NEED HELP ASAP!!
A boat is heading towards a lighthouse, whose beacon-light is 114 feet above the water. The boat's crew measures the angle of elevation to the beacon, 5º. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to
the nearest hundredth of a foot if necessary.

Answer:

\(2\sqrt[3]{5}\)

Step-by-step explanation:

40 = 8 x 5 and 8 is the cube of 2, so 2 goes on the outside but 5 can't be simplified

Given the statement:

Vertical angles are always equal to each other

The answer is: True

Because they are inclosed by the same lines

The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2

To solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:

8x²(x² - 4) = 0

Now we can use the difference of squares identity to factor the quadratic expression:

8x²(x + 2)(x - 2) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

8x² = 0 or x + 2 = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = -2 or x = 2

So the solution set for the equation is {0, -2, 2}.

To check the solution, we can substitute each value into the original equation and verify that it equals zero.

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Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

Substituting the given values, we get:

Volume = 2 meters x 4 meters x 2 meters

Simplifying this expression, we get:

Volume = 16 cubic meters

Therefore, the volume of the prism is 16 cubic meters.

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Answer:

The area of the triangle is 168 meters

Step-by-step explanation:

Formula to find the area of a triangle:

Area = 1/2 Base x Height

So, first you need to identify the base and the height. The base is 16m + 8m, and the height is 14m. All you have to do is plug in the numbers:

Area = 1/2 (16 + 8) x 14

Then, you solve:

Area = 1/2 (16 + 8) x 14

Area = 1/2 24 x 14

Area = 1/2 336

Area = 168 meters

So, the area of the triangle is 168 meters

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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Hello :

    3/8 = x/(15 + x)

⇔ 3(15 + x)/8 = x

⇔ (45 + 3x)/8 = x

⇔ 45 + 3x = 8x

⇔ 8x - 3x = 45

⇔ 5x = 45

⇔ x = 45/5

⇔ x = 9

Answer:

a) True

b) True

C) false

Step-by-step explanation:

just a guess..... Merry Christmas

Answer:1.6

Step-by-step explanation:

Answer:

  B)  47.1°

Step-by-step explanation:

The tangent relation is useful here.

  Tan = Opposite/Adjacent

The original height of the tree is the side of the triangle that is opposite the angle of elevation:

  Opposite = Adjacent × Tan

  original height = (25 ft)×tan(34°) ≈ 16.863 ft

__

After growing an additional 10 ft, the tree has a height of ...

  16.863 ft + 10 ft = 26.863 ft

Then the angle of elevation is found from ...

  tan(angle) = (26.863 ft)/(25 ft) ≈ 1.07451

  angle of elevation = arctan(1.07451) ≈ 47.057°

The angle of elevation to the top of the tree is about 47.1°.

Answer:

85%

Step-by-step explanation:

The students who read less than six magazines would be placed in the intervals: 0-1, 2-3, and 4-5 on the graph. Adding up the total amount in those intervals gives us:

2 + 15 = 17

So, using the answer from b, we can say that 17/20 kids read magazines. Now, we need to convert it into a percent by multiplying by 100:

17/20 *100

17 * 5

85%

Answer:

y = -2/3x + 3

Step-by-step explanation:

Parallel lines have the same slope so we already know

y = -2/3x + b

Solve for b using the point given

-1=-2/3(6)+b

-1+4=b

b=3

y = -2/3x + 3

Answer:

210 students

Step-by-step explanation:

30%=63

10%=63÷3

      =21

100%=21×10

        =210

Answer:

1 1/3

Step-by-step explanation:

if ashley wants to make HALF of the batch you simply divided 2 2/3 by 2 :)

Answer:

1 1/3 cups

Step-by-step explanation:

If it takes 2 2/3 cups for a whole batch and Ashely only wants half a batch you would have to multiply 2 2/3 by 1/2.

2 2/3 x 1/2= 1 1/3

The value of yp is equal to negative two divided by the expression 27x raised to the power of 27/4 and multiplied by e raised to the power of 3x.. This could be found using the Method of Undetermined Coefficients.

To find the particular solution using the Method of Undetermined Coefficients, we assume that the particular solution is of the form:

yp = Axⁱe⁽³ˣ⁾

where A is a constant to be determined and i is the smallest positive integer that makes yp linearly independent from the complementary function.

First, we find the complementary function by solving the characteristic equation:

r² - (4/3)r + 1 = 0

Using the quadratic formula, we get:

r = (4/3 ± √(16/9 - 4))/(-9/4) = -3/4 or -1

So the complementary function is:

yc = c₁e⁻ˣ + c₂e⁽-(3/4)x⁾

To determine the value of A, we substitute yp into the differential equation and equate coefficients of like terms.

yp' = A(xⁱe⁽³ˣ⁾)' = A(xⁱe⁽³ˣ⁾)(3e⁽³ˣ⁾ + i)

yp" = A(xⁱe⁽³ˣ⁾)" = A(xⁱe⁽³ˣ⁾)(9e⁽³ˣ⁾ + 6ie⁽³ˣ⁾ + i(i+3))

Substituting these into the differential equation and simplifying, we get:

(81/4)A(xⁱe⁽³ˣ⁾) + 4A(xⁱe⁽³ˣ⁾)(3e⁽³ˣ⁾ + i) + Axⁱe⁽³ˣ⁾ = 2xe⁽³ˣ⁾

Simplifying further, we get:

A(81/4 + 12i)e⁽³ˣ⁾xⁱ = 2x

To satisfy this equation for all x, we must have:

A(81/4 + 12i) = 0

and

A = 2/(xⁱe⁽³ˣ⁾)

Since A cannot be zero, we must have:

81/4 + 12i = 0

i = -27/4

Therefore, the particular solution is:

yp = -2/(27x⁽27/4⁾e⁽³ˣ⁾)

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Answer:

The last one is a perfect cube.

