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2 years ago

A woman's weekly salary is increased from $350 to $380. The percent of increase is most nearly

Mathematics

1 answer:

Kay [80]2 years ago

3 0

Find the amount of the difference and then divide it by the original amount:

380 - 350 = 30

30 / 350 = 0.0857 = 8.6% increase. Round the answer as needed.

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After being dropped from a platform, a ball bounces several times. The graph shows the height of the ball after each bounce.

Paul [167]

Answer-

End behavior for increasing x represents that the height of each bounce will approach 0.

Solution-

From the graph the exponential equation is,

$y=100e^{(-0.35x)}$

From the properties of negative exponential function properties, as x increases, the value of y decreases.

So, in this case, as x or number of bounce increases, y or the height of bounce decreases. And eventually the value becomes zero.

Therefore, end behavior for increasing x represents that the height of each bounce will approach 0.

5 0

2 years ago

Initially 5 grams of salt are dissolved into 10 liters of water. Brine with concentration of salt 5 grams per liter is added at

DiKsa [7]

Salt flows in at a rate of (5 g/L)*(3 L/min) = 15 g/min.

Salt flows out at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

So the net flow rate of salt, given by $x(t)$ in grams, is governed by the differential equation,

$x'(t)=15-\dfrac{3x(t)}{10}$

which is linear. Move the $x$ term to the right side, then multiply both sides by $e^{3t/10}$ :

$e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}$

$\implies\left(e^{3t/10}x\right)'=15e^{3t/10}$

Integrate both sides, then solve for $x$ :

$e^{3t/10}x=50e^{3t/10}+C$

$\implies x(t)=50+Ce^{-3t/10}$

Since the tank starts with 5 g of salt at time $t=0$ , we have

$5=50+C\implies C=-45$

$\implies\boxed{x(t)=50-45e^{-3t/10}}$

The time it takes for the tank to hold 20 g of salt is $t$ such that

$20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}$

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2 years ago

Helga [31]

There both types of numbers but a whole number is a number with no exponents or decimals, but decimals are like a broken un half whole number

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2 years ago

Read 2 more answers

An angle t is drawn from the center of the unit circle. Find a formula in terms of t for the straight line distance d between th

Doss [256]

Answer:

$d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}$

Step-by-step explanation:

Let suppose that one of the radii meets the circle at the point (1,0). The straight line distance formula is:

$d = \sqrt{(\cos t - 1)^{2}+(\sin t - 1)^{2}}$

$d = \sqrt{(\cos^{2}t - 2\cdot \cos t + 1)+(\sin^{2}t - 2\cdot \sin t + 1)}$

$d = \sqrt{2-2\cdot (\cos t + \sin t )}$

$d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}$

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2 years ago

Alinethatincludesthepoint(6, 3)hasaslopeof 2 . what isitsequationin slope -intercept form?

Marianna [84]

Hi Kay, the point-slope form of a line is given by: y - y1 = m(x - x1). Substituting the given point, (6, -8), and the slope, -2, gives: y - (-8) = -2 * (x - 6) This becomes: y + 8 = -2x + 12

3 0

1 year ago