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3 years ago

Which of the following shows the table represents of the exponential function f(x)=5*2^x?

1 answer:

4 0

The correct answer is D
When x = 0, f(0) = 5 × 1= 5

When x = 1, f(1) = 5 × 2 = 10

When x = 2, f(2) = 5 × 4 = 20

When x = 3, f(3) = 5 × 8 = 40

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3 years ago

Write the equation of the line in fully simplified slope intercept form

yan [13]

The equation of the given line is y = 5/6x - 2

The standard equation of a line in slope-intercept form is expressed as

y = mx + b

m is the slope of the line

b is the y-intercept

Using the coordinate point (0, -2) and (-6, 3)

Slope m = 3-(-2)/-6-0

m = 5/6

Since the line cuts the y-axis at y = -2, hence the y-intercept is -2.

Find the equation of a line;

y = mx + b

y = 5/6x + (-2)

y = 5/6x - 2

Hence the equation of the given line is y = 5/6x - 2

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2 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$