mia uses triangle A and says the slope of this line is 6/4.Elena use triangle B and say no,the slope is 1.5

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

A referendum failed by a vote of 36 No's and 24 Yes's. To make a pie chart of this result, what is the lesser measure in degrees

Daniel [21]

From the given number of people who voted Yes and No to the referendum, there are 60 people all in all. The fewer of which is 24 which voted as Yes. If we are to construct a pie chart and calculate the measure of the smaller angle, we take the ratio of 24 and 60 and multiply it to 360.

measure of angle ACB = (24/60)(360)
measure of angle ACB = 144°

Thus, the angle measure 144°.

3 0

2 years ago

Mark and Sofia walk together down a long, straight road. They walk without stopping for 4 miles. At this point Sofia says their

Marina CMI [18]

Answer:

Sofia is correct.

Step-by-step explanation:

Mark's statement depends on the starting point. He can be correct if they started at the 0 mile, but in this case we don't know where they started. They could had started at the 12 mile and their current position after the walking would be 16 miles.

On the other hand, Sofia's statement doesn't depend on where they started. She refers to how much they walked, not to where they are after the walking. Since they stopped after 4 non-stopping miles, their displacement was exactly 4 miles. So Sofia is correct.

5 0

2 years ago

An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. the yard has 3 sprinkler head

frutty [35]

Answer:

Option D. 5890.5 feet²

Step-by-step explanation:

An individual head of a sprinkler system covers a circular are of grass with a radius of 25 feet.

Yard has three sprinkler heads that each cover circular area with no overlap.

We have to calculate the approximate area watered by these 3 sprinkler heads.

Area covered by one sprinkler = π×r² = π×(25)² = 625π feet²

Therefore area covered by three sprinkler heads = 3 × 625π = 5892.85 feet²

which matches the approximate value of Option D. 5890.5 feet²

3 0

1 year ago

Read 2 more answers

A rectangular prism has a volume of 320 cubic cm. Its height is 8 cm. What is the area of its base? A 40 square cm B 4 square cm

Airida [17]

Volume of a prism is height x base x length. the area of the base would be calculated from the volume/ height so
320/8 = 40 cm squared

3 0

1 year ago