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GenaCL600 [577]

3 years ago

11

A number is written in scientific notation when it is the product of a number less than 10 but greater than or equal to 1 and a

power of 10. All numbers in scientific notation have the following form.
Aâœ•10^n
The mass of the Sun is 1,990,000,000,000,000,000,000,000,000,000 kg. Express the mass in kg using scientific notation. (Enter your answer using one of the following formats: 1.2e-3 for 0.0012 and 1.20e+2 for 120. WebAssign allows you to enter answers using scientific notation. For example, a number in scientific notation such as 1.32 104 would need to be entered as 1.32e4. The system requires that you do not use spaces. Enter your answer to two decimal places.)Â
____________kg

1 answer:

Bess [88]3 years ago

7 0

Answer:

$Mass = 1.99 * 10^{30} kg$

Explanation:

Given

$Mass = 1,990,000,000,000,000,000,000,000,000,000\ kg$

Required

Rewrite using scientific notation

The format of a number in scientific notation is

$Digit = a * 10^n$

Where $1 \geq\ a\geq\ 10$

So the given parameter can be rewritten as

$Mass = 1.99 * 1,000,000,000,000,000,000,000,000,000,000\ kg$

Express as a power of 10

$Mass = 1.99 * 10^{30} kg$

Hence, the equivalent of the mass of the sun in scientific notation is:

$Mass = 1.99 * 10^{30} kg$

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. A mass m is traveling at an initial speed of 25.0 m/s. It is brought to rest in a distance of 62.5 m by a net force of 15.0 N.

harkovskaia [24]

Answer:

m = 3 kg

The mass m is 3 kg

Explanation:

From the equations of motion;

s = 0.5(u+v)t

Making t thr subject of formula;

t = 2s/(u+v)

t = time taken

s = distance travelled during deceleration = 62.5 m

u = initial speed = 25 m/s

v = final velocity = 0

Substituting the given values;

t = (2×62.5)/(25+0)

t = 5

Since, t = 5 the acceleration during this period is;

acceleration a = ∆v/t = (v-u)/t

a = (25)/5

a = 5 m/s^2

Force F = mass × acceleration

F = ma

Making m the subject of formula;

m = F/a

net force F = 15.0N

Substituting the values

m = 15/5

m = 3 kg

The mass m is 3 kg

7 0

3 years ago

What do each of the variables mean ? <br> F=__________ m=_________<br>a=___________<br>

wariber [46]

Answer:

F = Force (Measured in Newtons, N), m = Mass (Measured in kilograms, kg), and a = acceleration (Measured in metres per second squared, $m/s^{2}$

Explanation:

This is Newton's Second Law!

Hope this helps!

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8 0

3 years ago

A heavy boy and a lightweight girl are balanced on a mass-less seesaw. If they both move forward so that they are one-half their

Rom4ik [11]

Answer:

b) Nothing will happen, the sea saw will still be balanced.

Explanation:

b) Nothing will happen, the sea saw will still be balanced.

Reason:-

When two kids are balanced, the sum of torques on the seesaw will be zero.

if each kid, reduces their distances by half, then the torque of each kid will be half and the sum of torque of each on the seesaw will be zero.

Therefore the seesaw is balanced

4 0

3 years ago

Read 2 more answers

Assume that the amplifiers on the stage operate at a combined power of 5,000 Watts, and that 80% of this is converted to sound.

rusak2 [61]

Answer:

0.04

Explanation:

Fraction of power converted to sound = 80% = 0.08

Fraction incident upon each eardrum onstage = 0.08/2 = 0.04

6 0

3 years ago

In a flying ski jump, the skier acquires a speed of 110 km/h by racing down a steep hill and then lifts off into the air from a

matrenka [14]

Answer:

Approximately $\displaystyle\rm \left[ \begin{array}{c}\rm191\; m\\\rm-191\; m\end{array}\right]$ .

Explanation:

Consider this $45^{\circ}$ slope and the trajectory of the skier in a cartesian plane. Since the problem is asking for the displacement vector relative to the point of "lift off", let that particular point be the origin $(0, 0)$ .

Assume that the skier is running in the positive x-direction. The line that represents the slope shall point downwards at $45^{\circ}$ to the x-axis. Since this slope is connected to the ramp, it should also go through the origin. Based on these conditions, this line should be represented as $y = -x$ .

Convert the initial speed of this diver to SI units:

$\displaystyle v = \rm 110\; km\cdot h^{-1} = 110 \times \frac{1}{3.6} = 30.556\; m\cdot s^{-1}$ .

The question assumes that the skier is in a free-fall motion. In other words, the skier travels with a constant horizontal velocity and accelerates downwards at $g$ ( $g \approx \rm -9.81\; m\cdot s^{-2}$ near the surface of the earth.) At $t$ seconds after the skier goes beyond the edge of the ramp, the position of the skier will be:

$x$ -coordinate: $30.556t$ meters (constant velocity;)
$y$ -coordinate: $\displaystyle -\frac{1}{2}g\cdot t^{2} = -\frac{9.81}{2}\cdot t^{2}$ meters (constant acceleration with an initial vertical velocity of zero.)

To eliminate $t$ from this expression, solve the equation between $t$ and $x$ for $t$ . That is: express $t$ as a function of $x$ .

$x = 30.556\;t\implies \displaystyle t = \frac{x}{30.556}$ .

Replace the $t$ in the equation of $y$ with this expression:

$\begin{aligned} y = &-\frac{9.81}{2}\cdot t^{2}\\ &= -\frac{9.81}{2} \cdot \left(\frac{x}{30.556}\right)^{2}\\&= -0.0052535\;x^{2}\end{aligned}$ .

Plot the two functions:

$y = -x$ ,
$\displaystyle y= -0.0052535\;x^{2}$ ,

and look for their intersection. Refer to the diagram attached.

Alternatively, equate the two expressions of $y$ (right-hand side of the equation, the part where $y$ is expressed as a function of $x$ .)

$-0.0052535\;x^{2} = -x$ ,

$\implies x = 190.35$ .

The value of $y$ can be found by evaluating either equation at this particular $x$ -value: $x = 190.35$ .

$y = -190.35$ .

The position vector of a point $(x, y)$ on a cartesian plane is $\displaystyle \left[\begin{array}{l}x \\ y\end{array}\right]$ . The coordinates of this skier is approximately $(190.35, -190.35)$ . The position vector of this skier will be $\displaystyle\rm \left[ \begin{array}{c}\rm191\\\rm-191\end{array}\right]$ . Keep in mind that both numbers in this vectors are in meters.

4 0

3 years ago