If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds is given by the parametric equations x=(v0cos(α))t andy=(v0sin(α))t−16t2
(where x and y are measured in feet).
Suppose a gun fires a bullet into the air with an Initial speed of 2048 ft/s at an angle of 30 o to the horizontal.
(a) After how many seconds will the bullet hit the ground?
(b) How far from the gun will the bullet hit the ground? (Round your answer to one decimal place.)
(c) What is the maximum height attained by the bullet? (Round your answer to one decimal place.)

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Step-by-step explanation:

the down function clearly is

y = x - 5, -2 <= x <= 8

the reasons :

1. it is linear. so, we have only a form of ax+b

2. x=0 => y=-5

x=5 => y=0

so, with these 2 points alone we can see

y = ax + b

-5 = a×0 +b = b

0 = a×5 - 5

5 = a×5

1 = a

the inverse function is based on

y = x - 5

=>

x = y + 5

now renaming the variables so that y is the result and x the input variable delivers

y = x + 5

and because the original function only delivered y- values between -7 and +3, this is also the defined domain for the inverse function.

so,

y = x + 5, -7 <= x <= +3

so, we have the points

x=-7 => y=-2

x=+3 => y=8

you need to draw the line between these 2 points with filled dots at the end points (as they are included in the function).

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]

but this clearly does not match the joint density.

Answer:

B

substract the variables

Answer:

60 ft

Step-by-step explanation:

The answer has to be in feet units

Now that we know the height is 5 cm equivalent to 150 feet, what is the width of the building in feet units

5 cm = 150 ft

Rule: multiply cm by 30 to get the ft

2 cm = ?

2 cm × 30 = 60 ft

2 cm = 60 ft

Answer:

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

45 - + 14 is 45 - 14 is 33

Answer:

ok so its is 5 dollars for a pencil and 420 dollars for a pen(dang)

a40+2100=2140

now

b6 pencil 462 pen

60+3696=3756

Hope This Helps!!!

(a) Afua paid ¢44,500.00 for 8 pencils and 5 pens.

(b) Afua will pay ¢71,400.00 for 10 pencils and 8 pens after the price increase.

(a) To find how much Afua paid altogether for 8 pencils and 5 pens, we need to calculate the total cost for each item and then add them together.

Given:

Cost of a pencil, [tex]Pencil_{cost}[/tex] = ¢500.00

Cost of a pen, [tex]Pen_{cost}[/tex] = ¢42,000.00

Number of pencils bought, [tex]n_{pencils}[/tex] = 8

Number of pens bought, [tex]n_{pens}[/tex] = 5

Total cost of pencils,

[tex]Total_{pencil}_{cost} = Pencil_{cost} * n_{pencils}[/tex]

                      = ¢500.00 × 8

                      = ¢4,000.00

Total cost of pens,

[tex]Total_{pen}_{cost} = Pen_{cost} * n_{pens}[/tex]

                   = ¢42,000.00 × 5

                   = ¢210,000.00

Altogether, [tex]Total_{cost} = Total_{pencil}_{cost} + Total_{pen}_{cost}[/tex]                                      

                                  = ¢4,000.00 + ¢210,000.00

                                  = ¢214,000.00.

Therefore, Afua paid ¢214,000.00 for 8 pencils and 5 pens.

(b) Now, let's calculate the new total cost after the price increase.

The price of a pencil increased by 20%, which means the new pencil cost is:

[tex]New_{pencil}_{cost}[/tex] = [tex]Pencil_{cost}[/tex]+ (20% × [tex]Pencil_{cost}[/tex])

                                  = ¢500.00 + (0.20 × ¢500.00)

                                  = ¢500.00 + ¢100.00

                                  = ¢600.00

Similarly, the price of a pen increased by 10%, which means the new pen cost is:

[tex]New_{pen}_{cost}[/tex] = [tex]Pen_{cost}[/tex] + (10% × [tex]Pen_{cost}[/tex])

                          = ¢42,000.00 + (0.10 × ¢42,000.00)

