1. What is the difference in height between 30 m up a cliff and 87 m up a cliff? The difference in height is m 2. What is the distance between these positions? The distance is m

Answer:

  320 square units

Step-by-step explanation:

The four rectangles that approximate the area are shown in the graph. They have heights of 48, 64, 48, and 0. The width of each is 2. Then the total area is the sum of the products of length and width:

  2·48 +2·64 +2·48 +2·0 = 2·160 = 320 . . . square units

Scott's age is 11x

Georgia's age is 6x = 4y

therefore y=1.5x

Fiona's age is 7x

Oscar's age is 3y

therefore 3(1.5x)=4.5x

Fiona's age: Oscar's age

7x : 4.5x

7 : 4.5

To find the rate at which the light projected onto the wall is moving along the wall, we can use trigonometry and calculus. Let's denote the angle between the rotating light and the wall as θ.

Given:

Distance from the light to the wall, r = 15 feet

Rate of rotation, dθ/dt = 1 rotation every 4 seconds

We need to find the rate at which the light's projection moves along the wall, which is represented by dx/dt.

Using trigonometry, we know that the tangent of the angle θ is equal to the ratio of the distance along the wall (dx) to the distance from the light to the wall (r).

tan(θ) = dx / r

Differentiating both sides of the equation with respect to time t, we get:

sec^2(θ) * dθ/dt = dx/dt

Since we are given that the angle θ is 15 degrees, we can substitute the values and solve for dx/dt.

sec^2(15°) * (1 rotation / 4 seconds) = dx/dt

Simplify and calculate the value to find the rate at which the light's projection moves along the wall in feet per second.

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Let \(f(x) = x^3 - 2x - 2\). Then differentiating, we get

\(f'(x) = 3x^2 - 2\)

We approximate \(f(x)\) at \(x_1=2\) with the tangent line,

\(f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18\)

The \(x\)-intercept for this approximation will be our next approximation for the root,

\(10x - 18 = 0 \implies x_2 = \dfrac95\)

Repeat this process. Approximate \(f(x)\) at \(x_2 = \frac95\).

\(f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}\)

Then

\(\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}\)

Once more. Approximate \(f(x)\) at \(x_3\).

\(f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}\)

Then

\(\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}\)

Compare this to the actual root of \(f(x)\), which is approximately 1.769292354, matching up to the first 5 digits after the decimal place.

Answer:

\(28\), \(82\)

Step-by-step explanation:

\(10 \times 3 -2=28\\28 \times 3 - 2 = 82\)

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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For every equation, we have to choose a value for x, and solve for y.

For part a) we have that the equation is:

If we choose the following value for x:

And substitute it in the equation, we find the value of y:

Answer for part a) when x=1, the value of y is y=6/7

For part b) we have the equation:

If we choose the following value for x:

and substitute it in the equation to find y:

To solve for y, first, we solve the multiplication between 5 and 3:

Now we subtract 15 to both sides:

Finally, divide both sides by 3:

Answer for part b) when x=3, the value of y is y=-2

For part c) we have the equation:

In this case, we can choose a value for x in such a way that we eliminate the fraction. For this, we can again choose the value:

And we substitute it:

1/3 by 3 is equal to 1:

Next, combine the like terms on the left side 5-1 which is 4:

And finally, subtract 4 to both sides:

Answer for part c) when x=3, the value of y is y=3

When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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Answer: They ate at the same pace.

Step-by-step explanation: assuming you want to know who ate more faster you can do 18 / 30 and 24 / 4 to find out who ate more in 10 seconds each.

18 / 3 = 6 and 24 / 4 = 6. So they ate at the same speed / pace.

Hope this helps! Brainliest and / or a rating out of 5 stars would be appreciated :)

The man got an 18.92% discount on the jacket during the sale if he pays $150, saving $35 on the normal price.

What was the percentage discount on the jacket purchased by the man?

