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3 years ago

If seven consecutive numbers equal to 182, which one is the smallest?

Mathematics

2 answers:

Dafna1 [17]3 years ago

7 0

Answer:

23.

Step-by-step explanation:

My assumption: You mean when you add the numbers, they equal 182.

Let $x$ be the smallest number. Then we are asked to solve the following equation:

$x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 182.$

Rearranging the equation gives us:

7x + 21 = 182 => x + 3 = 26 => x = 23.

So the smallest number is 23 (since our assumption was that x is the smallest number.

----

You could very well have stated that x was the middle number as a lot of cancellations would occur. That is:

(x - 3) + (x - 2) + (x - 1) + x + (x + 1) + (x + 2) + (x - 3) = 182.

7x = 182 => x = 26 so the smallest would be 26 - 3 = 23.

____ [38]3 years ago

4 0

Answer:

the seven consecutive numbers would be 23 24 25 26 27 28 29

Step-by-step explanation:

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4 years ago

Find the function y = f(t) passing through the point (0, 18) with the given first derivative.

monitta

Answer:

$\displaystyle y = \frac{t^2}{16} + 18$

General Formulas and Concepts:

Pre-Algebra

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

Algebra I

Functions
Function Notation
Coordinates (x, y)

Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

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

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

Step-by-step explanation:

Step 1: Define

Identify

Point (0, 18)

$\displaystyle \frac{dy}{dt} = \frac{1}{8} t$

Step 2: Find General Solution

Use integration

[Derivative] Rewrite: $\displaystyle dy = \frac{1}{8} t\ dt$
[Equality Property] Integrate both sides: $\displaystyle \int dy = \int {\frac{1}{8} t} \, dt$
[Left Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle y = \int {\frac{1}{8} t} \, dt$
[Right Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle y = \frac{1}{8}\int {t} \, dt$
[Right Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C$
Multiply: $\displaystyle y = \frac{t^2}{16} + C$