Write in point slope form the equation for the line that goes through the point (-1,-6) and has a slope of 16

If v(t) and h(t) denote the ball's velocity and height at time t, respectively, then we have h(0) = 1.2 m and v(0) = 58 m/s.

The ball is in free fall after being tossed, so its acceleration is constant at any time t :

[tex]a(t) = -9.8 \dfrac{\rm m}{\mathrm s^2}[/tex]

By the fundamental theorem of calculus, the velocity function is given by

[tex]\displaystyle v(t) = v(0) + \int_0^t a(u) \, du[/tex]

Compute the integral:

[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) \int_0^t du[/tex]

[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t - 0)[/tex]

[tex]\displaystyle \boxed{v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t}[/tex]

Similarly, the height function is given by

[tex]\displaystyle h(t) = h(0) + \int_0^t v(u) \, du[/tex]

[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \int_0^t \left(58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t\right) \, du[/tex]

[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) (t - 0) - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t^2 - 0^2)[/tex]

[tex]\displaystyle \boxed{h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) t - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t^2}[/tex]

Answer:

V(t) = 58-9.8t

h(t)=1.2+58t-4.9[tex]t^{2}[/tex]

Step-by-step explanation:

Using the standard formula

a=V f-Vi/t --rearrange

at=V f-Vi

V f=V i + a t

therefore

V(t)=58-9.8t

same with height

H= Hi+Vit+1/2at^2

therefore

h(t)=1.2+58t-4.9t^2

Answer:

D Option is the correct one.

Step-by-step explanation:

As,

Distance covered = 40km = 40000m(1k=1000m)

time = 10:15-9:00 = 1:15hours = 75mins

We need to find the rates of the bicyclist in one hour so, for this first we need to calculate the total distance which covered in one hour.

For calculating distance for one hour,

40000/75 = 533.33m/min (means they covered 533.33m distance in one min)

for one hour:

533.33*60= 32000m = 32km

They covered 32km distance in one hour.

Now from the given options D is the correct one because according to give condition north bicyclist covered 4km more that south one. And other reason is we also need to check the sum of distance covered by the both cyclist which must be equal to 32km.

So for A,

Sum = 19 + 15 =34 (wrong not equal to 32)

For B,

Sum = 18 + 13 = 31 (wrong)

For C,

Sum = 16 + 10 = 26(wrong)

For D,

Sum = 18 + 14 = 32 (Right)

And second distance b/w both distance is 4km.

18-14 = 4(Right)

So, D option is the right one.

I hope it will help you.

Answer:

bar chart..

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

Answer:

Step-by-step explanation:

the bottom left is the answer. I hope this helps.

Answer:

Each journal costs $2.48

Step-by-step explanation:

Let X be the cost of a single journal.

You can write this equation to represent the problem:

26x = 64.48

(26 times the cost of the journal is $64.48)

Then just solve for x by dividing both sides by 26:

[tex]26x=64.48\\\frac{26x}{26} =\frac{64.48}{26}\\x=2.48[/tex]

Each journal costs $2.48

should I call 911 !!!!!!!!!!!!!!

Answer:

Here you go

Step-by-step explanation:

it's all in the screenshot

Answer:

145°

Step-by-step explanation:

[Finding the non-label angled in the triangle] 180° - 75° = 105°

Finding 3: (x = angle 3)

[Sum of a triangle's angles] 105° + 40° + x (angle 3) = 180

[combine like terms] 145° + x = 180°

[subtracting 145 from both sides] 35° = x

    () We can test that this is correct by adding 40 and 35 together, to get angle 1 as it is an exterior angle

Finding 4: (x = angle 4)

180 - 35 = 145°

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

  0 solutions

Step-by-step explanation:

The two equations describe parallel lines, so will have no point of intersection. There are no solutions to this system of equations.

__

The equations can be put into slope-intercept form by eliminating the parentheses.

  6(x +2) = y   ⇒   y = 6x +12

  y = 3(2x +3)   ⇒   y = 6x +9

These have the same slope (6), but different y-intercepts (9 and 12). They are parallel lines.

