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aleksandr82 [10.1K]

2 years ago

13

Kelly joins Powerhouse Gym. The cost is $30 per month and a one-time $100 joining fee. Lisa joins MegaMuscle Gym for $35 per mon

th and a $50 joining fee. In how many months will Lisa have paid more than Kelly?

1 answer:

11Alexandr11 [23.1K]2 years ago

8 0

it will take Lisa 11 months to have paid more than Kelly

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A child wanders slowly down a circular staircase from the top of a tower. With x,y,zx,y,z in feet and the origin at the base of

babymother [125]

Answer:

a) The tower is 90 feet tall

b) She reaches the bottom at t = 18 minutes.

c) Her speed at time t is 5 \sqrt[]{5} ft/minute

d) Her acceleration at time t is 10 ft/minute^2

Step-by-step explanation:

Consider the path described by the child as going down the tower to have the following parametrization $\gamma(t) = (10\cos t, 10 \sin t, 90-5t)$

a) Assuming that the child is at the top of the tower when she starts going down, we have that at the initial time (t=0) we will have the value of the height of the tower. That is z = 90-5*0 = 90 ft.

b) The child reaches the bottom as soon as z =0. We want to find the value of t that does that. Then we have 0 = 90-5t, which gives us t = 18 minutes.

c) Given the parametrization we are given, the velocity of the child at time t is given by $\frac{d\gamma}{dt}= (\frac{d}{dt}(10\cos t), \frac{d}{dt} (10 \sin t ), \frac{d}{dt}(90-5t)) = (-10 \sin t, 10 \cos t, -5)$ . The speed is defined as the norm of the velocity vector,

so, the speed at time t is given by $v = \sqrt[]{(-10 \sin t)^2+(10 \cos t)^2+(-5)^2} = \sqrt[]{100(\sin^2 t + \cos^2 t)+25} = \sqrt[]{125}= 5 \sqrt[]{5}$

d) ON the same fashion we want to know the norm of the second derivative of $\gamma$ .

We have that $\gamma ^{''}(t) =(-10\cost t, -10 \sin t , 0)$ so the acceleration is given by $\sqrt[]{100(\cos^2 t+ \sin^2 t )} = 10$

6 0

1 year ago

Find the p-value in a test of the claim that the mean College Algebra final exam score of engineering majors equal to 88, give

Orlov [11]

Answer: 0.9332.

Step-by-step explanation:

Claim : College Algebra final exam score of engineering majors equal to 88.

Given that : The test statistic is z equals to 1.50.

To find the p-value (Probability value), we use standard normal distribution table, and search the p-value corresponds to the z-score.

In a Standard Normal Distribution Table below, the p-value corresponds z equals 1.5 is 0.9332.

Hence, the p-value is 0.9332.

8 0

1 year ago

Please solve (-3×+15)+(-3×+2)

koban [17]

(-3x + 15) + (-3x + 2)
Simplify by combining like terms.
-6x + 17

-6x + 17

3 0

1 year ago

Read 2 more answers

Malik buys and sells car parts. He bought two tires for $45.00 each and later sold them for $65.00 each. He bought three rims fo

Tamiku [17]

Malik total profit will be $213

3 0

2 years ago

Given right triangle ABC which of the following statements must be true? Check all that apply.

Pachacha [2.7K]

Answer:

Option A. <A and <B are complementary angles

Option D. $Sin(C)=Cos(90\°-C)$

Step-by-step explanation:

we know that

If ABC is a right triangle

then

------> by complementary angles

and

$Sin(C)=Cos(A)$

$Cos(C)=Sin(A)$

Remember that

$A=90\°-C$

so

$Sin(C)=Cos(90\°-C)$

$Cos(C)=Sin(90\°-C)$

5 0

1 year ago