I would prefer to solve this in a decimal form
I will show this to u in 2 ways
1:.75::X:2.25
(1*2.25)/.75x
2.25/.75x
X=3
2.25/.75=3
when we divide the number of hours played by hors for one game we get the number of games that could be played
Answer:
-938 ft
Step-by-step explanation:
the bird will be going down in elevation. the distance between -422 and -1360
-1360+422= -938
A true equation from these numbers can be:
82 ÷ 2 = 41 ÷ 2 = 20.5
Hope this helps!
Answer:
x-intercept:
A line that crosses the graph at x-axis.
i.e substitute y = 0 and solve for x.
As per the statement:
A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water
Given the graph:

Substitute y = 0 we have;

⇒
⇒
⇒
⇒
⇒
By zero product property we have;
x-20 =0 and x+10 = 0
⇒x = 20 and x = -10
Therefore, the x-intercept represents the water has no larvae at −10 degrees Celsius and 20 degrees Celsius.
The derivatives of the functions are listed below:
(a)
(b) 
(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²
(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]
(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶
(f)
(g)
(h) f'(x) = cot x + cos (㏑ x) · (1 / x)
<h3>How to find the first derivative of a group of functions</h3>
In this question we must obtain the <em>first</em> derivatives of each expression by applying <em>differentiation</em> rules:
(a) ![f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%20%5Ccdot%20x%5E%7B-%5Cfrac%7B7%7D%7B2%7D%20%7D%20-%20x%5E%7B2%7D%20%2B%204%20%5Ccdot%20x%20-%20%5Cfrac%7Bx%7D%7B5%7D%20%2B%20%5Cfrac%7B5%7D%7Bx%7D%20-%20%5Csqrt%5B11%5D%7B2022%7D)
Given
Definition of power
Derivative of constant and power functions / Derivative of an addition of functions / Result
(b) ![f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%20%2B%203%7D%20%5Ccdot%20%5Csqrt%5B3%5D%7Bx%20%2B%205%7D)
Given
Definition of power
Derivative of a product of functions / Derivative of power function / Rule of chain / Result
(c) f(x) = (sin x - cos x) / (x² - 1)
- f(x) = (sin x - cos x) / (x² - 1) Given
- f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result
(d) f(x) = 5ˣ · ㏒₅ x
- f(x) = 5ˣ · ㏒₅ x Given
- f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result
(e) f(x) = (x⁻⁵ + √3)⁻⁹
- f(x) = (x⁻⁵ + √3)⁻⁹ Given
- f'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant function
- f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result
(f) 
Given
Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions
Distributive property / Result
(g) 
Given
Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result
(h) f(x) = ㏑ (sin x) + sin (㏑ x)
- f(x) = ㏑ (sin x) + sin (㏑ x) Given
- f'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions
- f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / Result
To learn more on derivatives: brainly.com/question/23847661
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