solve the following if you're good at math ​

a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta , I = k cos x / r² can be used to find the illumination at point p.

Light must be at the height of 7.07 for maximum illumination.

I = k cos x / r²

r² = h² + 10²

cos θ = h / [tex]\sqrt{h^{2} +10^{2} }[/tex]

then

I =  [tex]k \frac{h}{(h^{2} + 100)^{2/3}}[/tex]

on differentiating, we get,

[tex]\frac{dI}{dh} = k\frac{h^{2} + 100^{3/2 - 3h^{2}(h^{2} + 100 )^{1/2} } }{(h^{2} +100)^{3} }[/tex]

[tex]= k\frac{100 - 2h^{2} }{(h^{2} + 100)^{5/2} } \\\frac{dI}{dh} = 0\\ It gives that \\h = \sqrt{50} = 7.07\\on differentiating again,\\\frac{d^{2} I}{dh^{2} } = k \frac{(6h^{3} - 900h )}{(h^{2} + 100)^{7/2} }[/tex]

for h = 7.07,

[tex]\frac{dI^{2} }{dh^{2} } = -10267.6[/tex]

So , we can conclude that the light must be at the height of 7.07 for maximum illumination.

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Answer:

4x + 3y = 6

A = 4

B = 3

C = 6

Step-by-step explanation:

A line have a function:

y = ax + b

Because the line has a slope of - 4/3

=> a = - 4/3

=> y = - 4/3 x + b

Because the line go through point (6; - 6)

=> - 6 = - 4/3 .6 + b

=> b - 8 = - 6

=> b = 2

=> The function of the line

y = - 4/3 x + 6

=> 3y = - 4x + 6

=> 4x + 3y = 6

We get the equation for the points of the data as x  y + 6 = 0

We are given the data as:

X              g(x)

10            - 16

11             - 17

12            - 18

13            - 19

We need to find the equation for the data.

Slope = ( - 17 + 16 ) / ( 11 - 10)

m = - 1 / 1 = - 1

Now, the equation will be:

y - y₁ = m (x - x₁)

Substituting the values, we get that:

y + 16 = - 1( x - 10)

y + 16 = - x + 10

x + y + 16 - 10 = 0

x + y + 6 = 0

Therefore, we get the equation for the points of the data as x  y + 6 = 0

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Answer:

calculators are available

Step-by-step explanation:

[tex] \large \bf \implies{32 {m}^{15} {n}^{10} }[/tex]

[tex]\bf \longrightarrow{(2m^{3}n^{2})^{5} } \\ \\ \bf \longrightarrow {2}^{5} \times ( {m}^{3})^{5} \times ( {n}^{2})^{5} \\ \\ \bf \longrightarrow32( {m}^{3})^{5}( {n}^{2})^{5} \\ \\ \bf \longrightarrow32 {m}^{15} {n}^{10} [/tex]

Note : We have used the two exponent rules:

[tex](1) \: \: \large \bf \boxed{ \bf \green{(ab)^{n} = {a}^{n} \times {b}^{n} }}[/tex]

[tex](2) \: \: \large \bf \boxed{ \bf \green{(a^{n})^{m} = {a}^{nm} }}[/tex]

Answer: -6.62 x 10^-8

Step-by-step explanation:

Answer:

n=7

Step-by-step explanation:

Which flaw most accurately illustrates the graphed function's domain?

The inequality most accurately depicts the part's intended domain, which should be -9<x ≤2.

Domain here refers to the x change. The values of with regard to function should be the domain in this case. Additionally, we need to pay attention to the blank line that starts at -9 to 2 in x values.

Since 9 should not be filled however 2 should be.

Therefore, The inequality most accurately depicts the part's intended domain, which should be -9<x ≤2.

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The word phrases given can be written in algebraic expressions as:

1. B. 4g

2. B. 6/(x + y).

"Product" means multiplication.

"The product of g and 4" can be written as an algebraic expression as: 4 × g = 4g.

"Quotient" means the result you get by dividing a number by another number.

"Sum" means addition, or what you get by adding two quantities together.

Therefore, "the sum of x and y" is written in algebraic expression as: x + y.

Thus, the quotient of 6 and (x + y) would be written in algebraic expression as: 6/(x + y).

Therefore, the word phrases given can be written in algebraic expressions as:

1. B. 4g

2. B. 6/(x + y).

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Answer: [tex]\frac{3}{4s}[/tex]

Step-by-step explanation:

3s^2 / 4(s)^3=

3s^2 / 4s^3=

3/4 * s^2/s^3=

3/4 * s^(2-3)=

3/4 * s^(-1)=

3/4 * 1/s=

3*1 / 4s=3/(4s)

Answer:

Min = 0

Max = 51

M = 25.5

Q1 = 16.5

Q3 = 39

Hope this helps! <3

Answer:

(-5,5)

Step-by-step explanation:

Using composite functions, the expression that models the distance that she runs is:

D. 5.5 - 0.1t.

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

In this problem, we have that:

Hence the distance as a function of the temperature is given as follows:

(D ∘ S)(t) = D(S(t)) = 0.5(11 - 0.2t) = 5.5 - 0.1t.

Which means that option D is correct.

