PLEASE I NEED SO MUCH HELP HERE!!!!!!

Answer:

a) The bullet hits the ground after 64 seconds.

b) The bullet hits the ground 113,511.7 feet away.

c) The maximum height attained by the bullet is of 16,384 feet.

Step-by-step explanation:

Equations of motion:

The equations of motion for the bullet are:

[tex]x(t) = (v_0\cos{\alpha})t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]

In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.

Initial speed of 2048 ft/s at an angle of 30o to the horizontal.

This means that [tex]v_0 = 2048, \alpha = 30[/tex].

So

[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]

(a) After how many seconds will the bullet hit the ground?

It hits the ground when [tex]y(t) = 0[/tex]. So

[tex]1024t - 16t^2 = 0[/tex]

[tex]16t^2 - 1024t = 0[/tex]

[tex]16t(t - 64) = 0[/tex]

16t = 0 -> t = 0 or t - 64 = 0 -> t = 64

The bullet hits the ground after 64 seconds.

(b) How far from the gun will the bullet hit the ground?

This is the horizontal distance, that is, the x value, x(64).

[tex]x(64) = 1773.62(64) = 113511.7[/tex]

The bullet hits the ground 113,511.7 feet away.

(c) What is the maximum height attained by the bullet?

This is the value of y when it's derivative is 0.

We have that:

[tex]y^{\prime}(t) = 1024 - 32t[/tex]

[tex]1024 - 32t = 0[/tex]

[tex]32t = 1024[/tex]

[tex]t = \frac{1024}{32} = 32[/tex]

At this instant, the height is:

[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]

The maximum height attained by the bullet is of 16,384 feet.

Answer:

7

Step-by-step explanation:

Substitute 2 for x.

[tex] {2}^{2} + 3 = 7[/tex]

Answer:

1. centimeter

2. kilogram

3. gram

4. milligram

5. centimeter

6. meter

7. kilometer

8. liter

9. kiloliter

10. millimeter

Step-by-step explanation:

you really cannot answer that yourself ?

you don't understand yet the difference between length or distance, area, volume, weight, ... ?

I how this helps then

1. is length, and it is rather short. so, we use a rather small unit to express it.

2. is weight. and a big one. so, we use a bigger unit.

3. is weight. but a small one.

4. is weight. and a really tiny one.

5. is length. similar dimension of size as the finger.

6. is length. and a bigger one.

7. is length. and a truly big one.

8. is volume. liquid volume at that. but rather small.

9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...

10. is length. and a very tiny one.

Hello!

3a = 7b =>

=> 3 × a = 7 × b =>

=> a/b = 7/3

Good luck! :)

Step-by-step explanation:

The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)

9514 1404 393

Answer:

  (a) max: None; min: -5

  (b) max: 5; min: None

Step-by-step explanation:

a) The upward pointing arrow on the end of the graphed curve tells you that the graph extends upward indefinitely. There is no absolute maximum value.

The solid dot at (-4, -5) is the lowest point on the graph. That tells you the absolute minimum is -5.

__

b) The solid dot at (-4, 5) is the highest point on the graph. That tells you the absolute maximum is 5.

The open dot at (3, -5) is the lowest point on the graph. This means values of the function can be arbitrarily close to -5, but -5 is not one of them. There is no absolute minimum value.

Answer:

40 years old.

Step-by-step explanation:

We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.

[tex]x+5=y[/tex]

We also know that the sum of their ages is 85.

[tex]x+y=85[/tex]

We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:

[tex]x+(x+5)=85[/tex]

We can combine like terms to get

[tex]2x+5=85[/tex]

Subtracting 5 from both sides results in

[tex]2x=80[/tex]

After that, we can divide both sides by 2 to get

[tex]x=40[/tex]

Thus, Elga is 40 years old.

Answer:

e = 40

a=45

Step-by-step explanation:

a + e = 85

a = e+5

e + 5 + e = 85

2e = 80

e = 40

a=45

Answer:

8:35

Step-by-step explanation:

Answer:

8:35

Step-by-step explanation:

-25+60=35

9h-1h(60 above)=8h

=8:35

9514 1404 393

Answer:

  372 m²

Step-by-step explanation:

A vertical line down the center of the figure will divide it into two congruent trapezoids, each with bases 13 and 18, and height 12.

The area of one of them is ...

  A = 1/2(b1 +b2)h

So, the area of the two of them together is ...

