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3 years ago

Write the equation -4x^2+9y^2+32x+36y-64=0 in standard form. Show each step of the process.

Mathematics

1 answer:

Blizzard [7]3 years ago

3 0

Answer:

The answer to your question is below

Step-by-step explanation:

-4x² + 9y² + 32x + 36y - 64 = 0

-4x² + 32x + 9y² + 36y = 64

-4(x² + 8x ) + 9(y² + 4x ) = 64 Factor coefficients

-4(x² + 8x + 4²) + 9(y² + 4x + 2²) = 64 - 64 + 36 Complete trinomials

-4(x + 4)² + 9(y + 2)² = 36 Factor trinomials

$\frac{-4(x+4)^{2} }{36} + \frac{9(y + 2)^{2} }{36} = \frac{36}{36}$

Divide by 36

$- \frac{(x+ 4)^{2} }{9} + \frac{(y + 2)^{2} }{4} = 1$ Simplify

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

Step 3: Find Particular Solution

Substitute in point [Function]: $\displaystyle 18 = \frac{0^2}{16} + C$
Simplify: $\displaystyle 18 = 0 + C$
Add: $\displaystyle 18 = C$
Rewrite: $\displaystyle C = 18$
Substitute in C [Function]: $\displaystyle y = \frac{t^2}{16} + 18$

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

Unit: Integration

Book: College Calculus 10e

4 0

2 years ago

How much will it cost to ride if the cab travels 13.5 miles?

MrMuchimi

Please provide more information. This question is not able to be answered with the information provided. Try giving the full problem!

6 0

3 years ago

Read 2 more answers

Complete this statement: 45ax2 + 27ax + 18a = 9a(

mihalych1998 [28]

Answer:

9 a (5 x^2 + 3 x + 2)

Step-by-step explanation:

Simplify the following:

45 a x^2 + 27 a x + 18 a

Factor 9 a out of 45 a x^2 + 27 a x + 18 a:

Answer: 9 a (5 x^2 + 3 x + 2)

7 0

3 years ago

The GRE is an entrance exam that many students are required to take in order to apply to graduate school. In 2014, the combined

zlopas [31]

The probability that a randomly selected score is greater than 334 will be 0.02275.

<h3>What is a normal distribution?</h3>

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The GRE is an entrance exam that many students are required to take in order to apply to graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.

Then the probability that a randomly selected score is greater than 334 will be

The z-score is given as

z = (x - μ)/σ

z = (334 - 310)/12

z = 24/12

z = 2

Then the probability will be

P(x > 334) = P(z > 2)

P(x > 334) = 1 - P(x<334)

P(x > 334) = 1 - 0.97725

P(x > 334) = 0.02275

More about the normal distribution link is given below.

brainly.com/question/12421652

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6 0

2 years ago

Can someone help me with these two questions?The last answer choice is 90 degrees.

gizmo_the_mogwai [7]

For the first one:

The radian of 60º is 1.047. you just have to find one that has the same value, which would be $\pi$ /3. (the last choice).

for the second one:

you do it the other way. The answer is 45 degrees.

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3 years ago