Step-by-step explanation:

I did the math

Answer:

Step-by-step explanation:

The volume is found by multiplying all the sides of the rectangular shape.

Thus the volume = 6 * 8 * 10 = 480 cubic feet

Hope that helps!

Answer:

480 cubic feet

Step-by-step explanation:

The volume of any prism is Bh, where B = AREA of the base and h = height of prism.

We're given:

Now, we solve the volume.

Therefore, the answer is 480 cubic feet.

Answer:

75.408 ft

Step-by-step explanation:

In 20 minutes, the angle swept by a minute hand is calculated as

(20/60) x 360° = 120°

The length of the minute hand = 36 ft

To calculate the distance moved by the minute hand, we solve for the fraction of the circumference of a circle swept by the minute hand in going through this 20 min.

we use the expression

Distance moved by the tip of the minute hand d = (θ/360) x 2πR

where

θ is the angle swept in the 20 minutes = 120°

R is the length of the minute hand, which is the radius of the circle formed if the minute hand moves completely in a 360° motion round the clock.

R = 36 ft

substituting values, we have

d = (120/360) x (2 x 3.142 x 36) = 75.408 ft

The tip of the minute hand moves 0.21 ft in 20 minutes.

The minute hand sweeps an arc of length L given by

L = Ф/360° × 2πR where

So, substituting the values of the variables into the equation, we have

L = Ф/360° × 2πR

L = 1/3°/360° × 2π × 36 ft

L = 1/(3 × 360) × 2π × 36 ft

L = 1/(3 × 10) × 2π ft

L = 1/30 × 2π ft

L = 1/15 × π ft

L = 3.1416/15 ft

L = 0.2094 ft

L ≅ 0.21 ft

So, the tip of the minute hand moves 0.21 ft in 20 minutes.

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You will able to deposit  X=7000.182500⁴⁷⁴⁵/182537⁴⁷⁴⁵now under the scenario Below.

A minimum deposit or initial  deposit is the lowest minimum  amount of the  money required to open an object account with all the  financial institution, such as the bank or the brokerage firm.

Based on the given scenario the formulate is-

X×(1+7.4%÷ 365)¹³×365 = 70000

Now we have to solve the equation -

X×(1+0.074/365)¹³×365=70000

Convert the number

X× 1+ (74/365000)¹³×365=70000

Now reduce

X×(1+37/182500)¹³×365=70000

Now we have to calculate=

X× (1+ 37/182500)⁴⁷⁴⁵=70000

We have to transfer the edition

X× (1+ 37/182500)⁴⁷⁴⁵=70000

Devide both side

X= 70000/ ( 182537/182500)⁴⁷⁴⁵

By Calculation we can get

X= 70000×182500^4745/182537⁴⁷⁴⁵

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The graph represents a functional relationship between two variables X and Y. We get y=3 for the value x=2

Domain is defined as the set of values of independent variables.

In the question, all x coordinates are domain.

In a function, for each domain we get a possible output from the dependent variables which is termed as range. In this graph, the y coordinates are range because y value is dependent on x value.

The graph shows five points are plotted on XY coordinate system that represents a relationship between independent variable X and dependent variable Y.

hence, this graph is plotted from a function.

from the graph we get the domain as {-4, -2, 0, 2, 4}

the ranges are = {-3, -2, -1, 1, 3}

we get, y=3 for the value of x= 2  

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Answer:

\( m \angle \: 1 = 120 \degree\)

Step-by-step explanation:

Given figure is of a rhombus.

Measures of the opposite angles of a rhombus are equal.

Therefore,

\(m \angle \: 1 = 120 \degree\)

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.

bank A

Dollars ($)     Kroner

80                  408

100                 510

120                 612

Since $ 80 = 408 Kroner

=>       $ 1    = 408 / 80 = 5.1 Kroner   . . . . . . conversion rate of $ to Kroner)

=>   $ 1700 = 1700 x 5.1 = 8670 Kroner

Hence Mia will get 8670 Kroner in exchange for $ 1700

The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).

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Answer:

C. all possible input values of the function

Step-by-step explanation:

Answer:

C is right

Step-by-step explanation:

domain is f(x)=x^2 is all real numbers but domain g(x)=1/x is all real numbers except for 0 which is x but domains and the rang can be the same also

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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9514 1404 393

Answer:

  B.  x +6y = 4.45; x +12y = 5.65

Step-by-step explanation:

The problem statement defines the variables for you. Using x and y for the cost of a loaf and the cost of an egg, respectively, each purchase can be represented by an equation of the form ...

  (number of loaves)x + (number of eggs)y = (amount spent)

The first purchase is described as

The second purchase is of a dozen eggs, which is 12 eggs. The description of this purchase can be ...

The situation can be represented by the equations shown in the attachment.

Step-by-step explanation:

a,ar,ar

2

shortest side is 9cm.