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2 years ago

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1. To reach the artic wildlife refuge Aidan and James flew 238 miles from Fairbanks to artic village which is on the edge of the

park. The trip took 2 hours. What was the planes average speed.
2. From artic village they had to fly another 50 miles to the starting point of their hike at Red sheep creek. This trip lasted 0.36 hours. What was the planes speed rounded to the nearest whole number.

1 answer:

ArbitrLikvidat [17]2 years ago

7 0

1. 119mph
2. 138.888 forever

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kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle y = \sqrt{x - 3}$ <u />

<u /> $\displaystyle y' = \frac{1}{2}$ <u />

<u />

<u>Step 2: Differentiate</u>

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

<u>Step 3: Solve</u>

<em>Find coordinates</em>

<em />

<em>x-coordinate</em>

Substitute in <em>y'</em> [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

<em>y-coordinate</em>

Substitute in <em>x</em> [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

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

Unit: Derivatives

Book: College Calculus 10e

4 0

2 years ago

Evaluate the expression when a=4 and x=-3.<br> -2a +x

Serga [27]

Answer:11

Step-by-step explanation:

Step 1: you need to multiply-2x4 and you would get 8

Step2: you add 3 and you get 11

5 0

2 years ago

Read 2 more answers

What’s the measure of A

jeka94

Answer:Angle A is equal to 113

Step-by-step explanation:

If two angles are vertical, that would make them equal to each other.

7x-20=6x-1

Add on to both sides

7x-19=6x

Subtract Seven from both sides

-19=-x

Divide by negative one to get rid of the negative

19=x

Then plug x into the equation 7(19)-20

8 0

2 years ago

If a translation maps zl onto ZK, which of the following statements is true? G HS 1 K НІ is twice the measure of 2JK: GH is twic

murzikaleks [220]

9514 1404 393

Answer:

(d) ∠H ≅ ∠J

Step-by-step explanation:

We already know that ∠G is congruent to itself. If we show (by translation or other means) that ∠I ≅ ∠K, then we know that ΔGHI ~ ΔGJK. The third angle in each triangle will be congruent, too.

∠H ≅ ∠J

_____

The problem is concerned with angles, so the first two answer choices are irrelevant. If two angles are shown congruent, the triangles are congruent by AA similarity, so the third answer choice is incorrect.

6 0

1 year ago

What point slope form equation could be produced with the points(-3,-6)and (3,-3)

Irina-Kira [14]

Answer:

y+6=1/2(x+3)

Step-by-step explanation:

Hi there!

We want to find the equation of the line in point-slope form that passes through (-3, -6), and (3, -3)

Point-slope form is given as y- $y_{1}$ =m(x- $x_{1}$ ) where ( $x_{1}$ , $y_{1}$ ) is a point and m is the slope

We don't know the slope of the line, so let's find it

The formula for the slope (m) calculated from two points is $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where ( $x_{1}$ , $y_{1}$ ) and ( $x_{2}$ , $y_{2}$ ) are points

We have two points, but let's label their values to avoid any confusion

$x_{1}$ =-3

$y_{1}$ =-6

$x_{2}$ =3

$y_{2}$ =-3

Now substitute into the formula (remember: the formula has SUBTRACTION)

m= $\frac{-3--6}{3--3}$

simplify

m= $\frac{-3+6}{3+3}$

m= $\frac{3}{6}$

m=1/2

So the slope of the line is 1/2

Now that we have everything needed for point-slope form (a point and the slope), substitute the values into the formula (remember: the formula has SUBTRACTION)

y- $y_{1}$ =m(x- $x_{1}$ )

y--6=1/2(x--3)

simplify

<u>y+6=1/2(x+3)</u>

Hope this helps!

3 0

2 years ago