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Let [tex]x=2\cos(t)[/tex] and [tex]y=2\sin(t)[/tex], so that

[tex]x^2 + y^2 = 4\cos^2(t) + 4\sin^2(t) = 4[/tex]

is preserved. Then from the surface equation, we get

[tex]z = xy = 4\cos(t)\sin(t) = 2\sin(2t)[/tex]

The curve of intersection is then given by the vector function

[tex]\vec r(t) = 2\cos(t) \, \vec\imath + 2\sin(t)\,\vec\jmath + 2\sin(2t)\,\vec k[/tex]

Answer:

Ratios compare two numbers, usually by dividing them If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10

Step-by-step explanation:

hope this helps u :) have a good day! ^-^

Answer:

hey thank you it's I don't know lol thanks

A parabola has an axis of symmetry y =3 and passes through the point (2, 1), another point that lies on the graph of the parabola is (2,5).

Axis of symmetry:

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.

Given,

Axis of Symmetry y = 3.

One point = (2,1)

Here we need to find the another point that lies on the graph of the parabola.

Use the axis of symmetry.

Point given (2,1) is 2 units away from that axis, lower.

=> 1 + 2 = 3

Take two units higher,

=> 3 + 2 = 5

and is the another point (2,5), on the same parabola.

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The variables in the point-slope form of a line (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.

Given that the variables in the point-slope form of a line.

The general form of the equation of a line is y - y₁ = m (x-x₁) where  m is the slope of line, y₁ and x₁ is any point on the line

It is an equation of degree one x and y represent the coordinate of the point on the line represented in the coordinate plane

m = slope of the line

The general equation of a line is y = mx + c where

m = slope of line

(x₁ , y₁) = it is the given point on the line as data points are represented as (x₁,y₁) , (x₂,y₂) , (x₃,y₃) and so on

(x ,y) = it is any point line where x is any point on the x-axis and y is any point on y-axis

Hence, the variables in the point-slope form of a line where (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.

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The graphs of the equations can be obtained by finding the intercepts, and drawing a line through the intercepts.

1. Please find attached the graph of 2•x - y - 6 = 0

2. Please find attached the graph of 4•x + 2•y + 8 = 0

The graph of the linear equations using the x and y intercepts are found as follows;

1. 2•x - y - 6 = 0

Therefore;

2•x - y - 6 = 0

y = 2•x - 6

The y-intercept is given by the point where x = 0

The y-intercept is therefore;

y = 2×0 - 6 = -6

The x-intercept is given by the point where y = 0

Therefore;

0 = 2•x - 6

x = 6/2 = 3

Please find attached the graph of 2•x - y - 6 = 0, created using the x and y-intercept.

2. 4•x + 2•y + 8 = 0

Therefore;

4•x + 2•y + 8 = 0

y = -(4•x + 8)/2 = -2•x - 4

y = -2•x - 4

The y-intercept is therefore;

y = -2×0 - 4 = -4

The y-intercept is y = -4

The x-intercept is therefore;

0 = -2•x - 4

x = -4/2 = -2

The x-intercept is at x = -2

Please find attached the graph of 4•x + 2•y + 8 = 0, created using the x and y-intercept.

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Answer:

1194 ....................... is the answer

here's the coordinates

b'= (4,5)

c'= (5,3)

Step-by-step explanation:

30 cal for 1 lb

x cal for 38.45 lbs

x = 38.45lbs × 30 cals

x = 1153.5 cals

Answer:

False

Step-by-step explanation:

Without a graph, figure, or any other context the cost of grapefruit in 1995 in not related to the other years by any other facts or figures.

Answer: n= -1/2 -3m

Step-by-step explanation:

The  total value of the uniform Aileen sold is x= 2260 on monthly Commission sells.

Given,

Let us assume the all little League uniform = x

Aileen first commission 10% of 2000$ in sales.

Aileen Second Commission 12% of (x-2000)$

Total Commission Aileen Earner = 10% ×2000 + 12% × (x-2000)

                                       231.2   = 0.1× 2000 + 0.12× (x-2000)

                                        231.2   = 200 + (0.12x - 240 )

                                        231.2   = 200 +  0.12x - 240

   After Transformation, we get

                                        0.12x = 231.2 - 200 +240

                                        0.12x = 271.2

                                               x = 271.2/.12

                                               x = 2260

Aileen Sell the total value of Lopez Sporting Goods Uniform is 2260.

So the final Answer is  x = 2260$.

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Answer:

0.75

Step-by-step explanation:

it goes tenths hundredths thousandths....

Answer:

0.75

Step-by-step explanation:

4 is the hundredth in this number. The number after 4 is 5. The rule is if its 5 and over you round up and if not, you round down. In this case the number is 5 so we round up. So the number becomes 0.75 instead of 0.74

Answer:

x = 7

Step-by-step explanation:

3x = 21 ( isolate x by dividing both sides by 3 )

x = 7

Answer:

d. p+1

a negative 1 point something decimal plus one negative decimal.

gl sh awty

It is true that if a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function.

Without further explanation, matrices represent linear maps and enable explicit computations in linear algebra. In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or a property of such an object. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices. The composition of linear maps, for instance, is represented by matrix multiplication.

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