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3 years ago

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A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall . The ladder makes an angle of 74° with the

level ground . How high in the wall does the ladder reach .? Show a diagram.

1 answer:

gayaneshka [121]3 years ago

8 0

Answer:6.25

Step-by-step explanation:

Let the height of the wall be h

Sin 74=h/6.5

h =6.5sin 74

h=6.25

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Help with b please. thank you<br>

erastovalidia [21]

Answer:

See explanation.

General Formulas and Concepts:

<u>Algebra I</u>

Terms/Coefficients
Factoring

<u>Algebra II</u>

Polynomial Long Division

<u>Pre-Calculus</u>

Parametrics

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

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

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Parametric Differentiation: $\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle x = 2t - \frac{1}{t}$

$\displaystyle y = t + \frac{4}{t}$

<u>Step 2: Find Derivative</u>

[<em>x</em>] Differentiate [Basic Power Rule and Quotient Rule]: $\displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}$
[<em>y</em>] Differentiate [Basic Power Rule and Quotient Rule]: $\displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}$
Substitute in variables [Parametric Derivative]: $\displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}$
[Parametric Derivative] Simplify: $\displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}$
[Parametric Derivative] Polynomial Long Division: $\displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}$
[Parametric Derivative] Factor: $\displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)$

Here we see that if we increase our values for <em>t</em>, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence $\displaystyle \frac{dy}{dx} < \frac{1}{2}$ .

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametrics

Book: College Calculus 10e

7 0

3 years ago

At a football stadium, 25% of the fans in attendance were teenagers. If there were 130 teenagers at the football stadium, what w

Trava [24]

Answer:

Total number of people in the stadium = 520

Step-by-step explanation:

Let the total number of people in the stadium = x

Since, 25% of the fans are teenagers, number of teenagers in the stadium

= 25% of x

= $\frac{25}{100}\times x$

= 0,25x

If the number of teenagers in the stadium = 130

0.25x = 130

x = $\frac{130}{0.25}$

x = 520

Therefore, total number of fans in the stadium = 520.

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4 years ago

What percent of 90 is 72?

Effectus [21]

Answer:

80

Step-by-step explanation:

i hope this is right

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NeX [460]

14/25 is bigger, when you divide these numbers and look for their decimals, you can tell which one is greater

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