                          = ¢42,000.00 + ¢4,200.00

                          = ¢46,200.00

Now, we can find the total cost for 10 pencils and 8 pens with the increased prices:

Number of pencils to be bought, [tex]n_{pencils}_{new}[/tex] = 10

Number of pens to be bought, [tex]n_{pens}_{new}[/tex] = 8

Total cost of pencils with new prices,

[tex]Total_{pencil}_{cost}_{new}[/tex] =[tex]New_{pencil}_{cost}[/tex] × [tex]n_{pencils}_{new}[/tex]

                                        = ¢600.00 × 10

                                        = ¢6,000.00

Total cost of pens with new prices,

[tex]Total_{pen}_{cost}_{new}[/tex] = [tex]New_{pen}_{cost}[/tex] × [tex]n_{pens}_{new}[/tex]

                                    = ¢46,200.00 × 8

                                    = ¢369,600.00

Altogether, [tex]New_{total}_{cost}[/tex] = [tex]Total_{pencil}_{cost}_{new}[/tex] + [tex]Total_{pen}_{cost}_{new}[/tex]

                                               = ¢6,000.00 + ¢369,600.00

                                               = ¢375,600.00

Therefore, Afua will pay ¢375,600.00 for 10 pencils and 8 pens with the increased prices.

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Answer:

She had 8 doubles.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of singles.

y is the number of doubles

z is the number of triples.

46 hits

This means that [tex]x + y + z = 46[/tex]

46 hits totaled 66 bases

This means that:

[tex]x + 2y + 3z = 66[/tex]

4 times as many singles as doubles

This means that [tex]x = 4y[/tex]

So

[tex]x + 2y + 3z = 66[/tex]

[tex]4y + 2y + 3z = 66[/tex]

[tex]6y + 3z = 66[/tex]

And

[tex]x + y + z = 46[/tex]

[tex]4y + y + z = 46[/tex]

[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]

Then

[tex]6y + 3z = 66[/tex]

[tex]6y + 3(46 - 5y) = 66[/tex]

[tex]6y + 138 - 15y = 66[/tex]

[tex]9y = 72[/tex]

[tex]y = \frac{72}{9}[/tex]

[tex]y = 8[/tex]

She had 8 doubles.

Answer:

1. x + 4 = 9

Hint: the word 'sum' generally refers to addition.

2. 10a = 70

3. [tex]\frac{3}{4} t[/tex] = 15

4. [tex]\frac{1}{4} x[/tex] - 4 = 4

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

95°=6r°+47(being vertically opposite angle)

or,48°=6r

or,48=/6=r°

or,r=8°

Answer:

8

Step-by-step explanation:

By taking the number "3" and plus together with the number 5

Answer:

455 ways

Step-by-step explanation:

Given

[tex]n = 15[/tex] --- friends

[tex]r = 3[/tex] -- available postcard kinds

Required

Ways of sending the cards

The question is an illustration of combination and the formula is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{15}C_3 = \frac{15!}{(15 - 3)!3!}[/tex]

[tex]^{15}C_3 = \frac{15!}{12!*3!}[/tex]

Expand

[tex]^{15}C_3 = \frac{15*14*13*12!}{12!*3*2*1}[/tex]

[tex]^{15}C_3 = \frac{15*14*13}{3*2*1}[/tex]

[tex]^{15}C_3 = \frac{2730}{6}[/tex]

[tex]^{15}C_3 = 455[/tex]

Answer:

ii

Step-by-step explanation:

you have to look and read it it comes simple

Answer:

2nd choice

Step-by-step explanation:

Answer:

27

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = -3

y = 3

y - 8x

Step 2: Evaluate

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{y - 8x}\\\\\large\textsf{= 3 - 8(-3)}\\\\\large\textsf{8(-3) = \bf -24}\\\\\large\textsf{= 3 - \bf 24}\\\\\large\textsf{= \bf 27}\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf 27}}}}\huge\checkmark\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

yes

Step-by-step explanation:

She aims at the center of the target. If she is off by 1.5 in. or less, she hits the target. We need to find what distance from the bull's eye an angle of 0.2° will make at 150 ft distance.

tan A = opp/adj

tan 0.2° = opp/150

opp = 150 * tan 0.2°

opp = 0.52 in.

