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3 years ago

Traveling at 65 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 125 miles from San

Diego to Malibu?

Mathematics

1 answer:

DENIUS [597]3 years ago

6 0

$1h=60min\\\\65\ mi\ -\ 1\ h=60\ min\\\\125\ mi-\ x\ min\\\\cross\ multiply\\\\65\cdot x=125\cdot60\\\\65x=7500\ \ \ |divide\ both\ sides\ by\ 65\\\\x=\dfrac{7500}{65}\approx115\\\\Answer:\boxed{115\ min}$

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The ground temperature at an airport is 10 °C. The temperature decreases by 5.4 °C for every increase of 1 kilometer above the g

Paraphin [41]

The temperature outside a plane flying at an altitude of 5 kilometers is -17°C.

Given that,

The ground temperature at the airport is 10 °C.
The decrease in temperature is 5.4°C for each & every rise in 1 kilometer.

Based on the above information, the temperature outside should be

The decrease in the temperature should be

= 5.4×5

= 27°C

Now the final temperature is

= 10 - 27

= -17°C

Therefore we can conclude that the temperature outside a plane flying at an altitude of 5 kilometers is -17°C.

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Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$