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solniwko [45]
3 years ago
11

a marble is rolled down a ramp. The distance it travels is described by the formula d=490T^2 where d is the distance in centimet

ers that the marble rolls in t seconds. If the marble is released at the top of a ramp that is 3,920 cm long for what time period will the marble be more than halfway down the ramp?
Mathematics
1 answer:
Helga [31]3 years ago
5 0

Answer:

The period when its more than halfway

= 2 < t  ≤ 2.83 seconds   ( to nearest hundredth).

Step-by-step explanation:

When is is halfway down the ramp d = 3920/2 = 1960 cm, so:

1960 = 490 t^2

t^2 = 1960/490 = 4

t = 2 seconds.

When it reaches the bottom d = 3920 :

t^2 = 3920/490 =  8

t = 2.83 seconds.

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Step-by-step explanation:

4 0
3 years ago
Joes age (j) is half Martha’s (m). Combined, their age is 42. What are their ages?
svp [43]

Answer:

Joe is 14.

Martha is 28.

Step-by-step explanation:

Use the variables and information from the question to make equations.

If Joe's age is half Martha's:

(1/2)m = j     OR     2j = m

If their ages combined is 42:

m + j = 42

We can substitute the equation m=2j into equation m + j = 42, replacing "m".

m + j = 42    Substitute m for 2j

2j + j = 42     Combine like terms, terms with same varables

3j = 42     Divide both sides by 3 to isolate j

j = 14       Joe's age

Since j = 14, we can substitute it into equation m=2j to find "m".

m = 2j       Substitute j for 14

m = 2(14)     Simplify

m = 28       Martha's age

Therefore Joe is 14 and Martha is 28.

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3 years ago
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3 years ago
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1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa
Firdavs [7]

Answer:

0.0239\frac{in^{3}}{min}

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

r'=\frac{1/1000in}{3min}

which yields:

r'=\frac{1}{3000}\frac{in}{min}

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

V=\pi r^{2}h

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

V=\pi r^{2}(6)

or

V=6 \pi r^{2}

We can now take the derivative to this formula so we get:

\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}

Which simplifies to:

\frac{dV}{dt}=12\pi r \frac{dr}{dt}

We can now substitute the data provided by the problem to get:

\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})

which yields:

\frac{dV}{dt}=0.0239\frac{in^{3}}{min}

3 0
3 years ago
What is the area of the triangle?<br> 118 cm<br> 24 cm<br> 30 cm
Arada [10]

Answer:

360

Step-by-step explanation:

7 0
3 years ago
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