What is the image of (-7,-8) after a dilation by a scale factor of 4 centered at the origin

The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Area of a Rectangle: A = lw

l is length
w is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

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

Step-by-step explanation:

Step 1: Define

$\displaystyle l = 10 \ meters$

$\displaystyle \frac{dl}{dt} = 4 \ m/day$

$\displaystyle w = 23 \ meters$

$\displaystyle \frac{dw}{dt} = 1 \ m/day$

Step 2: Differentiate

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

Step 3: Solve

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
[Rate] Multiply: $\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day$
[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

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

Unit: Implicit Differentiation

Book: College Calculus 10e

8 0

3 years ago

HELP PLEASE!!! CLUELESS

statuscvo [17]

-3-8X≥9

Add 3 on both sides.

-8X≥12

Divide by negative 8 and flip the sign.

X≤-1.5

There isn't a number behind five, so I would just keep as is.

I hope this helps!
~kaikers

5 0

3 years ago

What is the mode and range of 45 50 47 52 53 45 51

marysya [2.9K]

Mode : 50.1 and range is 8

3 0

3 years ago

Read 2 more answers

18 Andy flies from the UK to Japan.

kotykmax [81]

Answer:

Leila pays more than Andy to fly from the UK to Australia.

Step-by-step explanation:

Given:

Andy flies from the UK to Japan.

His plane ticket costs £554.

Andy then flies from Japan to Australia.

His plane ticket costs 70 140 Japanese Yen.

The exchange rate is £1 = 140 Japanese Yen.

Leila flies from the UK to Australia.

Her plane ticket costs 1860 Australian dollars.

The exchange rate is 1 Australian dollar = £0.62.

Now, to find Andy or Leila who pays more to fly from the UK to Australia.

Andy flies from the UK to Japan.

His plane ticket costs = £554.

Andy then flies from Japan to Australia.

His plane ticket costs 70 140 Japanese Yen.

The exchange rate is £1 = 140 Japanese Yen.

So, by using conversion factor we convert Japanese Yen to £.

140 = £1

70140 = $70140\div 140=\£501.$

His plane ticket costs = £501.

Now, adding both the cost of tickets:

$501+554=\£1055.$

Andy total pays fly from the UK to Australia is £1055.

Now, to get the cost of plane ticket of Leila from the UK to Australia.

Her plane ticket costs 1860 Australian dollars.

The exchange rate is 1 Australian dollar = £0.62.

So, by using conversion factor:

1 Australian dollar = £0.62

1860 Australian dollar = $1860\times 0.62=\£1153.2$

Her plane ticket costs is £1153.2.

As, we see that cost of plane ticket of Andy is £1055 and cost of plane ticket of Leila is £1153.2.

Thus, Leila pays more.

Therefore, Leila pays more than Andy to fly from the UK to Australia.

4 0

3 years ago

The diagram below shows a circular pizza with a diameter of 8 inches. The pizza is in a square box with side lengths of 8 inches

deff fn [24]

Area of circle is about 50.30 inches squared.
Area of square box is 64 inches squared.
Lastly 64 inches minus 50.30 inches is 13.70.
So, 13.70 Square Inches Of The Box Is Empty.

4 0

3 years ago