Answer:

2/3

Step-by-step explanation:

     [] Since is the line is going up from bottom-left to top-right, we know it will be positive

     [] Because this graph has distinctive coordinate-points, we can use rise over run

     () The other method is to use the change in y divided by the change in x

We start at (-2, 0), then count 2 up and 3 over to get to (2, 1) which gives us a slope of 2/3

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

slope= [tex]\frac{2}{3}[/tex] or 0.6

y-intercept= -1

y= 0.6x+ -1

Step-by-step explanation:

slope= [tex]\frac{rise}{run}[/tex]

the y-intercept is where the line crosses the y axis

the equation for a line is y=mx+b where m is slope and  b is y

Answer:

Slope: 1.5

Y-intercept: (0,-1)

Equation of the line: y=1.5x-1

Step-by-step explanation:

Slope=

change of y/change of x=

3/2 (or 1.5)

Equation of the line:

y=1.5x+b

-1=1.5(0)+b

-1=b

y=1.5x-1

Answer:

∑[ (250)2 (400)2 (250)2 (350)^2 (100)2 (50)2] = 420,000.

Step-by-step explanation:

You first calculate the mean which is  is 2150.

You then subtract 2150 from the 6 values in turn

The first one = 2400 - 2150 = 250.

Then you square each of the 6 results and add them up - this comes to 420,000.

Taking into account the definition of corresponding angles and Corresponding Angles Theorem, if the corresponding angles are congruent, then two lines cut it by a transversal are parallel.

First of all, remember that a transverse line is a line that crosses or passes through two other lines. Sometimes the other two lines are parallel and the transversal passes through both lines at the same angle. However, the other two lines do not have to be parallel for a transversal to cross them.

Corresponding angles are angles formed when a transverse line crosses two straight lines. These angles are formed at equivalent corners or at corners corresponding to the transversal when two lines are intersected by a third line.

In other words, if a transversal line intersects two parallel lines, the corresponding angles are those that are on the same side of the parallels and on the same side of the transversal.

The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then the corresponding pairs of angles are congruent.

Remember that if two angles are congruent, then they have the same measure.

The opposite of this theorem is also true:  If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

In summary, if the corresponding angles are congruent, then two lines cut it by a transversal are parallel.

Learn more about corresponding angles theorem:

Using the concept of probability, the probability of rolling 2 sixes would be 1/25

From the tree diagram given :

The probability of rolling 2 sixes can be defined thus :

Hence,

P(2 6's) = 1/5 × 1/5 = 1/25

Hence, the probability of rolling 2 sixes is 1/25.

Learn more : https://brainly.com/question/14522818

Answer:

-2r = 2 - Subtract 11 from both sides

r = -1

Answer:

2

Step-by-step explanation:

x + 2y = 14

2y = -x + 14

y = -1/2 x + 7

m = -1/2

product of slopes is -1

so perpendicular slope is 2

Answer:

15 - 5 = 10 wow that was so hard

Answer:

the awnser is 10

Step-by-step explanation:

x=15 so

15-5=10

Answer:

He spent 3/4 of an hour reading stories

Step-by-step explanation:

Sorry I dont have time :(

Answer:

16

Step-by-step explanation:

(Trust me)

Answer:

20

Step-by-step explanation:

uvuctxtxyvuvigh ufydigifyds6dgbjj

Answer:

f(x + 2)

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the left of a units

Here f(x) is translated 2 units to the left , then f(x + 2)

Answer:

c

Step-by-step explanation:

it makes the most sense

Answer:

I can only answer ii.

A=Lxwxh

=6mx3mx4m

=18mx4m

A=40msquared .

A=Lxwxh

40msquared = 6mx3mxh

40msquared =18msquaredxh

40/18msquared=18xh/18msquared

131/3=h.

that's what I thought

Step-by-step explanation:

I think I should first find the area

of the figure.then I will use the area to find the height.

Answer:

An inverse of a fraction is a reciprocal of a fraction. In other words, flipping the numerator and denominator provides the reciprocal of fraction. For example, the reciprocal of fraction 3/5 is 5/3.

Step-by-step explanation:

12 ≡ 7 + 5 ≡ 5 (mod 7)

so

12 + 12 + 12 + 12 ≡ 4•12 ≡ 4•5 ≡ 20 ≡ 14 + 6 ≡ 6 (mod 7)