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3 years ago

Help for Geometry #6 and 7

Mathematics

1 answer:

Arturiano [62]3 years ago

8 0

Find the area of the rectangle and the 1/2 circle, then subtract the half circle's area from the rectangle's.
Area of the rectangle is 30in.
Area of the 1/2 circle is 19.625.
Subtract
30-19.625
10.375
(Round it to 10.4 in this case)

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What is the greatest common factor of 12 and 90?

qwelly [4]

The greatest common factor (gcf) is 6.

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3 years ago

Santos is a lifeguard and spots a drowning child 50 meters along the shore and 60 meters from the shore to the child. Santos run

Amanda [17]

Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

The distance along the shore of the child = 50 meters

The distance from the shore of the child = 60 meters

The rate at which Santos can run = 4 m/s

The rate he can swim = 0.9 m/s

Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

Simplifying using a graphing calculator gives;

$\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}$

1519·x² - 151900·x + 3505900 = 0

x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)

x ≈ 63.86 m or x ≈ 36.145 m

We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same

Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child

7 0

2 years ago

The break even point is the point at which income equals expenses. Ridgemont High School is paying $13,200 for thr writing and r

Nikolay [14]

Answer:880

Step-by-step explanation: They need to cover expense of $13200. If printing fee is $25 and they sell the books for $40 each, then that means when selling a book they cover expense of printing plus they earn $15 per book.

So if they earn $15 per book that means they have to sell 13200/15=880 books to break even.

If you want to solve this by using equation the this would look like this:

expenses: $13200 + $25x where x is number of books sold

earnings: $40x

Equation:

13200+25x=40x

13200=15x

x=880

4 0

2 years ago

100 POINTS Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the systems of equations

OLEGan [10]

Answer:

2x + y = 12 x = 9 − 2y x + 2y = 9 2x + 4y = 20 x + 3y = 16 2x − y = 11 y = 11 − 2x 4x − 3y = -13 y = 10 + x -3x + 3y = 30 2x + y = 11 x − 2y = -7 x = 2, y = 7 arrowRight x = 5, y = 2 arrowRight x = 3, y = 5 arrowRight x = 7, y = 6

Step-by-step explanation:

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2 years ago

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A mixture of 17 %disinfectant solution is to be made from 10% and 20% disinfectant solution. How much of each solution should be

8090 [49]

Since 20 total gallons are needed, the amount of 10% solutions can be x and the amount of 20% solutions can be (20-x) since they add up to 20. In addition, the 17% solution has 20 gallons. Putting this into an equation, we get that 10% is 0.1 (by moving the decimal 2 spots to the left) , 0.2=20%, and 0.17=17%. With that information, we can determine that 10%*x+20%*(20-x)=20*0.17 due to that with 20 gallons of the 27% solution, we need a certain amount of solution. For every gallon, we add 0.17 of the solution, so we have 20*0.17. Similarly, we want that total amount to be represented by the amount of 20% + the amount of 10%.

0.1x+0.2(20-x)=0.1x+4-0.2x=-0.1x+4 using the distributive property
-0.1x+4=20*0.17=3.4. Subtract 4 from both sides to get -0.1x=-0.6, and multiply both sides by -10 (to separate x) to get x=6. Therefore, the amount of 10% solution is 6 gallons and the amount of 20% solution is 20-5=14 gallons

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3 years ago