From atop a 15 m lighthouse, a man spots a dolphin 50 m out to sea. Find the angle of depression from the man to the dolphin, to nearest degree.

The Fourier series coefficients for T-2 and A-4 are Ao = 2, B(n-odd) = 0, and B(n-even) = -(4/nπ). The Fourier series for the function is then given by:Y(t) = A0 + ΣB(n)cos(nπt/T) + ΣB(n)

The Fourier series coefficients are used to determine the Fourier series of a given function. The Fourier series is an infinite series of sines and cosines which, when summed, gives an approximation of the original function.

The coefficients are determined by integrating the function over a period and solving for the coefficient of each term.

The coefficients for the function T-2 and A-4 are determined by first calculating the period of the function. The period of the function is T=4. The coefficients are then calculated by integrating the function from 0 to T and solving for each coefficient. The coefficients for T-2 and A-4 are then calculated as follows:

A0= 2

B(n-odd) = 0

B(n-even) = -(4/nπ)

Therefore,

Y(t) = A0 + ΣB(n)cos(nπt/T) + ΣB(n)

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The correct question should be: If T-2 And A-4, Calculate The Fourier Series Coefficients (Integers) Ao B (N-Odd) B (N-Even)- (N-1,2,3,..) Such That: Y(T)-A0 + ?

Answer:

[tex]\text{c)} \quad y=5(2)^x[/tex]

[tex]\text{d)} \quad y=6(2)^x[/tex]

[tex]\text{e)} \quad y=3(7)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 20=ab^2[/tex]

[tex]\implies 640=ab^7[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{640}{20}=\dfrac{ab^7}{ab^2}[/tex]

[tex]\implies 32=\dfrac{b^7}{b^2}[/tex]

Solve for b:

[tex]\implies 32=b^7 \cdot b^{-2}[/tex]

[tex]\implies 32=b^{7-2}[/tex]

[tex]\implies 32=b^5[/tex]

[tex]\implies b=2[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 20=a \cdot 2^2[/tex]

[tex]\implies 20=4a[/tex]

[tex]\implies a=5[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=5(2)^x[/tex]

---------------------------------------------------------------------------------------

Given points:

As a is the y-intercept, a = 6.

Substitute the point (3, 48) and the found value of a into the  exponential function formula and solve for b:

[tex]\implies 48=6b^3[/tex]

[tex]\implies 8=b^3[/tex]

[tex]\implies b=2[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=6(2)^x[/tex]

---------------------------------------------------------------------------------------

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 21=ab^1[/tex]

[tex]\implies 147=ab^2[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{147}{21}=\dfrac{ab^2}{ab^1}[/tex]

[tex]\implies 7=\dfrac{b^2}{b^1}[/tex]

Solve for b:

[tex]\implies 7=b^2 \cdot b^{-1}[/tex]

[tex]\implies 7=b^{2-1}[/tex]

[tex]\implies 7=b^1[/tex]

[tex]\implies b=7[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 21=7a[/tex]

[tex]\implies a=3[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=3(7)^x[/tex]

Answer:

x = 130°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

To simply put:

x = 85 + 55

x = 130°

System Linear equation has no solution , because it is paralell lines but no intersection.

What is system linear equation?

An equation for a line is known as a linear equation. alternatively, y + 0.5x 3.5 = 0 and others. (Note that each linear equation is the same.) When multiple linear equations interact, we get a system of linear equations.

Here the given system linear equations,

[tex]3y=\frac{3}{2}x+6[/tex] -------> 1    and [tex]\frac{1}{2}y-\frac{1}{4}x=3[/tex] --------> 2

Divide by 3  of equation 1 on both sides then,

[tex]y=\frac{1}{2}x+2[/tex]  -----------> 3

Now put 3 into 2 then,

=> [tex]\frac{1}{4}x+1-\frac{1}{4}x=3[/tex]

=> 1=3

Hence the given system equation has no solution , because it is paralell lines but no intersection.

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The equation for the proportional is y= 3x.

The correct option is (B).

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressionsprinted on the left and right sides.

LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Points taken as (2, 6) and (6, 18).

So, the slope is

slope = (18-6)/ (6-2)

slope = 12 /4

slope= 3

and, the equation of line is

y- 6 = 3(x- 2)

y-6 = 3x - 6

y= 3x

Hence, the equation is y= 3x.

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Answer:

I think the answer is 288.

Step-by-step explanation:

The greatest possible error of 4700 is equal to 2,350.

In Mathematics, precision can be defined as a quality which is independent of accuracy because it only describes how close together are numerical values that are obtained in a series of measurements.

In Mathematics, the greatest possible error (GPE) of a measurement can be defined as one-half of the value of a given smallest measuring unit, or one-half of a given precision.

