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3 years ago

CAN SOMEONE HELP PLZ

Mathematics

1 answer:

Vlad1618 [11]3 years ago

7 0

Answer:

Step-by-step explanation:

The solution to the system (c , p) represent the cost of each hot cocoa is c and the cost of each pretzel is p

Nothing changed just two equations were added to form another third equation which represent the total cost of 7 cups of hot cocoa and 8 pretzels

so the solution (c , p) would still be the same as the solution represents cost of each cup of hot cocoa c and cost of each pretzel p

No adding both the equations does not help us solve the equation, It just forms another equation further making the question longer and the third equation is not needed because to solve a system of equations with 2 variables to equations are enough, in this case c and p To solve the system of equations we multiply the first equation with 2 and the second equation with 5 and then subtract equation 1 from equation 2

$Equation\ 1 \\\\5c+4p=18.40\\Multiplying\ it\ with\ 2\\10c+8p=36.8\\\\Equation\ 2\\\\2c+4p=11.20\\Multiplying\ equation\ 2\ with\ 5\\10c+20p=56\\\\Now\ subtract\ equation\ 2\ from\ equation\ 1\\\\10c-10c+8p-20p=36.8-56\\0-12p=-19.2\\-12p=-19.2\\p=-19.2/-12\\p=1.6\\$

Now for the value of c we insert the value of p in any equation, lets insert it in equation 1

$5c+4p=18.40\\5c+4(1.6)=18.40\\5c+6.4=18.40\\5c=12\\c=12/5\\c=2.4$

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nirvana33 [79]

Answer:

$\frac{dr}{dt} = -1.325 \ cm/s$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Calculus

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

Step 1: Define

Given:

$V = \frac{4}{3} \pi r^3$

$\frac{dV}{dt} = -116 \ cm^3/s$

$V = 77 \ cm^3$

Step 2: Solve for r

Substitute: $77 = \frac{4}{3} \pi r^3$
Isolate r term: $\frac{77}{\frac{4}{3} \pi} = r^3$
Isolate r: $\sqrt[3]{\frac{77}{\frac{4}{3} \pi}} = r$
Evaluate: $2.63917 = r$
Rewrite: $r = 2.63917 \ cm$

Step 3: Differentiate

Differentiate the Volume Formula with respect to time t.

Define: $V = \frac{4}{3} \pi r^3$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}$
Simplify: $\frac{dV}{dt} = 4 \pi r^2 \cdot \frac{dr}{dt}$

Step 4: Find radius rate

Substitute in variables: $-116 \ cm^3/sec = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}$
Isolate dr/dt rate: $\frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}$
Evaluate: $-1.3253 \ cm/s = \frac{dr}{dt}$
Rewrite: $\frac{dr}{dt} = -1.3253 \ cm/s$
Round: $\frac{dr}{dt} = -1.325 \ cm/s$

Our radius is decreasing at a rate of -1.325 cm per second.

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