  A = (2)(1/2)(b1 +b2)h = (b1 +b2)h

  A = (13 m + 18 m)(12 m) = 372 m²

Answer:

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

Step-by-step explanation:

Given the data :

35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

The next to highest frequency group has a frequency of 4 and the highest frequency of 6

Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16

Answer:

Answer is 3bu2(DeEZ)=1

Step-by-step explanation:

Step-by-step explanation:

ii hope this will help you

please mark me as brinalist friend

Answer:

x = 1

x = -2

Step-by-step explanation:

Hello!

We can solve the quadratic by factoring the equation.

Standard Form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

Given our equation: [tex]x^2 + x - 2 = 0[/tex]

Find two numbers that multiply up to "ac" but add up to "b". The two numbers are 2 and -1. Expand x into 2x and -1x.

Set each factor to 0 and solve for x:

The solutions for x are 1 and -2.

Answer:

determine the number of miles the car drives in a year.

divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.

Step-by-step explanation:

Answer:

P>-6/5

Step-by-step explanation:

2(P+1)+3(P+2)>2

Use the distributive property to multiply 2 by P+1

2P+2+3(P+2)>2

Use the distributive property to multiply 3 by P+2

2P+2+3P+6>2

Combine 2P and 3P to get 5P

5P+2+6>2

Add 2 and 6 to get 8

5P+8>2

Subtract 8 from both sides

5P>2−8

Subtract 8 from 2 to get −6.

5P>−6

Divide both sides by 5. Since 5 is positive

P>−6/5

​  

Answer:

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

Given:

The domain of function that is translated down 3 is (0, 4), (-5, 8), (4, -2).

To find:

The range of the function.

Solution:

If a function is translated 3 units down, then

[tex](x,y)\to (x,y-3)[/tex]

Using this rule, we get

[tex](0,4)\to (0,4-3)[/tex]

[tex](0,4)\to (0,1)[/tex]

Similarly,

[tex](-5,8)\to (-5,5)[/tex]

[tex](4,-2)\to (4,-5)[/tex]

The range of the given function is (0, 1), (-5, 5), (4, -5).

Therefore, the correct option is A.

Answer:

is that the full question?

Answer:

Solution:-

Given,

ab =perpendicular (p)= 6cm

ac =hypotenuse (h)= 12cm

cd =base (b)= ?

using , Pythagoras theorem we have ,

b²=√h²-p²

or,cd²=√ac²-ab²

= √12²-6²

= √144-36

=√108

=√10.8²

=10.8cm

the length of cd is 10.8 cm

hope it is helpful to you

Answer:

1/2

Step-by-step explanation:

Convert 2/3 to 4/6

Subtract: 4/6 - 1/6

You get 3/6

Simplify: 1/2

Hope this helps!

Answer: The answer is 1/2

Answer:

C.

Step-by-step explanation:

The function shifted left five units instead of right five units.

There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.

Answer:

42÷2

Step-by-step explanation:

Answer: The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.

Step-by-step explanation:

Order the dataset from least to greatest:

-38 → -13 → -9 → -2 → 14 → 28

Then find the values that lies in the middle:

-38 → -13 → -9 → -2 → 14 → 28

Since there are 2 values, find the average of those 2 values:

[tex]\frac{-9+(-2)}{2} =\frac{-11}{2} =-5.5[/tex]

The median value = -5.5.

The median value of data set B is -5.5, which is less than the median value of  3.1 in dataset A.

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Answer:

WHAT IS THE FACTOR?

Step-by-step explanation:

Answer:

x = 2.7

Step-by-step explanation:

The given equation is :

[tex](3x)^2-10=56[/tex]

We need to solve it for x.

It can be rewrite as follows:

[tex]9x^2-10=56[/tex]

Adding 10 to both sides,

[tex]9x^2-10+10=56+10\\\\9x^2=66\\\\x=\sqrt{\dfrac{66}{9}}\\\\x=2.70[/tex]

So, the value of x is equal to 2.7.

Answer:

D. √2 : 1

Step-by-step explanation:

The hypotenuse = 4√2 (longest side of a right triangle)

The given side = 4

Ratio of the hypotenuse to the given side = 4√2 : 4

Simplify by dividing both numbers by 4

√2 : 1

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Answer:

16X+134

Step-by-step explanation:

Step-by-step explanation:

As total number of pages in each album is 42 pages, so

➝ Total number of pages in 10 albums = (42 × 10) pages

➝ Total number of pages in 10 albums = 420 pages

Now, as the number of stamps fit on 1 page is 40 stamps, so

➝ Stamps fit on 420 pages = (420 × 40) stamps

➝ Stamps fit on 420 pages = 16,800 stamps

Therefore, 16,800 stamps are in the total collection.