Expand: f(x)= x^4- x^3+x^2+x-

A lawn mower is pushed a distance of 100 ft. Along a horizontal path by a constant force of 60 lbs. Yhe handle of the lawn mower

stira [4]

For this case we have the following equation:
w = F • PQ
Where,
w: work done
F: is the force vector
PQ: is the vector of the direction of movement.
Rewriting the equation we have:
w = || F || • || PQ || costheta
Substituting values:
w = (60) * (100) * (cos (45))
w = (60) * (100) * (root (2) / 2)
w = 4242.640687 lb.ft
Answer:
The work done pushing the lawn mower is:
w = 4242.6 lb.ft

7 0

3 years ago

Create the equation of a line that is perpendicular to 2y=14+(2/3) x and passes through the point (-2,8).

anzhelika [568]

Answer:

y = -3x +2

Step-by-step explanation:

If you divide the equation for the given line by 2, it will be in slope-intercept form:

y = (1/3)x +7

This tells you its slope is 1/3. The slope of the perpendicular line is the negative reciprocal of this: -1/(1/3) = -3. The point-slope form of the equation for the perpendicular line can be written as ...

y = m(x -h) +k . . . . . line with slope m through point (h, k)

Your line is ...

y = -3(x -(-2)) +8

y = -3x +2

6 0

3 years ago

The length of a rectangle is 5 centimeters less than twice it’s width. The perimeter of the rectangle is 80 cm. What are the dim

algol [13]

<h3><u>The length is equal to 25.</u></h3><h3><u>The width is equal to 15.</u></h3>

l = 2w - 5

2l + 2w = 80

We have a value for l, so we can plug it into the second equation to solve for w.

2(2w - 5) + 2w = 80

Distributive property.

4w - 10 + 2w = 80

Combine like terms.

6w - 10 = 80

Add 10 to both sides.

6w = 90

Divide both sides by 6.

w = 15

Now that we have a value for w, we can plug it into the original equation to solve for l.

l = 2(15) - 5

l = 30 - 5

l = 25

3 0

3 years ago

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti

melomori [17]

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that $m = 100, \mu = \frac{1}{100} = 0.01$

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

$P(X > x) = e^{-\mu x}$

This is P(X > 190). So

$P(X > 190) = e^{-0.01*190} = 0.1496$

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

$P(X > x) = 0.08$

So

$e^{-0.01x} = 0.08$

$\ln{e^{-0.01x}} = \ln{0.08}$

$-0.01x = \ln{0.08}$

$x = -\frac{\ln{0.08}}{0.01}$

$x = 252.6$

Capacity of 252.6 cubic feet per second

5 0

3 years ago

A pair of pants with a marked price of $35.00 has a discount of 20%. How much is the discount? Can someone help me learn to do p

andreyandreev [35.5K]

When you see a "%" you need to ask " a percent of what"?

Here, it's a percent of the original prize, so the discount is 20% of the original prize, that is 20% of 35.

20% is also 20/100 or 1/5, so we can calculate this like this:

$\frac{1}{5} *35=7$

so the discount is 7 dollars.

6 0

3 years ago