Mathematics, 19.09.2019 23:50 kyleescott9525

6.
2.find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin

6.2.find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendic

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Answer from: ceelow

First.

We need to find the triangle bounded by the y-axis the line $f(x)=9-\frac{6}{7}x$ and the line perpendicular to it that passes through the origin.

This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:

The y-axis has been identified by the green line.The line $f(x)=9-\frac{6}{7}x$ has been identified by the red line.To plot the line perpendicular to the previous one that passes through the origin, we need to know that the product of the slopes of two perpendicular lines is $m_{1}m_{2}=-1 \therefore Since \ m_{1}=-\frac{6}{7} \ then \ m_{2}=\frac{7}{6}$

Therefore, this line is the blue one and is written as:

$f(x)=\frac{7}{6}x$

Second.a.

To find y(t) we need to find the slope and y-intercept. So, taking two points:

$P_{1}(15,150) \ and \ P_{2}(25,450) \\ \\m=\frac{450-150}{25-15}=30$

So:

$Using \ P_{1}(15,150) \\\\y=30t+b\\\\150=30(15)+b \therefore b=-300 \\\\\boxed{y(t)=30t-300}$

Third.b.

The y-intercept is b=-300 and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.

Fourth.c.

The x-intercept can be found when y=0 (year 1980), that is:

$y(t)=30t-300 \\\\0=30t-300 \therefore t=10$

This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.

Fifth.d.

The slope of this function is m=30

This value tells you that the profit increases $30.000 each year.

6.2.find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it t

Answer from: Quest

£56

step-by-step explanation:

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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