Since 0.52 in. < 1.5 in. she will hit the target.

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Answer:

all real numbers

Algebra Examples

The domain of the expression is all real numbers except where the expression is undefined

Hello!

The domain of an exponential function is the crowd of all real numbers, so: x ∈ ℝ.

Good luck! :)

Answer:

"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Step-by-step explanation:

Let be the following system of linear equations:

[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)

[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)

[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)

1) We eliminate [tex]y[/tex] by adding (1) and (2):

[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]

[tex]6\cdot x +2\cdot z = 24[/tex] (4)

2) We eliminate [tex]y[/tex] by adding (1) and (3):

[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]

[tex]9\cdot x -4\cdot z = 36[/tex] (5)

Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Answer:

B.

Step-by-step explanation:

there is not much to explain.

a strong correlation means there is a direct connection.

so, a change in a causes immediately a change in b.

and positive means that the changes go in the same sign direction. increase => increase. decrease => decrease.

Answer:

2b-7

Step-by-step explanation:

Given that,

Bernie's hamster completed the maze in b seconds.

Annic's hamster completed the maze 7 seconds less than twice the time it took Bernie's hamster to complete the maze.

Twice the time it took Bernie's hamster to complete the maze is 2b.

7 seconds less than twice the time it took Bernie's hamster = 2b-7

So, the correct option is (b) "2b-7".

Answer:

(x - 3)^2 + (x + 2)^2 = 4

Step-by-step explanation:

Equation of circle:

(x - h)^2 + (x - k)^2 = r^2

(h, k) = (3, -2)

r = 2

(x - 3)^2 + (x - (-2))^2 = 2^2

(x - 3)^2 + (x + 2)^2 = 4

Answer:

c

Step-by-step explanation:

when we take the 5 inside the root the 5 vil be 5^2 times 2 which is equal to 50

2 kg dough = 1 hour

1 kg dough = 1 hour/2 = 1/2 hour

6 kg dough = 6 × (1/2 hour) = 6/2 hours = 3 hours

Answer: 3 hours

Step-by-step explanation: x represents the number of hours she works

2x=6

x=6/2

x=3

Answer:

Step-by-step explanation:

The formula for arc length is

[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where theta is the measure of the central angle and r is the radius. We have both of those pieces of info; filling in:

[tex]AL=\frac{30}{360}*2(3.14) (4)[/tex] and simplifying a bit:

[tex]AL=\frac{1}{12}(8)(3.14)[/tex] and a bit more:

[tex]AL=\frac{25.12}{12}[/tex] and finally, to

AL = 2.09 m

9514 1404 393

Answer:

  (t, u, w) = (1, -2, -2)

Step-by-step explanation:

A graphing calculator makes short work of this, giving the solution as ...

  (t, u, w) = (1, -2, -2)

__

There are many ways to solve this "by hand." Here's one of them.

Add the first and third equations. Their sum is ...

  -3t +4w = -11 . . . . . [eq4]

Add this to twice the second equation. That sum is ...

  (-3t +4w) +2(-4t -2w) = (-11) +2(0)

  -11t = -11

  t = 1

Substituting this into the second equation gives ...

  -4(1) -2w = 0

  w +2 = 0 . . . . divide by -2

  w = -2 . . . . add -2

Substituting for t in the third equation lets us find u.

  2(1) -2u = 6

  -1 +u = -3 . . . . . divide by -2

  u = -2 . . . . add 1

The solution is (t, u, w) = (1, -2, -2).

Answer:

42 degrees

Step-by-step explanation:

We already have the two angles for the triangle, we just need the third. For triangles, the can only add up to 180 degrees. 101+37=138 degrees, now we subtract 138 from 180.

180-138=42.

Step-by-step explanation:

678-72=606/2=303+72=375