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3 years ago

A person is watching a boat from the top of a lighthouse. The boat is approaching

Mathematics

1 answer:

Lapatulllka [165]3 years ago

7 0

9514 1404 393

Answer:

445.10 feet

Step-by-step explanation:

The relation between angle of depression and distance to the boat is ...

Tan = Opposite/Adjacent

tan(angle of depression) = (200 ft)/(distance to boat)

Then the distance to the boat is ...

distance to boat = (200 ft)/tan(angle of depression)

We want the change in distance between the two angles, so ...

change in distance = (200 ft)/tan(17°31') -(200 ft)/tan(46°41')

= (200 ft)(cot(17°31') -cot(46°41'))

change in distance ≈ 445.10 ft

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A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co

zubka84 [21]

Answer:

a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy

ii) What is the maximum amount of butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b.The excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.

Step-by-step explanation:

a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat?

From the question, we are told that:

Milk from dairy I costs $2.40 per gallon, Milk from dairy II costs $0.80 per gallon.

Let's represent:

Number of gallons of Milk from dairy I = x

Number of gallons of Milk from dairy II = y

At most $144 is available for purchasing milk.

$2.40 × x + $0.80 × y = 144

2.40x + 0.80y = 144........ Equation 1

x + y = 100....... Equation 2

x = 100 - y

2.40(100 - y) + 0.80y = 144

240 - 2.4y + 0.80y = 144

-1.60y = 144 - 240

-1.6y = -96

y = -96/-1.6

y = 60

From Equation 2

x + y = 100....... Equation 2

x + 60 = 100

x = 100 - 60

x = 40

Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y

The company should buy 40 gallons from dairy I and 60 gallons from dairy

II. What is the maximum amount of butterfat?

From the question

Dairy I can supply at most 50 gallons averaging 3.9% butterfat,

50 gallons = 3.9% butterfat

40 gallons =

Cross Multiply

= 40 × 3.9/50

= 3.12%

Dairy II can supply at most 90 gallons averaging 2.9% butterfat.

90 gallons of milk = 2.9% butter fat

60 gallons of milk =

Cross Multiply

= 60 × 2.9%/90

=1.9333333333%

≈ 1.93%

The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.

Excess capacity of Diary I =

50 gallons - 40 gallons = 10 gallons

Excess capacity of Diary II =

90 gallons - 60 gallons = 30 gallons

Therefore, the excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.

3 0

3 years ago

[(51 + 3) − 32] ÷ 9 ⋅ 2.

galina1969 [7]

Your answer is 4.88 using PEMDAS

7 0

3 years ago

4C. Quintin is using the three different shaped

Sauron [17]

The smallest number of tiles Quintin will need in order to tile his floor is 20

The given parameters;

number of different shapes of tiles available = 3

number of each shape = 5

area of each square shape tiles, A = 2000 cm²

length of the floor, L = 10 m = 1000 cm

width of the floor, W = 6 m = 600 cm

To find:

the smallest number of tiles Quintin will need in order to tile his floor

Among the three different shapes available, total area of one is calculated as;

$A_{one \ square \ type} = 5 \times 2000 \ cm^2 = 10,000 \ cm^2$

Area of the floor is calculated as;

$A_{floor} = 1000 \ cm \times 600 \ cm = 600,000 \ cm^2$

The maximum number tiles needed (this will be possible if only one shape type is used)

$maximum \ number= \frac{Area \ of \ floor}{total \ area \ of \ one \ shape \ type} \\\\maximum \ number= \frac{600,000 \ cm^2}{10,000 \ cm^2} \\\\maximum \ number= 60$

When all the three different shape types are used we can get the smallest number of tiles needed.

The minimum or smallest number of tiles needed (this will be possible if all the 3 different shapes are used)

$3 \times \ smallest \ number = 60\\\\smallest \ number = \frac{60}{3} \\\\smallest \ number = 20$

Thus, the smallest number of tiles Quintin will need in order to tile his floor is 20

Learn more here: brainly.com/question/13877427

3 0

3 years ago

Veronica owns stocks worth $11,200. She owes $4,500 on her student loans and $800 on her credit cards. She owes $6,000 on her ca

tatyana61 [14]

Answer:

Her net worth would be 26,900

Step-by-step explanation:

8 0

3 years ago

Demand for your tie-dyed T-shirts is given by the formula q = 510 − 90p0.5 where q is the number of T-shirts you can sell each m

telo118 [61]

Answer:

The demand will drop approximately 23 T-shirt per month.

Step-by-step explanation:

Consider the provided formula.

$q = 510-90p^{0.5}$

You currently sell T-shirts for $15 each and you raise your price by $2 per month,

That means p=$15 and $\frac{dp}{dt}=2$

We need to find how fast demand will drop.

So differentiate the above function with respect to time.

$\frac{dq}{dt} =0-45p^{0.5-1}\frac{dp}{dt}$

$\frac{dq}{dt} =-45p^{-0.5}\frac{dp}{dt}$

Substitute the respective values as shown:

$\frac{dq}{dt} =-45(15)^{-0.5}(2)$

$\frac{dq}{dt} \approx-23.24$

Hence, the demand will drop approximately 23 T-shirt per month.

3 0

3 years ago