Solve for x ax+ b= r

What is the image point of (-1,1) after a translation left 2 units and down 2 units?

AveGali [126]

Answer:

The new point is (-3,-1)

Step-by-step explanation:

yessir

3 0

3 years ago

NO LINKS OR FILES!

Archy [21]

(a) If the particle's position (measured with some unit) at time t is given by s(t), where

$s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}$

then the velocity at time t, v(t), is given by the derivative of s(t),

$v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}$

(b) The velocity after 3 seconds is

$v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}$

(c) The particle is at rest when its velocity is zero:

$\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}$

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

$\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|$

In interval notation, this happens for t in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt$

By definition of absolute value, we have

$|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)$

In part (d), we've shown that v(t) > 0 when -√11 < t < √11, so we split up the integral at t = √11 as

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt$

and by the fundamental theorem of calculus, since we know v(t) is the derivative of s(t), this reduces to

$s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}$

7 0

2 years ago

Kristin has 3 2/3 yards of plaid ribbon. She has 2 5/6 yards of polka - dot ribbon. Estimate how many yards of ribbon Kristin ha

AveGali [126]

Answer:

Step-by-step explanation:

Kristin has 3 2/3 yards of plaid ribbon. Converting 3 2/3 yards to improper fraction, it becomes 11/3 yards of plaid ribbon.

She has 2 5/6 yards of polka - dot ribbon. Converting 2 5/6 yards to improper fraction, it becomes 17/6 yards of polka - dot ribbon.

The total number of yards of ribbon that Kristin has would be

11/3 + 17/6 = (22 + 17)/6 = 39/6 yards of ribbon.

Converting to decimal, it becomes 6.5 yards of ribbon. Approximating 6.5 to the nearest yards, it becomes 7 yards. This is because the first digit after the decimal point is 5 and thus, can be rounded up

6 0

3 years ago

A linear function is parallel to the line y= 4x + 8 and also goes through the point (2,15).What is the linear equation for this

horrorfan [7]

When written in the $y=mx+q$ form, the slope of a line is given by the coefficient $m$ . Moreover, two lines are parallel if the have the same slope.

Now, the slope of the known line is 4, so our line's slope will be four as well.

In general, when you know the slope $m$ of a line and one of its points $(x_0,y_0)$ , the equation of the line can be derived from the following formula:

$y-y_0 = m(x-x_0)$

Which in your case becomes

$y-15 = 4(x-2)$

Expand the right hand side and solve for y:

$y = 4x+7$

3 0

3 years ago

Cheryl is moving to a new house. Her old house is 3 kilometers and 457meters from her new house. How many meters is her old hous

MrRissso [65]

Answer:

Her old house is 3000m+457m = 3457m from her new house.

Step-by-step explanation:

Conversion of units problems can always be modeled as a rule of three problem.

Rule of three problem:

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In the case of a conversion of units problem, the measures are:

- the value in one unit

- the value in another unit

As the value of the first unit increases, so will the value of the second unit. It means that in a conversion of units problem, we will always have a direct rule of three.

The problem states that Cheryl's new house is 3 kilometers and 457meters from her old house. The problem wants to know this distance purely in meters, so we have to convert 3km to meters. 1km = 1000m, so:

1km - 1000m

3km - xm

x = 1000*3

x = 3000m

Her old house is 3000m+457m = 3457m from her new house.

5 0

3 years ago

Solve for x ax+ b= r​

Solve for x ax+ b= r