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Wittaler [7]
3 years ago
9

Complete the equation of the line whose yyy-intercept is (0,-1)(0,−1)left parenthesis, 0, comma, minus, 1, right parenthesis and

slope is 4.
y=
Mathematics
1 answer:
ioda3 years ago
7 0

Answer:

y=4x-1

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

m=4

b=-1

Substitute

y=4x-1

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Find the volume of the prism
Gnom [1K]

The volume of a prism is given by its base area multiplied by its height.

The bases are two right triangles. If we project everything on the xy plane, we can see that the vertices of the base triangle is

A = (0,0),\quad B = (3,0),\quad C = (0,4)

So, leg AB is 3 units long, and leg AC is 4 units long. This means that the area of the triangle is

A = \dfrac{\overline{AB}\times\overline{AC}}{2} = \dfrac{3\times 4}{2} = 6

The height of the prism connects, for example, points (0,0,0) and (0,0,5), so it's 5 units long. So, the volume of the prism is

V = A \times h = 6 \times 5 = 30

4 0
3 years ago
How to take derivative of absolute value.
zhenek [66]

The absolute value function is defined as

|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}

If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.

If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.

But if x = 0, the derivative doesn't exist!

In order for the derivative of a function f(x) to exist at x = c, the limit

\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}

must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.

If x approaches 0 from below (so x < 0), we have

\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1

whereas if x approaches 0 from above (so x > 0), we have

\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1

But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.

Putting everything together, you can define the derivative of |x| as

\dfrac{d|x|}{dx} =  \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1  & \text{for }x < 0 \end{cases}

6 0
3 years ago
A motarcar is running at the rate of 66 km per hour. Each other its wheels makes 500 revolutios per minute. find the radius of t
wolverine [178]

Answer:

simple

Step-by-step explanation:

The radius of the wheel can be solved from its given speed and RPM.

Converting km/h to m/min

speed = 66 km / h = 66000 m / 60 min

speed = 1100 m / min

Converting one revolution to meters

1100 m / min = 500 revolution / min ... (given)

500 revolutions = 1100 m

1 revolution = 2.2 m

Solving for the radius of the wheels in meters

1 revolution = 2.2 m

2 * pi * radius = 2.2 m

radius = 2.2 m / 2 * pi

radius = 1.1 m / pi

radius = 0.3501 m

3 0
3 years ago
Ben earns $750 a month plus 4% commission on all his sales over $900. Find the minimum sales that will allow Ben to earn at leas
e-lub [12.9K]
$750 + s x 4% = $2,500 | - $750

s x 4% = $1,750 | : 4%

s = $43.750
4 0
3 years ago
La temperatura a una distancia r del centro de una lámina está dada por T=40 (r2?2r) . La variación instantánea de la temperatur
PilotLPTM [1.2K]

For this, the first thing to do is to assume that the function of temperature with respect to r is written in one of the following ways:

Way 1:

T = 40 (r ^ 2 + 2r)

Way 2:

T = 40 (r ^ 2-2r)

To find the instant variation we must find the derivative of the temperature with respect to the distance r.

We have then:

For function 1:

\frac {dT} {dr} = 40 \frac {d ((r ^ 2 + 2r))} {dr}\\

\frac {dT} {dr} = 40 (2r + 2)

Rewriting

\frac {dT} {dr} = 80r + 80

For function 2:

\frac {dT} {dr} = 40 \frac {d ((r ^ 2-2r))} {dr}

\frac {dT} {dr} = 40 (2r-2)

Rewriting

\frac {dT} {dr} = 80r-80

Answer:

The instantaneous variation of the temperature with respect to r is given by:

Assuming function 1:

\frac {dT} {dr} = 80r + 80

Assuming Function 2:

\frac {dT} {dr} = 80r-80

6 0
3 years ago
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