The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 196 pounds on the surface of the Earth, what will this astronaut weigh 300 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)

Answer:

[tex]x =\sqrt{5} ,-\sqrt{5} ,-i,i[/tex]

Step-by-step solution:

[tex]0=x^4-4x^2-5[/tex]   [tex]u = x^2[/tex]
[tex]0 = u^2-4u-5[/tex]
[tex]0 = (u -5)(u+1)[/tex]
[tex]u = 5[/tex]  [tex]u=-1[/tex]
[tex]x^2 =5[/tex]    [tex]x^2 = -1[/tex]
[tex]x= +-\sqrt{5}[/tex]   [tex]x = +-i[/tex]

Answer:

the length of the shorter leg : 7 cm

the length of the longer leg : 24 cm

the length of the Hypotenuse : 25 cm

Step-by-step explanation:

a = 3b + 3

c = 3b + 4

and we know the general Pythagoras :

c² = a² + b²

(3b + 4)² = (3b + 3)² + b²

9b² + 24b + 16 = 9b² + 18b + 9 + b²

24b + 16 = 18b + 9 + b²

6b + 7 = b²

b² - 6b - 7 = 0

the general solution to such a quadratic equating is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x is called b.

a = 1

b = -6

c = -7

b = (6 ± sqrt((-6)² - 4×1×-7))/(2×1) = (6 ± sqrt(36 + 28))/2 =

= (6 ± sqrt(64))/2 = (6 ± 8)/2

b1 = (6+8)/2 = 14/2 = 7 cm

b2 = (6-8)/2 = -2/2 = -1 cm

a negative number did not make sense for a side length, so,

b = 7 cm

is our solution for one leg.

a = 3b + 3 = 3×7 + 3 = 24 cm

c = 3b + 4 = 25 cm

The Surface area of the cylindrical tower is 5181 ft cube.

Surface area of cylinder = 2πr² + 2πrh

where

Therefore,

r = 30 / 2 = 15 ft

h = 40 ft

Surface area of cylinder = 2πr(r + h)

Surface area of cylinder = 30π(40 + 15)

Surface area of cylinder = 30π(55)

Surface area of cylinder = 1650π

Surface area of cylinder = 5181 ft³

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The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

The ratio by which the new image is bigger or smaller than the original image is the scale factor.

It is given that

Triangle A″B″C″ is formed using the translation (x + 0, y + 2)

and the dilation by a scale factor of 2 from the origin.

coordinate plane with triangle ABC at A (- 3,  3), B (1, - 3), and C (- 3, -3).

segment AC is equal to A''C'' over 2

Scale factor = 2

The coordinates are

A (- 3,  3), B (1, - 3), and c (- 3, -3) is translated using  (x + 2, y + 0),

new coordinates

A'(- 1,  3), B'(3, - 3), and C'(- 1, -3).

The dilation by a scale factor of from the origin

A″ (-2, 6), B″ (6, -6) and C″(-2, -6)

By the distance formula

AB = [tex]\rm \sqrt {52}[/tex]

A''B'' = [tex]\rm \sqrt{ 8^2 + 12^2}\\[/tex] = 2 [tex]\rm \sqrt {52}[/tex]

Therefore

AB = A''B'' /2

Similarly AC = A''C'' /2

The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

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Answer:

Step-by-step explanation:

its  A y+6=-2

The probabilities on each branch are shown in the tree diagram, and P(HT) = 2/9.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The probability of H is 2/3 and the probability of T is 1/3.

P(HT) = P(H in the first trial)P(T in the second trial)

From the tree diagram:

P(HT) = (2/3)(1/3) = 2/9

Thus, the probabilities on each branch are shown in the tree diagram, and P(HT) = 2/9.

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The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)

The formula for exponential growth is;

P = P₀e^(rt)

where;

P = current population at time t

P₀ = starting population

r = rate of exponential growth/decay

t = time after start

Thus, from our question we have;

4500 = 1500 * e^(r * 1)

4500/1500 = e^r

e^r = 3

In 3 = r

r = 1.0986

Thus, the function that represents the growth of this culture of bacteria as a function of time is;

P = 1500e^(1.0986t)

For the culture to double, then;

P/P₀ = 2. Thus;

e^(1.0986t) = 2

In 2 = 1.0986t

t = 0.6931/1.0986

t = 0.631 hours

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Answer:

13.5

Step-by-step explanation:

8x+y-10x-y=-27

-2x=-27

x=13.5

Answer:

64

Step-by-step explanation:

Answer:

1,2

Step-by-step explanation:

Recall the Pythagorean identity,

[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]

Since [tex]\theta[/tex] belongs to Q3, we know both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are negative. Then

[tex]\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}[/tex]

Recall the half-angle identities for sine and cosine,

[tex]\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2[/tex]

[tex]\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2[/tex]

Then by definition of tangent,

[tex]\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}[/tex]

[tex]\theta[/tex] belonging to Q3 means [tex]180^\circ < \theta < 270^\circ[/tex], or [tex]90^\circ < \theta < 135^\circ[/tex], so that the half-angle belongs to Q2. Then [tex]\sin\left(\frac\theta2\right)[/tex] is positive and [tex]\cos\left(\frac\theta2\right)[/tex] is negative, so [tex]\tan\left(\frac\theta2\right)[/tex] is negative.

It follows that

[tex]\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}[/tex]

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

                      If two lines are perpendicular to each other, their slopes

                     are negative inverses of each other.

                     Thus,

                    [tex]\boldsymbol{\sf{Slope\:of\:this\:line=4}}}[/tex]

                    [tex]\boldsymbol{\sf{Negative \ Inverse=-\displaystyle\frac{1}{4}}}[/tex]. See how this works?

