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2 years ago

¿Se pueden reducir términos semejantes en la expresión? y +3x +4y+x+3y+2x. ¿Por qué?

Mathematics

1 answer:

ludmilkaskok [199]2 years ago

6 0

Answer:

8y + 6x

Step-by-step explanation:

Combine like terms

y + 3x +4y + x + 3y + 2x

= (y + 4y + 3y) + ( 3x + x + 2x)

= 8y + 6x

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Identify whether the equation represents an exponential growth or exponential decay function.1. y = 1/4 (1/e)^-2x2. y = (1/e)^4x

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The general formula for exponential growth and decays is:

$y=y_0e^{kx}$

if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.

Now we need to classify each of the functions:

The function

$y=\frac{1}{4}(\frac{1}{e})^{-2x}$

can be wrtten as:

$\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}$

comparing with the general formula we notice that k=2, therefore this is an exponential growth.

The function

$y=(\frac{1}{e})^{4x}$

can be written as:

$\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}$

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The function

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9 months ago

A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time

FinnZ [79.3K]

If the ball was thrown straight up at 24 ft/sec when it was 5 ft above the ground, the ball reached a maximum height of 7.25 m

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<h3>Further explanation</h3>

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

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An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = \frac{-b}{2a} } }$

Let us now tackle the problem!

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<u>Given:</u>

$p(t) = 3gt^2 + v_ot + p_o$

$p(t) = 3(-32)t^2 + 24t + 5$

$p(t) = -64t^2 + 24t + 5$

<u>Asked:</u>

$p_{max} = ?$

<u>Solution:</u>

<em>At the maximum height , velocity is 0 m/s:</em>

$v = \frac{dp(t)}{dt}$

$v = \frac{d}{dt} ( -64t^2 + 24t + 5 )$

$v = (-64)(2)t^{2-1} + 24$

$v = -128t + 24$

$0 = -128t + 24$

$128t = 24$

$t = 24 \div 128$

$t = 3 \div 16$

$t = 0.1875 \texttt{ s}$

$\texttt{ }$

$p(t) = -64t^2 + 24t + 5$

$p(0.1875) = -64(0.1875)^2 + 24(0.1875) + 5$

$p(0.1875) = 7.25 \texttt{ m}$

$\texttt{ }$

<h3>Learn more</h3>

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

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<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

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Keywords: Quadratic , Equation , Discriminant , Real , Number

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