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trapecia [35]
3 years ago
10

69 minutes equals how many hours and minutes?

Mathematics
1 answer:
Anestetic [448]3 years ago
7 0

Answer:

1 hour and 9 minutes

Step-by-step explanation:

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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   }

which simplifies down, finally, to

x ≈ 6.325 units

8 0
3 years ago
What is the value of each expression (-3)2
k0ka [10]

First you had to remove parenthesis first.

-3*2=-6

Multiply by the numbers.

3*2=6

Final answer \boxed{=-6}

6/3=2

2*3=6

6/2=3

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

5 0
3 years ago
what is the equation of a line that passes through the point (6,1) and is perpendicular to the line whose equation is y=2x-6?
alexandr402 [8]

Answer:

y = -(1/2)x + 4

Step-by-step explanation:

Use the standard form on an equation:  y = mx + b

A line that is perpendicular has a slope that is the opposite reciprocal of the other line.  We also have a point (x, y) that is on the line, so our equation begins as..

1 = -(1/2)(6) + b           We must solve for b (  -1/2 is the opposite reciprocal of 2)

1 = -3 + b

4 = b  

so our equation is

y = -(1/2)x + 4

3 0
3 years ago
Read 2 more answers
Help on questions 11 and 15 Add and simplify if possible
Svetllana [295]
\frac{16+x}{x^3}+\frac{7-4x}{x^3}=\frac{16+x+7-4x}{x^3}=\frac{23-3x}{x^3}\\\\======================================\\\\\frac{5}{t-1}+\frac{3}{t}=\frac{5t}{t(t-1)}+\frac{3(t-1)}{t(t-1)}=\frac{5t+3t-3}{t^2-t}=\frac{8t-3}{t^2-t}
7 0
3 years ago
Read 2 more answers
7. What polynomial remains after the greatest common factor is factored out of the
lara31 [8.8K]

Answer:the answer is A

Step-by-step explanation:

7 0
3 years ago
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