                    We took 4, then took its opposite, and flopped that over

[tex]\orange\hspace{300pt}\above3[/tex]

Definition-:

Perpendicular lines are lines that intercept each other at a 90 deg. angle, which is usually called the right angle.

Answer:

Spain

Step-by-step explanation:

Pablo Picasso was born in Malaga, Spain.

Answer:

Málaga, Spain

Step-by-step explanation:

Answer:

You need to attach the pictures and ask again.

Step-by-step explanation:

I cannot see any attachments.

Answer:

The diagonal length of the desk is 7.42462120246 inches.

Step-by-step explanation:

Since it is a square then all sides are equal which means we can easily formulate the pythagorean theorem on the diagonal length of the desk.

a^2 + b^2 = c^2

A and B are the same (width and length) since it is a square.

5.25^2 + 5.25^2 = c^2

27.5625 + 27.5625 = c^2

55.125 = c^2

Put c^2 under a square root (apply to both sides)

square root of 55.125 = 7.42462120246 = c

The value of the expression [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]

The equation is given as:

[tex]x^2 - 2xy - 3y^2 = 0[/tex]

Add 3y^2 to both sides

[tex]x^2 - 2xy = 3y^2[/tex]

Add 3y^2 to both sides

[tex]x^2 + 3y^2 - 2xy = 6y^2[/tex]

Add 2xy to both sides

[tex]x^2 + 3y^2 = 6y^2 + 2xy[/tex]

Divide through by xy

[tex]\frac{x^2 + 3y^2}{xy} = \frac{6y^2 + 2xy}{xy}[/tex]

Hence, the value of [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]

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Answer:

8.2

Step-by-step explanation:

We can find the unit rate of this problem by dividing 18.68 by 24 to get .82. .82*10 is equal to 8.2.

Answer:I can’t see

Step-by-step explanation:show fullscreen

The value of card(B) is card(B) = 4954

The set is given as:

B={1,3,5,7,9,….9907}

The above set is the set of odd numbers from 1 to 9907.

The number of elements is the cardinality

And it can be calculated using

L = a + (n - 1)d

Where

L = 9907

a = 1

d = 2

So, we have:

9907 = 1 + (n - 1)2

Subtract 1 from both sides

9906 = (n - 1)2

Divide by 2

n - 1 = 4953

Add 1 to both sides

n = 4954

This means that

card(B) = 4954

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Answer:

Volume: x(x+6)(x+2) Area: [tex]x^{2}[/tex] + 8x +12

Step-by-step explanation:

Volume Explanation:

To find the volume of a 3d figure, we must multiply the length, width, and the height. Therefore we multiply (x)(x+6)(x+2)= [tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 12x. Simplify this equation and we will get x(x+6)(x+2) for the formula to find the volume of the 3D figure.

Area:

To find the area of a 2D figure, we must multiply length x height. Therefore, we multiply the equations (x+6)(x+2)= [tex]x^{2} + 2x + 6x +12[/tex] to get a final answer of [tex]x^{2} +8x +12[/tex].  This will be the formula when you find the area of the 2D figure in question.

Answer:

80 mm

Step-by-step explanation:

the same amount (and that means the same volume) of pepper is in each shaker.

the volume of a cylinder is

base area × height = pi×r² × height

with r being the radius (which is always half of the diameter).

the volume of the filled in pepper in the first shaker is then

pi×(32/2)²×45 = pi×16²×45 = pi×256×45 = 11,520pi mm³ =

= 36,191.14737... mm³

now let's see what height in the second shaker we will reach by filling the same 11,520pi mm³ of pepper into it.

so, we have

pi×(24/2)²×height = 11,520pi

12²×height = 11,520

144×height = 11,520

height = 11,520/144 = 80 mm

so, the shaker on the right is filled up to 80 mm with pepper.

Answer:

80 mm

Step-by-step explanation:

I got it right on edmentum

Answer:

2 y + x = 5 , 5 x − y = 3

Step-by-step explanation:

suppose x represents the smaller number and y represent the larger number.

Then

• The statement: “Twice a number added to a smaller number is 5”

means  2 y + x = 5

On the other hand,

•• The statement: “The difference of 5 times the smaller number and the larger number is 3”

means  5 x − y = 3

Answer:

Making comparisons of numbers or values and considering relationships are also aspects of proportional reasoning.

Example:
A worker being paid by the number of hours he/her worked.

#EDIT #1

Substituting into vertex form, we can write the equation of the parabola as

[tex]y=a(x-0)^{2}+9\\\\y=ax^{2}+9[/tex]

To find the value of a, we can substitute in the coordinates of another point the graph passes through, such as (3,0).

[tex]0=a(3)^{2}+9\\\\0=9a+9\\\\-9=9a\\\\a=\boxed{-1}[/tex]

[tex]m = \frac{ - u}{v} = \frac{ - 9}{3} = - 3 [/tex]

[tex]km = - 1 \\ k = - \frac{1}{m} = \frac{ - 1}{-3}=1/3 [/tex]

The slope of the perpendicular line will be 1/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

9x + 3y = 36

3y = 36 - 9x

y = 12 - 3x

The slope of the given equation is - 3.

Let m be the slope of the perpendicular line. Then the slope of the perpendicular line will be 1/3.

m (-3) = -1

Simplify the equation, then we have

m (-3) = -1

3m = 1

m = 1/3

The slope of the perpendicular line will be 1/3.

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Answer: B. False

Step-by-step explanation:

You assume the inverse of what you intend to prove is true, not the converse.