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3 years ago

8

A leg of a right triangle measures 84 units, and the hypotenuse measures 85 units. What is the length of the remaining side roun

ded to the nearest hundredth unit?

1 answer:

kondaur [170]3 years ago

7 0

Answer:

13 units

Step-by-step explanation:

pythagorean theorem: a²+b²=c²

c= 85

b= 84

a²+(84)²=85²

a²+7056=7225

a²=169

square root of a² = square root of 169

a=13

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The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

<u>Geometry</u>

Area of a Rectangle: A = lw

l is length
w is width

<u>Calculus</u>

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

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

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle l = 10 \ meters$ <u />

<u /> $\displaystyle \frac{dl}{dt} = 4 \ m/day$ <u />

<u /> $\displaystyle w = 23 \ meters$ <u />

<u /> $\displaystyle \frac{dw}{dt} = 1 \ m/day$ <u />

<u />

<u>Step 2: Differentiate</u>

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

<u>Step 3: Solve</u>

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
[Rate] Multiply: $\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day$
[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

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

Unit: Implicit Differentiation

Book: College Calculus 10e

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Y_Kistochka [10]

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

erastova [34]

Answer:

1st ∡ = 15.5°

2nd ∡ = 77.25°

3rd ∡ = 87.25°

Step-by-step explanation:

1st ∡: x

2nd ∡: y

3rd ∡: z

Equations we can create from data given in problem:

y + z = 5x

z = 5x + 10

We have enough expressions to create an equation:

x + 5x + 5x + 10 = 180

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x = 15.5

y = 5(15.5) = 77.25

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2 years ago