This ultimately implies that, the greatest possible error (GPE) of a measurement can calculated by dividing the precision by two and this is represented by this mathematical expression;

Greatest possible error (GPE) = precision/2

Greatest possible error (GPE) = 4700/2

Greatest possible error (GPE) = 2,350.

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Answer:

2 3/4

Step-by-step explanation:

11-4=7-4=3 there is 4 twice and 3 remaining making 2 and 3/4

Answer: 2 3/4

Step-by-step explanation: To convert 11/4 in a mixed fraction, we will divide 11 by 4.

When 11 is divided by 4, the quotient is 2, the remainder is 3 and the divisor is 4.

After getting the new numerator, simplify and the fraction that will give us the final answer in the mixed number form.

Hence, 11/4 can be written as a mixed number, 2 3/4.

Answer:

blank = 18.2

Step-by-step explanation:

17/10 = 1.7

66/|0 = 6.6

Then:

23.1 + 17/10 - x =66/10

is equivalent to:

23.1 + 1.7 - x =  6.6

24.8 - x = 6.6

24.8 - 6.6 = x

18.2 = x

Check:

23.1 + 1.7 - 18.2 = 6.6

Step-by-step explanation:

commn this number agen division

The cost of 4.25kg of potatoes will be £2.38

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 4(for every one boy there are 3 girls) 1 / 4 are boys and 4 / 5 are girls. 0.20 are boys (by dividing 1 by 5). It can also be defined as the size, number, or amount of one thing or group as compared to the size, number, or amount of another.

The cost of 2.5kg of potatoes is £1.40

Therefore the cost of 1kg potatoe = 1.40/2.5 = £0.56

This means that the cost of 4.25 kg = 0.56× 4.25

= £2.38

Therefore the cost of 4.25kg of potatoes is £2.38

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Where one would like to see either a World War II movie or one that is based on a comic book character but does not feature aliens. The set of movies they are interested in seeing is: "WWII U (Comix n Aliens')" (Option C) Note that this is a prompt related to sets.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form. Sets are often expressed by curly brackets; for example, A = 1,2,3,4 is a set.

Some examples of sets include the empty set, finite set, equivalent set, subset, universal set, superset, and infinite set.

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There are 750 women runners at the festival out of 1050 runners.

What is the arithmatic calcaltion?

Arithmetic is a branch of mathematics that deals with the manipulation of numbers and the properties of operations such as addition, subtraction, multiplication, and division. It is often referred to as "elementary mathematics" or "number theory" and is one of the oldest and most basic branches of mathematics.

If 5/7 of the runners at the festival are women, we can use this information to find how many runners are women.

Let's call the number of women runners W. We know that 5/7 of the runners are women, so we can set up the following proportion:

W / 1050 = 5/7

To find the value of W, we can cross-multiply and then solve for W:

W * 7 = 5 * 1050

W = 750

Hence, there are 750 women runners at the festival out of 1050 runners.

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Answer:

Step-by-step explanation:

Item Selling Price

Pizza $5.00

Sub $3.00

---------------

Quantity Equation : s = p + 11

Value Equation : 3s+5p = 233

---------------------------

Substitute for "s" and solve for "p"

3(p+11) + 5p = 233

8p + 33 = 233

8p = 200

p = 25 (# of pizzas)

----

s = p+11 = 36 (# of subs)

Therefore , the solution of the given problem of ratio comes out to be  300,000.

A portion or fraction in mathematics displays how frequently one number is included in another. For instance, if there are eight orange and six lemons in a fruit plate, the proportion of oranges to lemonade is eight to six, or 8:6, which is comparable to the ratios 4:3 or the decimal 1.333.

Here,

We must use our grasp of proportionality to establish the maximum amount of shares that can be owned in this exercise.

The 20 huge variations will allow Blackbird Oil to store a total of 300,000 gallons.

The details in the assertion can be summed up as follows:

20 brand-new, sizable oil storage tanks.

The ratio is 4:5 for 12,000 gallons.

Because of the proportional ratio of 4.05, the enormous receptacles are 1.25 times larger than the ordinary ones, giving us:

=> 1200 * 1.25 = 15000

=> 15000 * 20 = 300000

As a result, the supplied problem's answer equals 300,000.

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The expressions that have the same product as 0.056 x 0.34 is A. A.56 * 0.34/100, 000.

The concept that will be used is finding of the products or quotient then compare .

The product of the given value 0.056 x 0.34 is 0.01904

The we can compare to the given options as;

A.56 * 0.34/100, 000 = 0.01904

B.0.56*3.4= 1.904

C. 56*34*0.001= 1.904

D. 56*34*1/100 *1/100 = 0.1904

Therefore, option A is correct because it have the same value with the given values.

