A cube can hold 525 cm of water. How many liters of water can the cube hold?

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

3 years ago

Ana is a scuba diver who has completed 5 dives for a total depth of 230 feet. Choose an equation using integers to represent the

galben [10]

Answer:

Step-by-step explanation:

-230/5=-46

7 0

3 years ago

Rewrite the following linear equation to slope form :y+2=7(2x-4)

garik1379 [7]

Answer:

y = 14x -30

Step-by-step explanation:

The slope intercept form is:

y = mx + b,

Slope intercept form is useful for finding the slope and y intercept of a line, hence why it is called "slope intercept" because it is easy to see the slope and the y intercept of a line in this form. Since the slope denoted by m, and y intercept denoted by b are clearly given.

y + 2 = 7(2x - 4)

Distribute 7 across the parentheses by multiplying x and 2x and 4 by 7.

y+2 = 14x - 28

subtract 2 from both sides. This cancels the 2 on the left and moves it to the right, while keeping the equation balanced.

y+2 -2 = 14x - 28 -2

y = 14x - 30

y = 14x -30

As you can see our y = 14x -30 now looks like the point slope equation we had above. m = 14, and b = -30. This means the line goes up 14 for every single unit you move to the right, and intersects the y axis at (0, -30).

Please mark me brainliest.

4 0

4 years ago

Please answer ASAP! Thank you in advance, and remember to use wash your hands for 1 minute with antibacterial soap!!

Anastasy [175]

Answer: x=80

Step-by-step explanation:

x/8=10

x=8*10

x=80

5 0

3 years ago

Smallest two digit number using 6, 2, 7, 3

kogti [31]

Answer:

23

Step-by-step explanation:

5 0

3 years ago