Someone please help
Me with this

Answer:

The beam of the light is moving along the shoreline at the rate of [tex]\mathbf{ 160 \ \pi \ mi/min}[/tex]

Step-by-step explanation:

From the given information: Let say x is the distance between the lighthouse and the shoreline. Then, the  tangent of  trigonometry can be written as:

[tex]tan (\theta )=\dfrac{x}{4}[/tex]

In respect to time, the expression can be derived as:

[tex]sec^2 (\theta) \dfrac{d \theta}{dt} = \dfrac{1 }{4}\dfrac{dx}{dt}[/tex]

[tex]\dfrac{dx}{dt}=\dfrac{4}{cos ^2 (\theta) }\dfrac{d \theta}{dt}[/tex]

To estimate the value of [tex]\dfrac{dx}{dt}[/tex], we need to know cos²(θ) and D

where;

D = [tex]\sqrt{4^2+4^2}= \sqrt{32}\ mi[/tex]

[tex]cos (\theta) = \dfrac{4}{D}[/tex]

[tex]cos (\theta) = \dfrac{4}{\sqrt{32}}[/tex]

[tex]cos (\theta) = \dfrac{4}{\sqrt{16 \times 2}}[/tex]

[tex]cos (\theta) = \dfrac{4}{4 \sqrt{\ 2}}[/tex]

[tex]cos (\theta) = \dfrac{1}{ \sqrt{\ 2}}[/tex]

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

Finally, we substitute the value of [tex]cos^2(\theta)[/tex] and [tex]\dfrac{d \theta}{dt}[/tex] in the expression derived earlier.

i.e.

[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 10 \ rev/min[/tex]

where;

10 rev/min = (10 × 2π) rad/min = 20π rad/min

Then:

[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 20 \ \pi[/tex]

[tex]\mathbf{\dfrac{dx}{dt} = 160 \ \pi \ mi/min}[/tex]

Answer:

The volume  [tex]V = \frac{75}{2}[/tex] units

Step-by-step explanation:

From the question we are told that

 The equation of the plane is  [tex]z = 2x + 5y + 1[/tex]

The range of the rectangle on the x and y axis is  [tex]\{ (x, y) | -1 \le x \le 0 , 1 \le y \le 4 \}[/tex]

Generally the volume is mathematically represented as

        [tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {z} \, da[/tex]

Here stands for the area of the solid

So    

           [tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {(2x + 5y + 1 )} \, dxdy[/tex]

           [tex]V = \int\limits^{4}_{1} [{(\frac{2x^2}{2} + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]

            [tex]V = \int\limits^{4}_{1} [{(x^2 + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]

          [tex]V = \int\limits^{4}_{1} [{((0)^2 + 5(0)y + (0) )} ] -[{((-1)^2 + 5(-1)y + (-1) )} ] \, dy[/tex]

        [tex]V = \int\limits^{4}_{1} 5y \, dy[/tex]

        [tex]V = 5 [ \frac{y^2}{2} ]|\left \ 4 } \atop { 1 }} \right. \, dy[/tex]

       [tex]V = 5( [ \frac{4^2}{2} ] - [ \frac{1^2}{2} ] )[/tex]

        [tex]V = \frac{75}{2}[/tex]

Answer:

1 and 2/4

or 2

Step-by-step explanation:

Answer:

The range of the following set of points is {4, -2, -8}

Step-by-step explanation:

∵ The set of points is {(3, 4), (7, -2), (11, -8)}

∵ The range is the y-coordinates of these points

∵ The y-coordinates of the points are 4, -2, -8

∴ The range is {4, -2, -8}

∴ The range of the following set of points is {4, -2, -8}

Answer:

y = - [tex]\frac{1}{32}[/tex] x²

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

[tex]\sqrt{(x-0)^2+(y+8)^2}[/tex] = | y - 8 |

Square both sides

x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides

x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )

x² + 32y = 0 ( subtract x² from both sides )

32y = - x² ( divide both sides by 32 )

y = - [tex]\frac{1}{32}[/tex]x²

The standard form of the equation of the parabola is y = -x²/32

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

The general form of a parabola is

(x-h)^2 = 4p(y-k)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

√(x-0)² + (y-8)² = | y - 8 |

Square both sides

x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides

x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )

x² + 32y = 0 ( subtract x² from both sides )

32y = - x² ( divide both sides by 32 )

y = - x²/32

Hence, The standard form of the equation of the parabola is y = -x²/32

learn more on parabola:

https://brainly.com/question/1615961

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Answer:

L=7

W=10

Step-by-step explanation:

W=2L-4

WL=70

(2L-4)L=70

2L^2-4L-70=0

2(L^2-2L-35)=0

2(L-7)(L+5)=0

L-7=0

so:

L=7 IS THE LENGTH OF THE RECTANGLE.

