/question/32850263#

#SPJ11

Chelsea will use 21 meters of dental floss in 7 days.

If Chelsea uses 1/10 of a dental floss every day, then in 7 days, she will use:

(1/10 dental floss/day) x 7 days = 7/10 dental floss

To determine the total length of dental floss Chelsea will use in meters, we need to know how long 1/10 of a dental floss is in meters. Let's assume that Chelsea uses a dental floss that is 30 meters long. Then, 1/10 of that dental floss is:

1/10 x 30 meters = 3 meters

So, in 7 days, Chelsea will use 7/10 of a dental floss, which is:

7/10 x 30 meters = 21 meters

Therefore, Chelsea will use 21 meters of dental floss in 7 days.

Learn more about length

brainly.com/question/9842733

#SPJ11

The equation of the parabola that similar to f(x) = \(7x^2\) but the vertex is (3, 5) in the standard form is y = \(7(x-3)^2\) + 5

The equation of the parabola

f(x) = \(7x^2\)

The standard vertex form of a parabola is

y = \(a(x-h)^2\) + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  \(7x^2\)

The value of a = 7

Substitute the values in the vertex form of a parabola

y = \(7(x-3)^2\) + 5

Hence, the equation of the parabola that is similar to f(x) = \(7x^2\) but the vertex is (3, 5) in the standard form is y = \(7(x-3)^2\) + 5

Learn more about standard vertex form here

brainly.com/question/22649174

#SPJ1

The correct option regarding the probabilities is given as follows:

a. P(X>16) is greater than P(X<16).

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

X = 16 is a negative value, meaning that it has a negative p-value, meaning that it's percentile is below 50%, thus:

Meaning that option a is correct.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units.

Given: The equation of the curve is y = 4√x on [21,77]

The formula for finding the surface area of a curve rotated about the x-axis on some interval [a, b] is given by:

\(S = \int\limits^b_a {2\pi f(x)\sqrt{1 +(f'(x))^{2} } } \, dx\)

where S is the surface area,

f(x) is y

a and b is the given interval such that a ≤ x ≤ b or [a, b]

Now in this question,

f(x) = 4√x

a = 21, b = 77

f'(x) = 4 * 1 / 2√x = 2 / √x

f'(x) = 2 /√x

Placing the respective values in the equation we get,

\(S = \int\limits^{77}_{21} {2\pi. 4\sqrt{x} \sqrt{1+(\frac{2}{\sqrt{x} } )^{2} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} \sqrt{1+\frac{4}{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} * \frac{\sqrt{x + 4} }{\sqrt{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x+4} } } \, dx\)

we know the formula for the integral

\(\int\limits^b_a {\sqrt{ax + b} } \, dx = \frac{2}{3a}(ax+b)^{\frac{3}{2} } | { {{b} \atop {{a}}} \right.\)

Therefore, by applying the formula, we get:

\(S = 8\pi *\frac{2}{3}(x+4)^{\frac{3}{2} } | { {{77} \atop {{21}}} \right.\)

\(S = \frac{16\pi }{3} \{ (77+4)^{\frac{3}{2}} - (21+4)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{ (81)^{\frac{3}{2}} - (25)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{729 - 125\}\)

\(S = \frac{16\pi }{3} * 604\)

\(S = \frac{9664\pi }{3}\)

Hence, The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units

Know more about "surface area generated by revolving curve" here: https://brainly.com/question/24132132

#SPJ4

Disclaimer: The given question is incomplete. The complete question is mentioned below:

Find the area of the surface generated when the given curve is rotated about the x-axis y= 4sqrt(x) on [21,77]

The area of the surface generated by revolving the curve about the x-axis is ___ square units (type an exact answer, using pi as needed)

The equation of the ellipsoid is\(\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1\)

The equation of an ellipsoid is represented as:

\(\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1\)

Given that the ellipsoid passes through the points (±6,0,0),(0,±7,0) and (0,0,±5)

It means that:

(±a,0,0)  = (±6,0,0)

(0,±b,0) = (0,±7,0)

(0,0,±c) = (0,0,±5)

By comparison, we have:

±a=±5

±b=±6

±c=±7

So, the equation of the ellipsoid becomes:

\(\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1\)

By substituting the values, the equation of the ellipsoid becomes is

\(\frac{x^{2} }{36}+\frac{y^{2} }{49} +\frac{z^{2} }{25} =1\)

.An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant. In an ellipse, there are two radius measures, one horizontally along the x-axis, the other vertically along the y-axis.For  a circle both these have the same value.

Learn more about ellipse:

brainly.com/question/9448628

#SPJ4

Emily runs at the fastest speed of 15 ft per second, Liz runs at 13.03 ft per second, and Zack runs at 12.8 ft per second.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that Emily runs 15 ft per second no one runs 358 ft and 36 seconds Liz runs 1 mi in 405 seconds Zack runs 768 feet in 1 minute.

Emily's speed = 15 ft/sec

Liz's speed = 1 mile per 405 sec = 5280/405 = 13.03 ft /sec

Zack's speed = 768 / 60 = 12.8 ft /sec

Therefore, Emily runs at the fastest speed of 15 ft per second, Liz runs at 13.03 ft per second, and Zack runs at 12.8 ft per second.

To know more about Speed follow

brainly.com/question/6504879

#SPJ2

Answer:

here man let me is 1 im sure the answer is =((1))

Step-by-step explanation:

6^(-3 * 10^(-10 * 27 * 25 / 5^(-8 * 3^(4 * 2^-3))))

Step-by-step explanation:

they are similar, that means for our case here that they're is one central scaling factor for all sides between the 2 triangles.

by looking at the forms of both triangles, we see that

ET corresponds to TR.

FT corresponds to TS.

FE corresponds to RS.

for TE and TR we have the length information :

25 and 40

so, the scaling factor between these 2 corresponding sides can then be used for the other pairs of corresponding sides.

the scaling factor to go from the large to the small triangle is

25/40 = 5/8

therefore,

FT = TS × 5/8 = 22 × 5/8 = 11×5/4 = 55/4 = 13.75

FE = RS × 5/8 = 54 × 5/8 = 27×5/4 = 33.75

the perimeter of TFE is therefore

25 + 13.75 + 33.75 = 72.5