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3 years ago

11

Please help with number 1

1 answer:

bezimeni [28]3 years ago

7 0

Answer:

19.0681

Step-by-step explanation:

Given in the question that,

angle from ted to the dog = 60° with the ground

height of ted from the ground = 16ft

To find,

distance between dog and the door of ted's building

Considering the scenario make a right angle triangle:

<h3>By using pythagorus theorem:</h3>

Tan 40 = opposite / adjacent

Tan 40 = height / distance between dog and the door

Tan 40 = 16ft / x

x = 16 / tan40

x = 19.068057

x ≈ 19.0681 (nearest to thousand)

So, the dog need to walk 19.0681ft to reach the open door directly below Ted.

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A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

3 0

3 years ago

You are planning to work in the summer (13 weeks). You

Llana [10]

Answer:

(a) Equations for both

$y = 500 + 12x$ --- lifeguard

$y = 15x$ --- camp counselor

(b) Total pay for 5 days

Lifeguard pays $800

Camp counselor pays $375

(c) Which pays more

Lifeguard job pays more

Step-by-step explanation:

Let

$x \to hours$

$y \to total\ pay$

Given

Lifeguard job

$Signing\ bonus = \$500$

$Rate = \$12/hr$

Camp counselor job

$Signing\ bonus =\$0$

$Rate = \$15/hr$

Solving (a): The equation for both

The total pay for each job is calculated as:

Total Pay = Signing Bonus + Rate * Hours

So, we have:

Lifeguard

$y = 500 + 12*x$

$y = 500 + 12x$

Camp counselor

$y = 0 + 15 * x$

$y = 15x$

Solving (b): Total pay for 5 days

First, we calculate the total hours worked in 5 days

$x = 5hrs/day * 5days$

$x = 25hrs$

So, the pay for each is:

$y = 500 + 12x$

$y =500 + 12*25$

$y =800$ --- Lifeguard

$y = 15x$

$y = 15 * 25$

$y = 375$ --- camp counselor

Solving (c): Which job pays more

By comparing the solution in (b)

$800 > 375$

<em>Hence, lifeguard job pays more</em>

6 0

3 years ago

Estimate the product. Then find the actual product.

Artist 52 [7]

Answer:

it is in the steps 4443.6 actual product

estimate is 4444

Step-by-step explanation:

483*9.2=4443.6 actual product

6 0

2 years ago

Read 2 more answers

Pythagorean triples are super important to know. If the hypotenuse of a triangle is 15, what are its legs ( hint - use the three

Triss [41]

Answer:

9, 12

Step-by-step explanation:

Just multiply the 3,4,5 triple by 3 and u get 9, 12, 15

8 0

3 years ago

Sarita used 54 ounces of apples to make an apple pie.How many pounds and ounces of apple did sarita use?

Inga [223]

Answer:

C

Step-by-step explanation:

16 ounces is equal to 1 pound

Divide 54 by 16 and you get 3.375

You know that there are 3 pounds now, so subtract 3 from what you got to get 0.375

Now multiply 0.375 by 16 to turn it back into ounces, which is 6

3 pounds and 6 ounces is answer choice C

8 0

3 years ago

Read 2 more answers