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3 years ago

Omg help me thissssss plsssss

Mathematics

1 answer:

igomit [66]3 years ago

4 0

Answer:

3.5

Step-by-step explanation:

If you multiply 3.5 for example by 2 (which is the number of gallons) you get 7 which is the cost (also a proportional relationship).

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What is the slope of a line perpendicular to the line whose equation is x+ 3y = -15 Fully simplify your answer.

alukav5142 [94]

Answer:

Step-by-step explanation:

We can find the slope of the given line in this two way:

1) the faster is calculate -a/b where a is the number the multiply x and b is the number the multiply y. In this case we have -1/3

2) the second method is rewrite the equation in slope intercept form and find the therm that multiply x

3y = -x-15

y = -1/3x - 5

Also in this case we have -1/3

Two perpendicular lines have the the product of the their slope that is -1

So the slope that we are finding is 3

In fact = 3 x -1/3 = -1

3 0

3 years ago

Find the distance from the point (1,4) to the line y = 1/3x - 3

Troyanec [42]

Answer:

Step-by-step explanation:

If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):

$d=\sqrt{(1-x)^2+(4-y)^2}$

but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:

$d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 }$ and simplify:

$d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }$

. No we'll expand each binomial by squaring:

$d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2) }$

. Combining like terms gives us

$d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50 }$

The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is

$\frac{20}{9}x-\frac{20}{3}$

Setting equal to 0 and getting rid of the denominators gives us

20x - 60 = 0

Solving for x gives us

20x = 60 and x = 3.

That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:

$d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50 }$