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1 year ago

A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgeham-

Mathematics

1 answer:

Marianna [84]1 year ago

8 0

Total internal energy increases by 1760 J

Step-by-step explanation:

The kinetic energy of an object is the energy possessed by the object due to its motion.

It is calculated as

$KE=\frac{1}{2}mv^2$

where

m is the mass of the object

v is its speed

For the hammer in this problem:

m = 2.50 kg

v = 65.0 m/s

So its kinetic energy is

$KE=\frac{1}{2}(2.50)(65)^2=5281 J$

Then the problem says that 1/3 of the hammer's kinetic energy is converted into internal energy: therefore, the total internal energy increases by

$\frac{1}{3}KE=\frac{1}{3}(5281)=1760 J$

Learn more about kinetic energy:

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In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is t

podryga [215]

Answer:

|0.254 ≤ p ≤ 0.286|

Step-by-step explanation:

Given that:

In a made up poll :

Proportion of people who like dark chocolate than milk chocolate (p) = 27%

Margin of Error = 1.6%

Hence,

p ± margin of error

27% ± 1.6%

(27 - 1.6)% ; (27 + 1.6)%

25.4% ; 28.6%

0.254 ; 0.286

Therefore ;

Lower bound = 0.254

Upper bound = 0.286

Expressing p as an absolute value Inequality ;

|0.254 ≤ p ≤ 0.286|

7 0

1 year ago

The triangles in the diagram are congruent. If mF = 40°, mA = 80°, and mG = 60°, what is mB?

maria [59]

Answer:

The answer is 40 degrees.

Step-by-step explanation:

Since the two triangles are congruent, which means they are the same shape and size, they share the same angle measures. Since angle B is the same as angle F, it equals 40 degrees.

I hope this helped! :-)

5 0

1 year ago

Read 2 more answers

the center of a circular sunflower with a diameter of 4 centimeters is (-2,1). Which equation represents the sunflower?

BigorU [14]

The standard equation the circle is given by:
(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2
Where,
(xo, yo): coordinates of the center of the circle
r: radius of the circle
Substituting values we have:
(x - (- 2)) ^ 2 + (y-1) ^ 2 = (4/2) ^ 2
Rewriting:
(x + 2) ^ 2 + (y-1) ^ 2 = 4
Answer:
An equation that represents the sunflower is:
(x + 2) ^ 2 + (y-1) ^ 2 = 4

6 0

1 year ago

Which hyperbola has one focus point in common with the hyperbola (y+11)^2/(15^2)-(x-7)^2/(8^2)=1

irina [24]

$\bf \textit{hyperbolas, vertical traverse axis }\\\\
\cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}, {{ k}}\pm a)
\end{cases}\\\\
-------------------------------\\\\
\cfrac{(y+11)^2}{15^2}-\cfrac{(x-7)^2}{8^2}=1\implies \cfrac{(y-(-11))^2}{15^2}-\cfrac{(x-7)^2}{8^2}=1\\\\
-------------------------------\\\\
c=\textit{distance from the center to either foci}\\\\
c=\sqrt{a^2+b^2}\implies c=\sqrt{15^2+8^2}\implies \boxed{c=17}$

now, if you notice, the positive fraction, is the one with the "y" variable, and that simply means, the hyperbola traverse axis is over the y-axis, so it more or less looks like the picture below.

now, from the hyperbola form, we can see the center is at (7, -11), and that the "c" distance is 17.

so, from -11 over the y-axis, we move Up and Down 17 units to get the foci, which will put them at (7, -11-17) or (7, -28) and (7 , -11+17) or (7, 6)

5 0

1 year ago

Read 2 more answers

From class we learned that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million

NemiM [27]

Question A: The per capita debt would be $43,888.75.

Per capita means the amount per person. To find this amount, we need to take the total debt and divide it by the number of people.

13,561,623 divided by 309 = 43,888.75

For Question B, you will need to have the other CPI value from the table.

7 0

2 years ago