What's the derivative of f(x)=x^3x

7(x+2)=2x-1 solve for the variable

Len [333]

Answer:

x = - 3

Step-by-step explanation:

Given

7(x + 2) = 2x - 1 ← distribute parenthesis on left side

7x + 14 = 2x - 1 ( subtract 2x from both sides )

5x + 14 = - 1 ( subtract 14 from both sides )

5x = - 15 ( divide both sides by 5 )

x = - 3

7 0

3 years ago

Equation in slope-intercept form:

Jobisdone [24]

Answer:

y = -x + 3

Step-by-step explanation:

Find the slope using the formula [ y2-y1/x2-x1 ]. We can use the points (0, 3) and (3, 0) to solve.

0-3/3-0

-3/3

-1

From the graph, the y-intercept is (0, 3). Input all the data we know into the slope intercept form expression [ y = mx + b ].

y = -x + 3

Best of Luck!

5 0

3 years ago

A particle moves according to a law of motion s = f(t), t ? 0, where t is measured in seconds and s in feet.

Usimov [2.4K]

Answer:

a) $\frac{ds}{dt}= v(t) = 3t^2 -18t +15$

b) $v(t=3) = 3(3)^2 -18(3) +15=-12$

c) $t =1s, t=5s$

d) $[0,1) \cup (5,\infty)$

e) $D = [1 -9 +15] +[(5^3 -9* (5^2)+ 15*5)-(1-9+15)]+ [(6^3 -9(6)^2 +15*6)-(5^3 -9(5)^2 +15*5)] =7+ |32|+7 =46$

And we take the absolute value on the middle integral because the distance can't be negative.

f) $a(t) = \frac{dv}{dt}= 6t -18$

g) The particle is speeding up $(1,3) \cup (5,\infty)$

And would be slowing down from $[0,1) \cup (3,5)$

Step-by-step explanation:

For this case we have the following function given:

$f(t) = s = t^3 -9t^2 +15 t$

Part a: Find the velocity at time t.

For this case we just need to take the derivate of the position function respect to t like this:

$\frac{ds}{dt}= v(t) = 3t^2 -18t +15$

Part b: What is the velocity after 3 s?

For this case we just need to replace t=3 s into the velocity equation and we got:

$v(t=3) = 3(3)^2 -18(3) +15=-12$

Part c: When is the particle at rest?

The particle would be at rest when the velocity would be 0 so we need to solve the following equation:

$3t^2 -18 t +15 =0$

We can divide both sides of the equation by 3 and we got:

$t^2 -6t +5=0$

And if we factorize we need to find two numbers that added gives -6 and multiplied 5, so we got:

$(t-5)*(t-1) =0$

And for this case we got $t =1s, t=5s$

Part d: When is the particle moving in the positive direction? (Enter your answer in interval notation.)

For this case the particle is moving in the positive direction when the velocity is higher than 0:

$t^2 -6t +5 >0$

$(t-5) *(t-1)>0$

So then the intervals positive are $[0,1) \cup (5,\infty)$

Part e: Find the total distance traveled during the first 6 s.

We can calculate the total distance with the following integral:

$D= \int_{0}^1 3t^2 -18t +15 dt + |\int_{1}^5 3t^2 -18t +15 dt| +\int_{5}^6 3t^2 -18t +15 dt= t^3 -9t^2 +15 t \Big|_0^1 + t^3 -9t^2 +15 t \Big|_1^5 + t^3 -9t^2 +15 t \Big|_5^6$

And if we replace we got:

$D = [1 -9 +15] +[(5^3 -9* (5^2)+ 15*5)-(1-9+15)]+ [(6^3 -9(6)^2 +15*6)-(5^3 -9(5)^2 +15*5)] =7+ |32|+7 =46$

And we take the absolute value on the middle integral because the distance can't be negative.

Part f: Find the acceleration at time t.

For this case we ust need to take the derivate of the velocity respect to the time like this:

$a(t) = \frac{dv}{dt}= 6t -18$

Part g and h

The particle is speeding up $(1,3) \cup (5,\infty)$

And would be slowing down from $[0,1) \cup (3,5)$

5 0

3 years ago

1 more than the product of a number and negative 8

castortr0y [4]

Answer:

-8x+1

or

1+(-8x)

3 0

3 years ago

A music industry researcher wants to estimate, with a 90% confidence level, the proportion of young urban people (ages 21 to 35

katrin2010 [14]

Answer:

21378

Step-by-step explanation:

The confidence level is 90%, which gives us a Z of 1.645.

Our equation is (Z^2*p*q)/e^2

(1.645^2*p*(1-.21))/ (.01^2)

E is the error proportion, .01

Q is 1-p or the proportion

P is the pop you need

With this, we can solve

and get p = 21377.5975 and rounded to 21378

5 0

3 years ago