W=2*7-4

W=14-4

W=10 IS THE WIDTH OF THE RECTANGLE.

PROOF:

7*10=70

70=70

Answer:

205.74 cm

Step-by-step explanation:

Answer: 5x — 260

Step-by-step explanation:

juss fye like that lol

Answer:

option C :5x – 260

Step-by-step explanation:

hope this helps

Answer:

Approximately 189 feet

Step-by-step explanation:

A complete one rotation around the path is the circumference of the garden.

Given that the diameter of the garden = 60 feet.

The circumference of a circle = 2[tex]\pi[/tex]r

where r is the radius.

So that:

r = [tex]\frac{diameter}{2}[/tex]

 = [tex]\frac{60}{2}[/tex] = 30 feet

The distance covered by Gina in one rotation around the path =  2[tex]\pi[/tex]r

                                           = 2 x [tex]\frac{22}{7}[/tex] x 30

                                           = [tex]\frac{1320}{7}[/tex]

                                           = 188.57

                                           ≅ 189 feet

Therefore, Gina covered a distance of approximately 189 feet around the path.

Answer:

C. 125%

Step-by-step explanation:

Because an entire box of 100 is colored, we automatically know it is at least 100%. Which means both A and B are incorrect. There are two tens filled, so we have 120%. There is another 5 boxes are filled, so we have 125%, which is C.

I hope that this helps! :)

Answer:2.00

Step-by-step explanation:

Answer:20

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C because the line is going through the origin and it is going at a constant rate

Answer:

the third one

Step-by-step explanation:

im pretty sure!

Answer:

14.98

Step-by-step explanation:

I used a calculater

Answer:

[tex]x_{1}[/tex]=3-[tex]\sqrt{6}[/tex] , [tex]x_{2}=3+\sqrt{6}[/tex]

Step-by-step explanation:

Answer:

4,500

Step-by-step explanation:

A number that ends with 0 and 5 is divisible by 5,and number that is a multiple of 9 can be divided by 9. 45 is divisible by 5 and 9, so 4500 is an easy 4 digit number to come up with.

Answer:

418

Step-by-step explanation:

Answer:

y=5/4x+-2, and y=-4/1x+3

Step-by-step explanation:

Answer:

t = 3.74165738677 or 3.74

Step-by-step explanation:

Step 1:

( t - 3 )² = 6      Equation

Step 2:

t² - 3² = 6       Open Parentheses

Step 3:

t² - 9 = 6          Exponents

Step 4:

t² = 14         Add 9 on both sides

Step 5:

t = [tex]\sqrt{14}[/tex]       Find the square root of 14

Answer:

t = 3.74165738677 or 3.74        Round

Hope This Helps :)

Answer:

The arrow is at a height of 48 ft after approximately 0.55s and after 5.45s.

Step-by-step explanation:

took the assignment

Answer:

Jorge ran 32 laps

Step-by-step explanation:

The equation is 8x4=32

Answer: 7.1% and 6%.

Step-by-step explanation:

Given data:

Sample size (n) = 11

Standard deviation = 2.2

Margin of error confidence level 95% = 1.96

Margin of error confidence level of 90% = 1.65

Solution:

P = 2.2/11

= 0.2.

ME = z √p (1-p)/n

at 95% interval

ME = 1.96 * √ 0.2 ( 1 – 0.2 ) / 11

= 1.96 * 0.03636

= 0.071.

= 7.1%

At 90% interval

ME = 1.65 * √ 0.2 ( 1 – 0.2 ) / 11

= 1.65 * 0.03636

= 0.06.

= 6%

how do you not know these kids lol

Answer:

k = 3.5

Step-by-step explanation:

From the graph in the picture attached,

Relation between balloons height (y) is directly proportional to the time (x)

y ∝ x

y = kx

Where 'k' is a proportionality constant.

Now we substitute the point (8, 28) in the equation,

28 = k(8)

k = [tex]\frac{28}{8}[/tex]

k = 3.5

k ≈ 3.5

Therefore, value of constant 'k' is 3.5

Answer:

31x+21

Step-by-step explanation:

7x+3(8x+7)

7x+24x+21

31x+21

Answer 31x + 21

Step-by-step explanation: can’t

Answer:

x = 8

Step-by-step explanation:

Step 1:

17x + 14 + 4x - 2 = 180          Sum of a line

Step 2:

21x + 12 = 180        Combine Like Terms

Step 3:

21x = 168       Subtract 12 on both sides

Step 4:

x = 168 ÷ 21      Divide

Answer:

x = 8

Hope This Helps :)

Step-by-step explanation:

4x - 2 + 17x + 14 = 180

21x + 12 = 180

Subtract 12 from both sides and you get :

21x = 168

Devide

[tex] \frac{21x}{21} = \frac{168}{21} \\ x = 8[/tex]

Answer:

Im pretty sure every hat and mask is 1 dollar