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Ann [662]
2 years ago
10

the sum of two numbers is 41. the smaller number is 13 less than the larger number. what are the numbers

Mathematics
1 answer:
tankabanditka [31]2 years ago
8 0

Answer:

another number =27

Step-by-step explanation:

Let X stand for the larger number. The smaller number is therefore X - 13. We can now write the sum of the two numbers as:

X + (X - 13) = 4

X + X - 13 = 41

Gather the X’s and rewrite as,

2X - 13 = 41

Add 13 to both sides to get

2X = 54

Divide both sides by 2 to solve for X,

X = 27

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl
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Answer:

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Step-by-step explanation:

The equation of a circle of radius 5 centered at (0,0) is:

x^{2} + y^{2} = 5^{2}.

x^{2} + y^{2} = 25.

Differentiate implicitly with respect to x to find the slope of tangents to this circle.

\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]

\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0.

Apply the power rule and the chain rule. Treat y as a function of x, f(x).

\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0.

\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0.

That is:

\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0.

Solve this equation for \displaystyle \frac{dy}{dx}:

\displaystyle \frac{dy}{dx} = -\frac{x}{y}.

The slope of the tangent to this circle at point (3, 4) will thus equal

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Apply the slope-point of a line in a cartesian plane:

y - y_0 = m(x - x_0), where

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For the tangent line in this question:

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The equation of this tangent line will thus be:

\displaystyle y - 4 = -\frac{3}{4} (x - 3).

That simplifies to

\displaystyle y= -\frac{3}{4} x + \frac{25}{4}.

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Hi,

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