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4 years ago

Solve for c of the right triangle

Mathematics

2 answers:

Ede4ka [16]4 years ago

5 0

In order to solve this triangle we must use cosine law:
$c^{2} = a^{2} + b^{2} - 2ab*cosC$

Now let's plug in the values we are given:
$c^{2} = 5^{2} + 8^{2} - 2(5)(8) * cos 67$
$c^{2} = 25 + 64 - 80*cos67$
$c = \sqrt{80-cos67}$

DochEvi [55]4 years ago

5 0

From the Law of Cosines, we know
b=8 a=5 angle C=67
side c² = a² + b² -2ab • cos(C)
side c² = 5^2 +8^2 -2*5*8 * cos (67)
side c² = 25 + 64 -(80*.39073)
side c² = 89 - 31.2584 
side c² = 57.7416 
side c = 7.5987893773

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The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched (a) in sq ft and the de

Lena [83]

Answer:

22 2/9

Step-by-step explanation:

When z "varies jointly" with x and y, it can be described by the formula

z = kxy

Here, we have bags of mulch (n) varying jointly with area (a) and depth (d), both in feet. The given information can let us find the value of k.

n = kad

10 = k·(120)(1/4)

10/30 = k = 1/3 . . . . . divide by the coefficient of k

Now, we can fill in the other values of interest.

n = (1/3)·(200)·(1/3) = 200/9

n = 22 2/9

You need 22 2/9 bags of mulch to cover 200 ft² to a depth of 4 inches.

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Comment on the problem

This problem requires the formula be written with both area and depth expressed in feet, yet it gives depth in inches. The formula can also be written using depth in inches. In that case, k = 1/36.

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3 years ago

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Oksi-84 [34.3K]

Answer:

Step-by-step explanation:

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3 years ago

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4 years ago

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Answer:

$\displaystyle y'(1, \frac{3}{2}) = -3$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \frac{3}{2x^2}$

$\displaystyle \text{Point} \ (1, \frac{3}{2})$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y = \frac{3}{2}x^{-2}$
Basic Power Rule: $\displaystyle y' = -2 \cdot \frac{3}{2}x^{-2 - 1}$
Simplify: $\displaystyle y' = -3x^{-3}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{-3}{x^3}$

Step 3: Solve

Substitute in coordinate [Derivative]: $\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1^3}$
Evaluate exponents: $\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1}$
Divide: $\displaystyle y'(1, \frac{3}{2}) = -3$