A + x + p + 8 = r solve for x all help is appreciated!!

Find f(-3) for f(x) = 4(2)^x. ОА. 1/8 O B. -32 O C. -24 OD. 1/2

Ipatiy [6.2K]

Answer:

D

Step-by-step explanation:

using the rule of exponents

$a^{-m}$ = $\frac{1}{a^{m} }$

substitute x = - 3 into f(x)

f(- 3) = 4( $(2)^{-3}$ = 4 × $\frac{1}{2^{3} }$ = 4 × $\frac{1}{8}$ = $\frac{1}{2}$

5 0

2 years ago

PLZZZZ HELP What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?

earnstyle [38]

$\bf 3y=-4x+2\implies y=\cfrac{-4x+2}{3} \\\\\\ y=\stackrel{\stackrel{slope}{\downarrow }}{-\cfrac{4}{3}}x+\cfrac{2}{3}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so the slope of that line above is really -4/3, now

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{4}\implies \blacktriangleright \cfrac{3}{4} \blacktriangleleft}}$

6 0

3 years ago

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'

vodka [1.7K]

Answer:

a) $v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9$

$a(t) = x''(t) = v'(t) =6t-12$

b) $0$

c) $a(t) = x''(t) = v'(t) =6t-12$

When the acceleration is 0 we have:

$6t-12=0, t =2$

And if we replace t=2 in the velocity function we got:

$v(t) = 3(2)^2 -12(2) +9=-3$

Step-by-step explanation:

For this case we have defined the following function for the position of the particle:

$x(t) = t^3 -6t^2 +9t -5 , 0\leq t\leq 10$

Part a

From definition we know that the velocity is the first derivate of the position respect to time and the accelerations is the second derivate of the position respect the time so we have this:

$v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9$

$a(t) = x''(t) = v'(t) =6t-12$

Part b

For this case we need to analyze the velocity function and where is increasing. The velocity function is given by:

$v(t) = 3t^2 -12t +9$

We can factorize this function as $v(t)= 3 (t^2- 4t +3)=3(t-3)(t-1)$

So from this we can see that we have two values where the function is equal to 0, t=3 and t=1, since our original interval is $0\leq t\leq 10$ we need to analyze the following intervals:

$0< t$

For this case if we select two values let's say 0.25 and 0.5 we see that

$v(0.25) =6.1875, v(0.5)=3.75$

And we see that for $a=0.5 >0.25=b$ we have that f(b)>f(a) so then the function is decreasing on this case.

$1$

We have a minimum at t=2 since at this value w ehave the vertex of the parabola :

$v_x =-\frac{b}{2a}= -\frac{-12}{2*3}= -2$

And at t=-2 v(2) = -3 that represent the minimum for this function, we see that if we select two values let's say 1.5 and 1.75

v(1.75) =-2.8125< -2.25= v(1.5) so then the function sis decreasing on the interval 1<t<2

$2$

We see that the function would be increasing.

$3$

For this interval we will see that for any two points a,b with $a>b$ we have $f(a)>f(b)$ for example let's say a=3 and b =4

$f(a=3) =0 , f(b=4) =9 , f(b)>f(a)$

The particle is moving to the right then the velocity is positive so then the answer for this case is: $0$

Part c

$a(t) = x''(t) = v'(t) =6t-12$

When the acceleration is 0 we have:

$6t-12=0, t =2$

And if we replace t=2 in the velocity function we got:

$v(t) = 3(2)^2 -12(2) +9=-3$

5 0

3 years ago

A construction crew is extending the length of the center line on a highway. The length of the line starts out as 6 meters long,

baherus [9]

Gradient of line,m=(17-6)/(20-0)=11/20

finding equation of line using a point (20,17)

y-17=11/20(x-20)
y-17=(11/20x)-11
y=11/20x+(17-11)
y=(11/20)*x+6

4 0

3 years ago

Read 2 more answers

ASAP WILL GIVE BRAINLIEST!!! DO NOT USE PICTURES PLEASE Part A: Solve the equation 7x + 3x − 18 = 6(x + 3), and show your work.

Brrunno [24]

The answer is x=9 because (look at the picture)

7 0

3 years ago