Mathematics, 29.05.2021 06:10 shaakiraak

If dy/dx = ysec^2(x) and y= 5 when x = 0, then y=? А. e^tanx +4
B. e^tanx +5
C. 5e^tanx
D. tanx + 5
E. tanx + 5e^x

Answers: 2

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Answers

Answer from: hannahhoskings6989

C. $\displaystyle y = 5e^{tan(x)}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

FunctionsFunction Notation|Absolute Values|Anything to the 0th power is 1

Algebra II

Logarithms and Natural logsEuler's number e

Calculus

Derivatives

Derivative Notation

Trig Derivatives

Differential Equations

Separation of variablesGeneral and particular solutions

Antiderivatives - Integration

Integration Constant C

Trig Integration

Logarithmic Integration

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \frac{dy}{dx} = ysec^2(x)$

x = 0, y = 5

Step 2: Rewrite Differential

Separation of variables

[Division Property of Equality] Isolate y terms together: $\displaystyle \frac{1}{y}\frac{dy}{dx} = sec^2(x)$ [Multiplication Property of Equality] Isolate x terms together: $\displaystyle \frac{1}{y}dy = sec^2(x)dx$

Step 3: Find General Solution

[Equality Property] Integrate both sides: $\displaystyle \int {\frac{1}{y}} \, dy = \int {sec^2(x)} \, dx$ [1st Integral] Integrate [Logarithmic Integration]: $\displaystyle ln|y| = \int {sec^2(x)} \, dx$ [2nd Integral] Integrate [Trig Integration]: $\displaystyle ln|y| = tan(x) + C$ [Equality Property] e both sides: $\displaystyle e^{ln|y|} = e^{tan(x) + C}$ Simplify: $\displaystyle |y| = Ce^{tan(x)}$ Rewrite: $\displaystyle y = \pm Ce^{tan(x)}$

Step 4: Find Particular Solution

Substitute in variables [Function]: $\displaystyle |5| = Ce^{tan(0)}$ Evaluate absolute value: $\displaystyle 5 = Ce^{tan(0)}$ Evaluate trig: $\displaystyle 5 = Ce^0$ Evaluate exponent: $\displaystyle 5 = C(1)$ Multiply: $\displaystyle 5 = C$ Rewrite: $\displaystyle C =5$ Substitute in C [General Solution]: $\displaystyle y = 5e^{tan(x)}$

∴ Our answer is C.

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Differential Equations

Book: College Calculus 10e

Answer from: Quest

50.6

step-by-step explanation:

Answer from: Quest

It is 5.8 you add all of the up to equat 180 then solve the equation
Need asap! brainliest and 15 points! triangle ghj has the exterior angles shown below.