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missing options:

A.56 * 0.34/100, 000

B.0.56*3.4

C. 56*34*0.001

D. 56*34*1/100 *1/100

Answer:

3.75 cm²

Step-by-step explanation:

Area of a triangle = 1/2bh = 1/2(2.5)(3) = 3.75 cm²

Answer:

Step-by-step explanation:

P=m/v

Density = mass / volume

30 is mass

160 is ml

P=30/160

0.1875

The vertex is (5,-9)

A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

The function is given as f(x) = (x - 8) (x - 2)

Taking the parentheses out

f(x) = x2 - 2x - 8x + 16

f(x) = x2 - 10x + 16

The function's vertex is (h, k)

h = -b / 2a

Changing the values

h = - (-10) / 2 (1) (1)

h = 10 / 2

the x coordinate for h = 5

changing the quadratic function's x value

f(5) = (5 - 8) (5 - 2) (5 - 2)

f(5) = (-3) (3) (3)

f(5) = k = -9

Consequently, the vertex is (5, -9).

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Answer and Explanation: To get the two terms on the right to combine into one term, we need the denominators of both terms to be the same. To do this we can plug in x+3 for the bottom left denominator and x-4 for the bottom right denominator. This makes both denominators (x+3)(x-4).

The numerators of both terms on the right just have to add up to 3x-2. One way we could do this is to the right one as 3x and the other as -2 or vice versa.

(x+3)(x-4) simplifies to x^2-x-12 which is why the denominator of the term on the left is that.

The next year population is 61500

step1

present population=60,000

increment per year=2.5%

next year population = 60000 + 2.5 % of 60,000

2.5% of 60000 =60000*2.5%

=60000*2.5/100

=1500*2.5

=3750

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Answer:

58500

Step-by-step explanation:

100

%

−

2.5

%

=

100%−2.5%=

97.5

%

97.5%

Whole population before decrease = 100%, then subtract decrease

97.5% of the current population means

97.5

100

of it.

97.5% of the current population means  

100

97.5

​

 of it.

"Percent" literally means "out of 100."

97.5

100

=

100

97.5

​

=

0.975

0.975

To find 97.5% of the current population, multiply by

0.975

:

To find 97.5% of the current population, multiply by 0.975:

60000

×

0.975

=

60000×0.975=

58500

58500

​

Method 2

Find the decrease, 2.5% of 60000:

Find the decrease, 2.5% of 60000:

2.5

100

=

100

2.5

​

=

0.025

0.025

60000

×

0.025

=

60000×0.025=

1500

1500

Subtract the decrease from the current pop:

Subtract the decrease from the current pop:

60000

−

1500

=

60000−1500=

58500

58500

​

population

percent

58500

97.5%

60000

100%

1500

current pop

current pop - decrease

2.5% decrease

Your Solution:

58500

Answer:

Brand Z

Step-by-step explanation:

Set up all of them up as a fraction x/y where x is the fluid ounces and y is the cost.

Next, find the values of all the fractions and note them down.

Brand Z had the highest cost per fluid ounce of 2, and therefore is the correct answer.

Answer:

Brand w.

Step-by-step explanation:

First thing you want to do is divide your fluid ounces by your given cost. Which ever is greatest is your answer.

Brand w: 20/12.00 = 1.66

Brand x: 15/11.25 = 1.33

Brand y: 10/6.50 = 1.53

Brand z: 5/2.50 = 2.00

Brand w has the greastest price per fluid ounce compared to the rest of the brands.

(a) At the top of the ride, her apparent weight is 518.5 N. This is because, at the top of the ride, the centripetal force acting on her is directed towards the center of the Ferris wheel, which acts in opposition to her weight. Since her weight is 520 N, and the centripetal force is 1.5 N, the net force acting on her is 518.5 N.

Apparent weight, also known as effective weight or net weight, is the weight that an object appears to have when it is in motion. It is the force that an object feels as a result of a combination of its true weight and any additional forces acting on it, such as the centripetal force.

(b) At the bottom of the ride, her apparent weight is 520.5 N. This is because, at the bottom of the ride, the centripetal force acting on her is in the same direction as her weight, so the net force acting on her is the sum of her weight and the centripetal force.

(c) The radius of the Ferris wheel can be determined using the formula v^2 = r * g, where v is the angular velocity, r is the radius and g is the acceleration due to gravity. Given that angular speed and the apparent weight is known, you can use this formula to find the radius.

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4.835

(full number)

4.8357033e+24

2^82 = 4.83 We have to add the decimal to fine the real number.

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

For example, [tex]= > 3^82 = 1.33[/tex] so:

→ 2^82

→ = 4.83 with a decimal.

Therefore, 2^82 = 4.83 We have to add the decimal to fine the real number.

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Answer:

Step-by-step explanation:

terms1+1ofx

Answer:

add 500 and 50 together then multiple that number my 20 then do the same but multiple by 50

Answer:nitrogine

Step-by-step explanation:

Answer:

Nitrogine. because all the others are in it