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3 years ago

Pls answer if u know :) This is a very important homework and i was gone for days so idk

Mathematics

1 answer:

aliya0001 [1]3 years ago

6 0

Answer:

Option B

Step-by-step explanation:

Slope of the line is calculated by the formula:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\$

We have the points ( -2 , 4) and (3 , -5) so plug in the values in the formula:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-5-4}{3-(-2)}\\\\m=\frac{-9}{5}\\$

so the slope(m) equals -9/5

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A city's population was 30,200 people in the year 2010 and is growing by 950 people a year. Give a formula for the city's popula

kolbaska11 [484]

the formula should look like this:

p=30200+950t

3 0

3 years ago

Read 2 more answers

Use the differential equation given by dy/dx=xy/3, y>0<br><br> complete the table of values

melisa1 [442]

The $\dfrac{\mathrm dy}{\mathrm dx}$ row is filled by just plugging in the corresponding values of $x$ and $y$ into the ODE.

For example, when $x=-1$ and $y=1$ , you have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{xy}3\implies\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=-1,y=1}=\dfrac{(-1)(1)}3=-\dfrac13$

and so on.

6 0

3 years ago

Could you please help me for this question?

Olin [163]

Answer:

See attached for graphs

g(x) -- domain: -∞ < x < ∞; range: 0 < y < ∞

g^-1(x) -- domain: 0 < x < ∞; range: -∞ < y < ∞

Step-by-step explanation:

g(x) is an exponential decay function. Its base is 1/3, so each increase of 1 unit in x will multiply the y-value by a factor of 1/3. The graph will rapidly approach its horizontal asymptote of y=0 as x gets large. The y-intercept is (0, 1). Just as y gets smaller as x increases, so it gets larger as x decreases. Each decrease of x by 1 unit causes the y-value to be multiplied by 3.

The graph of g^-1(x) is the graph of g(x) reflected across the line y=x. That is, each coordinate pair (x, y) on the graph of g(x) becomes a point (y, x) on the graph of the inverse function. In order to graph g^-1(x), you don't need to write down the function, you only need to know the relationship between the graphs.

Just as x- and y- are interchanged on the graph, so the domain, range, and intercepts are interchanged. g^-1(x) will have a vertical asymptote of x=0, and an x-intercept of (1, 0). The domain of g^-1(x) is the range of g(x): 0 < x < ∞; and the range of g^-1(x) is the domain of g(x): -∞ < y < ∞.

The attached graph shows g(x) in red and g^-1(x) in blue. As you can see, we created the graph simply by interchanging x and y. The line y=x is shown for reference, so you can see that each curve is a reflection of the other across that line.

_____

<em>Additional comment</em>

The explicit expression for g^-1(x) can be found by solving for y:

x = g(y)

$x=\left(\dfrac{1}{3}\right)^y=\dfrac{1}{3^y}=3^{-y}\\\\ \log(x)=-y\cdot\log(3)\qquad\text{take logarithms}\\\\y=-\dfrac{\log{x}}{\log{3}}=-\log_3{x}\qquad\text{use the change of base relation}\\\\\boxed{g^{-1}(x)=-\log_3{x}}$

If you're familiar with the log function, you know it has an x-intercept of 1 and a vertical asymptote at x=0. The base of the log function is simply a vertical scale factor. The minus sign reflects it across the x-axis.

6 0

2 years ago

Suppose 72 gallons of water came out of a pipe in 8 minutes.

Masteriza [31]

Answer:

9 gallons of water per minute

Step-by-step explanation:

First identify what you know:

1) The pipe was flowing water for eight minutes.

2) In that eight minutes, 72 gallons of water came out.

So, if 72 gallons of water came out in eight minutes, how many gallons flowed out in a single minute? Well, assuming that the flow rate was consistent, then simply divide the total number of gallons that flowed out, by the number of minutes the pipe was open!

72/8 = 9

The pipe released 9 gallons of water per minute, thus resulting in 72 gallons of water in 8 minutes!

Hope this helps! :)

4 0

2 years ago

A 14.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall (above the fire truck)

UkoKoshka [18]

Answer:

h = 7.47 m

Step-by-step explanation:

According to the question, we have a right triangle formed by the ladder with the wall and the floor.

The length of the ladder is the hypotenuse and the desired height is the opposite. This is due to the fact that "the ladder makes an angle of 21" 27" with the horizontal". Then, the trigonometric ratio to use is sine:

$sin(\theta)=\frac{opposite}{hypotenuse}$

Using the values given:

$sin(\21"27")=\frac{h}{14.5}$

Multiplying both sides by 14.5:

$14.5*sin(\21"27")=14.5*\frac{h}{14.5}$

$14.5*sin(\21"27")=h$

Then h = 7.47 m

8 0

3 years ago