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vladimir2022 [97]

3 years ago

14

An opaque cylindrical tank with an open top has a diameter of 3.25 m and is completely filled with water. When the afternoon Sun

reaches an angle of 22.8° above the horizon, sunlight ceases to illuminate the bottom of the tank. How deep is the tank

1 answer:

kicyunya [14]3 years ago

6 0

Answer:

10.69

Step-by-step explanation:

We must first know that the angle of refraction is given by the following equation:

n_water * sin (A_water) = n_air * sin (A_air)

where n is the refractive index, for water it is 1.33 and for air it is 1.

The angle (A) in the air is 22.8 °, and that of the water is unknown.

Replacing these values we have to:

1.33 * sin (A_water) = 1 * 0.387

sin (A_water) = 1 * 0.387 / 1.33

A_water = arc sin (0.2907) = 16.9 °

now for the tank depth:

h = D / tan (A_water)

D = 3.25

Replacing

h = 3.25 / tan 16.9 °

h = 10.69

Therefore the depth is 10.69 meters.

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4 0

3 years ago

A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is

eduard

Answer:

The number of nickels is 45 and the number of dimes is 72.

Step-by-step explanation:

Let

x ----> number of nickels

y ----> number of dimes

Remember that

$1\ nickel=\$0.05$

$1\ dime=\$0.10$

so

$0.05x+0.10y=9.45$ ------> equation A

$0.05x+0.10(2y)=16.65$

$0.05x+0.20y=16.65$ ------> equation B

<em>Solve the system by substitution</em>

we have

$0.05x+0.10y=9.45$ ------> equation A

$0.05x+0.20y=16.65$ ------> equation B

Multiply both equations by 100 both sides

$5x+10y=945$ ----> $5x=945-10y$ --> equation C

$5x+20y=1,665$ ----> equation D

substitute equation C in equation D

$(945-10y)+20y=1,665$

solve for y

$945+10y=1,665$

$10y=1,665-945$

$10y=720$

$y=72\ dimes$

Find the value of x

$5x=945-10y$

$5x=945-10(72)$

$5x=225$

$x=45\ nickels$

<em>Alternative Method</em>

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is the point (45,72)

therefore

The number of nickels is 45 and the number of dimes is 72.

7 0

3 years ago

Solve the system by substitution.<br> y = 8x<br> y = 10x - 4<br> Submit Answer

erik [133]

Answer:

x=1, y=8

Step-by-step explanation:

Plug y=8x into y=10x-4.

8x=10x-4

Subtract 10x from each side.

-2x=-2

Divide each side by -2.

x=1

Plug x=1 into y=8x.

y=8(1)

y=8

5 0

3 years ago

Find the equation of the line through (6,8) which is parallel to the line y=4x−6.

Ratling [72]

Answer:

$y=4x-16$

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when x is 0)
Parallel lines always have the same slope

<u>1) Determine the slope (m)</u>

<u /> $y=4x-6$ <u />

4 is in the place of m, making it the slope. Because parallel lines have the same slope, the slope of the line is therefore 4. Plug this into $y=mx+b$ :

$y=4x+b$

<u>2) Determine the y-intercept (b)</u>

$y=4x+b$

Plug in the given point (6,8) and solve for b

$8=4(6)+b\\8=24+b$

Subtract 24 from both sides to isolate b

$8-24=24+b-24\\-16=b$

Therefore, the y-intercept of the line is -16. Plug this back into $y=4x+b$ :

$y=4x-16$

I hope this helps!

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3 years ago

Paco solves the equation -3x-5=1

Levart [38]

Answer:

x= -2

Step-by-step explanation:

-3x-5=1

+5 on each side to balance the equation:

-3x=6

Divide by -3 on each side:

x=-2

7 0

3 years ago

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