Answer:
y = (∛x)/3
Step-by-step explanation:
To undo the multiplication by 27, you multiply by its inverse:
(1/27)y = (1/27)(27x^3)
y/27 = x^3 . . . . . . . . . . . simplify
To undo the cube, you take the cube root:
(∛y)/(∛27) = ∛(x^3)
(∛y)/3 = x
Apparently, you want the inverse function, so you swap the variables:
y = (∛x)/3
_____
You can swap the variables at the beginning or end. It doesn't matter. If you do it at the beginning, you have ...
x = 27y^3
and you're solving for y. You use the same inverse operations that we used above.
Answer:
La altura de la pirámide es de 8.14 unidades.
Step-by-step explanation:
Hay una pirámide cuadrangular regular cuyas caras laterales forman un ángulo que mide 53º con la base y el área de la superficie lateral es 60. ¿Qué altura tiene?
Dado que el área de superficie lateral = 60
Tenemos
Área del triángulo equilátero = (√3 / 4) × a²
(√3 / 4) × a² = 60
a² = 60 / (√3 / 4) = 80 · √3
a = √ (80 · √3) = 11.77 unidades
La altura inclinada = Altura de la superficie inclinada = a × sin (60) = 11.77 × sin (60)
La altura inclinada = 11.77 × sin (60) = 10.194 unidades
La altura de la pirámide = Altura inclinada × sin (ángulo de caras laterales con la base)
La altura de la pirámide = 10.194 × sin (53) = 8.14 unidades.
La altura de la pirámide = 8.14 unidades.
Answer:
Step-by-step explanation:
The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.
Write a function that gives the lion population size,
Each year, the population drops to 95% of its previous value. (100 - 5)%
That is, the population is multiplied by 0.95 each year.
Repeated multiplication is signified by an exponent.
Here, that exponent is the number of years from today (t).
<h3>There fore, The population function can be written as ...</h3><h3 /><h3> P(t) = 200·0.95^t</h3><h3>
</h3>
Answer:
Part A: option C. 135.2°F
Part B: 40 min
Step-by-step explanation:
<em>Part A:</em><em> What is the temperature in degrees Fahrenheit of the soup after 25 minutes?</em>
<u>1. Set an equation</u>:
- Temperature = Initial temperature - decrease in temperature
- decrease in temperature = rate of decrease × time
- Variables:
temperature: T
initial temperature: To = 192.7°F
decrease rate: 2.3°F / min
time = t
- Equation: T = 192.7°F - 2.3(°F/min) × t
2.<u> Substitute t = 25 min</u>
- T = 192.7°F - 2.3 (°F/min) × 25 min = 135.2 °F
Part B. <em>How many minutes will it take for the soup to cool to 100.7°F?</em>
2.<u> Solve the equation for t</u>
- T = 192.7°F - 2.3(°F/min) × t ⇒ t = (192.7 °F - T) / (2.3 °F/min)
3. <u>Substitute T = 100.7°F</u>
- t = (192.7°F - 100.7°F) / (2.3 °F/min) = 40 min
I believe it is 3.75 miles. 5 2/5=5.4 and 1 11/25=1.44. 5.4/1.44=3.75.
