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3 years ago

15

The mass of earth is 5.97 X 10^24 kilograms. The mass of the moon is 7.34 X 10^22 kilograms. What is the combined mass of earth

and the moon? Express your answer In scientific notation.

1 answer:

Juliette [100K]3 years ago

3 0

Just need to convert the mass of moon in terms of 10^24. So shift over 2 decimal places.

5.97 x 10^24 + 0.0734 x 10^24 = 6.04 x10^24

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Please help me with..... A rectangular garden is 50 feet longer than it is wide its perimeter is 284 feet

zmey [24]

P=2 (l+w)
we know P=284
we also know that l= w+50
so replace l in the equation with w+50

284=2 (w+50+w)
284=2 (2w+50)
divide both sides by 2
142=2w+50
subtract 50 on both sides
98=2w
divide both sides by 2
49=w
so width is 49, and we need to add 50 to it to find the length
l= 49 +50
l=99

8 0

3 years ago

A new DVD is available for sale in a store one week after its release. The cumulative revenue,

ratelena [41]

Answer:

f(2) = $180.22

f'(2) = $130.00/week

f'(2)/f(2) = 72.13%

Two weeks after the DVD was released, the revenue from sales is $180.22 and is increasing at a rate of $130 per week, or 72.13% per week.

Step-by-step explanation:

The revenue from sales, in dollars, as a function of time, in weeks, is given by:

$f(t)=260ln(t)$

After two weeks (t=2), the revenue from sales is:

$f(2)=260ln(2)\\f(2) = \$180.22$

The rate of change, which is given by the derivate of the revenue function, at t = 2 weeks is:

$f'(t)=\frac{d}{dt} 260ln(t)\\f'(t) = \frac{260}{t}\\f'(2) = \frac{260}{2}=\$130.00/week$

The relative rate of change is:

$\frac{f'(2)}{f(2)}=\frac{130}{180.22}=0.7213=72.13\%$

Therefore, Two weeks after the DVD was released, the revenue from sales is $180.22 and is increasing at a rate of $130 per week, or 72.13% per week.

5 0

3 years ago

Round $.9666 to the nearest cent

Burka [1]

Answer:

It would be $0.97

Step-by-step explanation:

You round the nearest cent so you round the second number from the dot

6 0

3 years ago

If the area of a rectangle is 24a2b and the length is 8ab2, what would be the width of the rectangle, given that width is found

Goshia [24]

(24ba^2)/(8ab^2)=3a/b=width

5 0

3 years ago

A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

4 0

3 years ago