∆ABC is isosceles, AB = BC, and CH is an altitude. How long is AC, if CH = 84 cm and m∠HBC = m∠BAC +m∠BCH?

A 3.00-g copper penny at 25.0°C drops from a height of50.0 m to the ground. (

Gnoma [55]

The potential energy, E, of the penny is given by E=mgh. The energy, Q, required to raise the temperature of an object by an amount ΔT is given by Q=mcΔT. We can equate these two to get the result but we must use proper units and include the 60%:
(0.6)mgh=mcΔT
We see we can divide out the mass from each side
0.6gh=cΔT, then 0.6gh/c=ΔT
(0.6)9.81(m/s²)50m/385(J/kg°C) = 0.7644°C
since this is the change in temperature and it started at 25°C we get
T=25.7644°C
As you can see the result does not depend on mass. The more massive the copper object the more potential energy it will have to contribute to the heat energy, but the more stuff there will be to heat up, and the effect is that the mass cancels.

6 0

2 years ago

The amount of caffeine in the body of a healthy adult after drinking espresso decreases exponentially, with a half-life of appro

yarga [219]

After 6 hours the amount of caffeine 40 mg. After another 6 hours the amount of caffeine is 20 mg. It takes 12 hours for the total amount of caffeine to drop down to 20 mg. the answer is 11 am -B. Hope this helps!

7 0

1 year ago

Read 2 more answers

The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of

Cloud [144]

Answer:

It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.

Step-by-step explanation:

The filling time of a gas tank can be given by a first order function in this format:

$F(t) = V - r*t$

In which $F(t)$ is the current amount of fuel in the tank(in L), $V$ is the volume of the tank(in L), $r$ is the discharge rate of the tank(in L/s) and t is the time in seconds.

Finding the values of the parameters:

The tank is completly empty, so $F(t) = 0$ .

The volume of the tank is 14 gallons. However, the problem states that the volume of the tank is measured in liters.

Each gallon has 3.78L.

So $V = 14*3.78 = 53L$

The discharge rate for the gas is 38.0 l/min. However, the problem states that the discharge rate is in L/s. So, to find the value of r, we solve the following rule of three.

38 L - 60s

r L - 1s

$60r = 38$

$r = \frac{38}{60}$

$r = 0.63$

Solving the equation:

$F(t) = V - r*t$

$0 = 53 - 0.63t$

$0.63t = 53$

$t = \frac{53}{0.63}$

$t = 84.12s$

It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.

6 0

2 years ago

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If clare doesn't

AVprozaik [17]

We have been given that Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount 1.03.

We are asked to write an expression for the amount of money Clare would have after 30 years if she never withdraws money from her account.

We will use exponential growth function to solve our given problem.

An exponential growth function is in form $y=a(1+r)^x$ , where