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3 years ago

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The equation g(t)=2+23.7t−4.9t2 models the height, in meters, of a pumpkin t seconds after it has been launched from a catapult.

Is the pumpkin still in the air 8 seconds later? Explain or show how you know.

1 answer:

inysia [295]3 years ago

5 0

Answer:

The pumpkin is not in the air

Step-by-step explanation:

The equation is

$g(t)=2+23.7t-4.9t^2$

Let us find when the pumpkin will reach the ground

$0=2+23.7t-4.9t^2\\\Rightarrow -49t^2+237t+20=0\\\Rightarrow t=\frac{-237\pm \sqrt{237^2-4\left(-49\right)\times 20}}{2\left(-49\right)}\\\Rightarrow t=-0.08,4.91$

So, the pumpkin will reach the ground at 4.91 seconds. Hence, at 8 seconds the pumpkin will reach the ground.

<h2>OR</h2>

At $t=8\ \text{s}$

$g(8)=2+23.7\times 8-4.9\times 8^2\\\Rightarrow g(8)=-122\ \text{m}$

The height of the pumpkin is negative 122 m. This means it is lower than the ground. So, the pumpkin is not in the air 8 seconds later.

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Ig nobody uses comments anymore :/

marta [7]

Answer:

19

Step-by-step explanation:

9+10 is 19.

8 0

2 years ago

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

As

$3^{\frac{1}{8}\cdot \:24}=3^3$

So

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

#learnwithBrainly

6 0

3 years ago

A bag contains 2 black balls, 4 yellow balls and 4 white balls. Event A is defined as drawing a white ball on the first draw and

arsen [322]

Answer: $P(B|A)=\dfrac{4}{9}$

Step-by-step explanation:

Given: A bag contains 2 black balls, 4 yellow balls and 4 white balls.

Event A is defined as drawing a white ball on the first draw.

Event B is defined as drawing a black ball on the second draw.

P(B|A) is expressed as the conditional probability of occurring B given that A.

i.e. it is the probability of happening B where A is already happended.

If a white ball is drawn at first, then the number of black ball(4) remains unchanged but the total number of balls (10) will become 9.

$Probability=\dfrac{Number\ of \ favorable \ outcomes}{Total\ outcomes}$

Then, $P(B|A)=\dfrac{4}{9}$

8 0

3 years ago

Hi:) for triangle inequalities , the sum of two sides of a triangle has to be greater than the third side.

Jet001 [13]

Answer:

NO

Step-by-step explanation:

Note :

Consider a triangle with sides‘s length a , b and c

triangle inequalities state that we must have c - a < b < c + a

now , is the third side always the longest ?

the answer is NO: (let’s take a counter example )

in a triangle with 2 sides‘s length 3 , 4

the third side could measure 2

because 4-3 < 2 < 4+3

8 0

3 years ago

What is the answer to this equation?<br> 1/2 (4i+8)=-2

Flauer [41]

Answer:

If your looking for I the answer is -3

Step-by-step explanation:

Simplify both sides of the equation

1/2(4i+8)=-2 - Distribute

(1/2) (4i) + (1/2) (8) = -2

The subtract 4 from both sides

Then divide both sides by 2

5 0

3 years ago