Find the distance between the two points to the nearest tenth (if necessary) (0,-8) and (-5,4)

IgorLugansk [536]

The equation of the sin function is y = 3sin(πx/2) + 1, and the graph of the function is shown in the picture.

<h3>What is sin function?</h3>

It is defined as a function that is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.

As we know the sin function is represented by:

y = Asin(Bx) + C

Here,

A = The amplitude = 3

C = The vertical shift = 1

B - The period in terms of π

B = 2π/amplitude

B = 2π/4

B = π/2

The becomes:

$\rm y = 3sin(\dfrac{\pi }{2}x)+1$

Thus, the equation of the sin function is y = 3sin(πx/2) + 1, and the graph of the function is shown in the picture.

Learn more about the sin function here:

brainly.com/question/14397255

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3 0

1 year ago

Steve paid 10% tax on a purchase of $40. Select the dollar amount of the tax and the total dollar amount Steve paid.

marta [7]

Amount of purchase that Steve made = $40
Percentage of tax that Steve needs to pay = 10%
Then
Amount of tax that Steve needs to pay for the purchase = (10/100) * 40
      = 1 * 4 dollars
      = 4 dollars
Then
The total amount including tax
that Steve needs to pay for the purchase = (40 + 4) dollars
   = 44 dollars
So the dollar amount of tax that Steve had to pay is $4 and the total amount that Steve had to pay was $44.

4 0

2 years ago

Multiples of 3 are always multiples of 6.

Elena L [17]

Answer:yes 3x2=6

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

If you place a 17-foot ladder against the top of a 8-foot building, how many feet will the bottom of the ladder be from the bott

Goshia [24]

Answer:

15 feet

Step-by-step explanation:

This problem involves using the Pythagorean theorem, since the figure made with the ladder, building, and ground would make a right triangle. You are given the values 17ft and 8ft, which is enough to plug into the Pythagorean theorem.

The ladder, 17ft, would be the longest side (hypotenuse). The 8ft building would be one of the legs of the right triangle.

1. Plug your given values correctly into the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

$8^{2} + b^{2} = 17^{2}$

2. Now solve for b, which is your unknown distance (the distance the bottom of the ladder is from the bottom of the building).

$8^{2} + b^{2} = 17^{2}$ --> Square 8 and 17

$64 + b^{2} = 289$ --> Subtract 64 from both sides

$b^{2} = 225$ --> Square root both sides to get b by itself

b = 15

3. The distance is 15 feet

*Note: to make solving this problem easier, try drawing out the given situation, namely the building and the ladder

7 0

2 years ago

Using Newton's Law of Cooling. You are a medical examiner called to an abandoned house in which a dead body has been discovered.

Artyom0805 [142]

A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
$\frac{dT}{dt} = \alpha(T -52)$

B) Find general solution by separating variables and integrating $\int\frac{dT}{T-52} = \alpha \int dt \\ ln (T-52) = \alpha t + C \\ T = C e^{\alpha t} +52$ :

C) Initial condition is t=0, T = 87
$87 = C +52 \\ C = 35$

D) Total time elapsed is 10 minutes, new temperature is 84
$84 = 35 e^{10\alpha} +52$
solve for alpha
$e^{10\alpha} =\frac{32}{35} \\ \alpha = \frac{ln(32/35)}{10} \\ \alpha = -.00896$

E) Temperature function is:
$T = 35 e^{-.00896 t} +52$
solving for t
$t = \frac{ln (\frac{T-52}{35})}{-.00896}$
Plug in T = 98.6
$t = -31.95$

This is approximately 32 minutes before he arrived or about 1:20 AM

3 0

2 years ago