The discount can be calculated as follows:

Discount = Normal price - Sale price

Discount = $35

Normal price = Sale price + Discount

Normal price = $150 + $35

Normal price = $185

So, the percentage discount is:

Percentage discount = (Discount / Normal price) x 100

Percentage discount = ($35 / $185) x 100

Percentage discount = 18.92%

Therefore, the man got a discount of 18.92% on the jacket.

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Answer:

B. add the opposite of four

Step-by-step explanation:

x + 4 = 6

x + 4 + (-4) = 6 + (-4)

x + 4 - 4 = 6 - 4

x + 0 = 2

x = 2

Answer:

\(\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}}\)

Step-by-step explanation:

Hello,

\(a=bc^2+d \\ \\ <=> a-d=bc^2+d-d=bc^2 \ \text{ subtract d }\\ \\ <=> c^2=\dfrac{a-d}{b} \ \text{ divide by b, assuming b is different from 0}\\ \\<=>\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}} \ \ \text{ take the root of both parts}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

$3806

Step-by-step explanation:

  230.0

    56.0

+   19.50

  305.50

305.5x12=3666

35x4=140

3666+140=3806

Answer:

7k-4

Step-by-step explanation:

(-3)(2.5)+(-3)(-k)+(0.5)(7)+(0.5)(8k)

-7.5+3k+3.5+4k

Then you combine like terms

-7.5k+3k+3.5+4k

(3k+4k)+(-7.5+3.5)

7k+-4

Answer:

It's the second inequalities. y<x and y (more than or equal to) -x

Answer:

\(y<x\\y\geq -x\)

Step-by-step explanation:

\(y<x\\y\geq -x\)

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Can u give more information on the equation so i can help further?

The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the the shape is going to end up in the third quadrant.the squadron only includes both negative X values and negative y values meaning that both X and y will be negative.

Answer:

57%

Step-by-step explanation:

The probability that the sample's mean length is greater than 6.3 inches is0.8446.

Here, we have,

Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.

We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.

Probability is the likeliness of happening an event.

It lies between 0 and 1.

Probability is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is mean and

σ is standard deviation.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the probability that the mean length is greater than 6.3 inches is 0.8446.

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You have a case in which you have the probability of obtaining six different results: 1, 2, 3, 4, 5 and 6

The probaility of getting a specific number is given by the formula:

p = 1/n = 1/6

where n is tha number of different cases, which is 6.

To calculate the probability of getting two results, you have to multiply the probability of one result with the probaility of the other one.

The probability of getting a 4 is:

1/6

The probability of getting a 3 is:

1/6

Then, the probaility of getting the two previous results is:

P = (1/6)(1/6) = 1/36

Answer:

p > 34

He wrote more than 34 pages before today.

Step-by-step explanation:

Eduardo wrote 16 more pages, increasing his total number of pages above 50.

p = pages he wrote before today

p + 16 > 50

p > 50 - 16

p > 34

He wrote more than 34 pages before today.

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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y=100000(0.25)^8 exponential decay​ is 1.526.

The formula represents exponential decay with a decay factor of 0.25 and an initial value of 100,000. To evaluate the formula, you can simply substitute 8 for the variable x (since the formula has y in terms of x) and calculate the result:

y = 100000(0.25)^8

y = 100000(0.00001525878906)

y ≈ 1.526

Therefore, the value of y for x = 8 is approximately 1.526. This means that after 8 units of time, the initial value of 100,000 has decayed to around 1.526.

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Answer:

  B.  NB and DH

  B.  converse of corresponding angles theorem

Step-by-step explanation:

The transversal in this geometry is line BH. The angles marked 36° are on the same side of the transversal, and on the same sides of the intersecting lines NB and DH. That makes these congruent angles "corresponding" angles.

Segments NB and DH are parallel by the converse of the corresponding angles postulate.

__

Additional comment

The corresponding angles postulate tells you corresponding angles are congruent where a transversal crosses parallel lines. Its converse tells you the lines are parallel if the corresponding angles are congruent.

Corresponding angles lie in the same direction from the vertex where the transversal meets one of the parallel lines. Here, the angles are "northwest" of the vertex.