Mathematics, 17.02.2021 03:50 amirasaleh1012

CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3. A. v(t) = sin(t) + cos(t) + 3
B. v(t) = sin(t) + cos(t) + 2
C. v(t) = sin(t) - cos(t) + 3
D. v(t) = sin(t) - cos(t) + 4

I picked A., which was marked wrong, although I truly believe that is the answer because I got sin(t) - (-cos(t)) + 3. Please tell me whether you believe this is right or am I doing something wrong. I really want to learn/master this concept. Thanks is advance.

CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t),

Answers: 3

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Answer from: zoeybuch5

B. v(t) = sin(t) + cos(t) + 2

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

Function Notation

Calculus

Antiderivatives - Integrals

Integration Constant C

Solving Integration Equations

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Step-by-step explanation:

*Note: Remember that the velocity function is the integral of the acceleration function/acceleration is the derivative of velocity.

$\displaystyle v'(t) = a(t)\\v(t) = \int {a(t)} \, dt$

Step 1: Define

a(t) = cos(t) - sin(t)

v(0) = 3

Step 2: Integrate

Set up integral: $\displaystyle v(t) = \int {cos(t) - sin(t)} \, dt$ [integral] Rewrite [Integration Property - Subtraction]: $\displaystyle v(t) = \int {cos(t)} \, dt - \int {sin(t)} \, dt$ [Integral] Trig integration: $\displaystyle v(t) = sin(t) - [-cos(t)] + C$ [Velocity Integration] Simplify: $\displaystyle v(t) = sin(t) + cos(t) + C$

Step 3: Find Function

We need to solve for the entire function, meaning we need to find constant C.

Substitute in given point [Velocity Integration]: $\displaystyle v(0) = sin(0) + cos(0) + C$ [Velocity Integration] Substitute: $\displaystyle 3 = sin(0) + cos(0) + C$ [Velocity Integration] Evaluate trig: $\displaystyle 3 = 0 + 1 + C$ [Velocity Integration] Add: $\displaystyle 3 = 1 + C$ [Velocity Integration] Isolate C [Subtraction Property of Equality]: $\displaystyle 2 = C$ [Velocity Integration] Rewrite: $\displaystyle C = 2$ [Velocity Function] Substitute in C [Velocity Integration]: $\displaystyle v(t) = sin(t) + cos(t) + 2$

Topic: Calculus

Unit: Basic Integration

Book: College Calculus 10e

Answer from: Quest

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to $\frac{1}{60} hr\\$

then mult. both sides by 75 we get the ratio

75 mi. to $\frac{75}{60} hr\\$

simplifying we get

75 mi. to $\frac{5}{4} hr$

or 1.25 hr.

Answer from: Quest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$

$\tan\left(x\right)=\frac{p}{r}$

$\frac{p}{r}=tan(x)$

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

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