All categories

4 years ago

How to do a Pythagorean theorem question

1 answer:

8 0

A Pythagorean theorem question is one that deals with the side lengths of a RIGHT triangle.

When solving a question you would use the formula, a^2 + b^2=c^2

A and B are both of the sides that aren’t the hypotenuse.

C is distinguishable from a and b as it is the side opposite from the 90 degree angle. (90 degree angles are formed by perpendicular lines)

Hope this helps :)

You might be interested in

Select the statement in if-then form.

SashulF [63]

The correct statement is C. If an angle is an acute angle, then the angle measures less than 90 degrees.
A and B are obviously incorrect, and D is incorrect because it can be other angle as well, not just acute.

3 0

3 years ago

F(x) = e^-x . Find the equation of the tangent to f(x) at x=-1

natima [27]

Answer:

The equation of the tangent line is given by the following equation:

$\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)$

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

$\displaystylef(x) = e^{-x} \\x = -1$

Step 2: Differentiate

[Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
$\displaystyle f'(x) = e^{-x}(-x)'$
[Derivative] Rewrite [Derivative Rule - Multiplied Constant]:
$\displaystyle f'(x) = -e^{-x}(x)'$
[Derivative] Apply Derivative Rule [Derivative Rule - Basic Power Rule]:
$\displaystyle f'(x) = -e^{-x}$

Step 3: Find Tangent Slope

[Derivative] Substitute in x = 1:
$\displaystyle f'(1) = -e^{-1}$
Rewrite:
$\displaystyle f'(1) = \frac{-1}{e}$

∴ the slope of the tangent line is equal to $\displaystyle \frac{-1}{e}$ .

Step 4: Find Equation

[Function] Substitute in x = 1:
$\displaystyle f(1) = e^{-1}$
Rewrite:
$\displaystyle f(1) = \frac{1}{e}$

∴ our point is equal to $\displaystyle \bigg( 1, \frac{1}{e} \bigg)$ .

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

$\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }$

∴ we have our final answer.

---

Learn more about derivatives: brainly.com/question/27163229

Learn more about calculus: brainly.com/question/23558817

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

3 0

2 years ago

A rectangle field is five times as long as it is wide. If the perimeter of the field is 288 yards, what are the field's dimensio

mr_godi [17]

$x + x + 5x + 5x = 288 \\ 12x = 288 \\ x = 24$

Width = 24 yards
Length = 24 x 5 = 120 yards

Area =
$24 \times 120 = 2880 \: sq. \: yrds$

Hope this helps. - M

7 0

3 years ago

Why do we subtract the x values and subtract the y values?

Anestetic [448]

Answer:

Because you have to get the answer

Step-by-step explanation:

5 0

3 years ago

Look at the drawing of a triangle within a rectangle. The triangle and the rectangle have the same base, b, and height, h.

lara [203]

the total area of sections 1 and 2 is 48 square units !

Step-by-step explanation:

Here we have , The triangle and the rectangle have the same base, b, and height, h. If the area of the triangle is 48 square units,We need to find what is the total area of sections 1 and 2 . Let's find out:

According to question , we have a triangle with same base and height as of rectangle inside a rectangle ! Following are the parameters of rectangle:

$Length= b\\width= h\\$