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aleksklad [387]
3 years ago
7

Carlos has a nail in his car tire. The tire is not flat, but he's on his way to get it fixed. He's driving at a constant speed,

and the diameter of the tire is 3 feet.
Which rule could model the height of the nail from the ground?

a) f(x)=1.5cos(16πx)+1.5
b) f(x)=1.5cos(16πx)−1.5
c) f(x)=3cos(16πx)+3
d) f(x)=16πcos(1.5x)+3
Mathematics
1 answer:
Paul [167]3 years ago
7 0

Answer:

f(x)=1.5cos(16πx)+1.5

(Question on a Quiz was correct)

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What is s?? <br> A 44° <br> B 35.3° <br> C. 37.9°<br> D. 22°
melisa1 [442]

Answer: Choice B) 35.3 degrees

======================================================

Work Shown:

Apply the law of sines

sin(S)/s = sin(R)/r

sin(S)/16 = sin(120)/24

sin(S) = 16*sin(120)/24

sin(S) = 0.57735026918962

S = arcsin(0.57735026918962)

S = 35.2643896827542

S = 35.3

Make sure your calculator is in degree mode.

7 0
2 years ago
An object is heated to 100°. It is left to cool in a room that
stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one.  It involves natural logs and being able to solve equations that require natural logs.  The formula is as follows:

T(t)=T_{1}+(T_{0}-T_{1})e^{kt} where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value.  That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

80=30+(100-30)e^{5k} which simplifies to

50=70e^{5k} Divide both sides by 70 to get

\frac{50}{70}=e^{5k} and take the natural log of both sides:

ln(\frac{5}{7})=ln(e^{5k})

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared).  That gives us:

-.3364722366=5k

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

T(20)=30+(100-30)e^{-.0672944473(20)} which simplifies to

T(20)=30+70e^{-1.345888946}

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

35=30+100-30)e^{-.0672944473t} which simplifies to

5=70e^{-.0672944473t}

Now divide both sides by 70 and take the natural log of both sides:

ln(\frac{5}{70})=ln(e^{-.0672944473t}) which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

3 0
3 years ago
Directions: identify weather the problem has a minimum or a maximum type an “X” in the box next to your answer
alekssr [168]

Answer:

A)   minimum

B)   maximum

C)   minimum

Step-by-step explanation:

A positive x² coefficent means the parabola opens up and the vertex is the minimum

A negative x² coefficent means the parabola opens up and the vertex is the maximum

---------------------------------

A)   minimum

B)   maximum

C)   minimum

3 0
3 years ago
-
Snezhnost [94]

Answer:

See below.

Step-by-step explanation:

The probability of an event happening is a number from 0 to 1. A probability of 1 means the event will definitely happen. A probability of 0 means there is no way the event will happen. There is no probability of 50.

6 0
3 years ago
Plzzzzz answer need it plzzz I say
dexar [7]

Answer:

360 square inches

Step-by-step explanation:

12*15 = 360

7 0
3 years ago
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