f(x) = x². What is g(x)?

A. g(x) = -x² – 3
B. g(x) = -3x²
C. g(x) = x² - 3
D. g(x) = -x²​

The maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

For this case, the height of the bullet from the ground is modeled by the equation:

[tex]h(t) = -16t^2 + 200t + 3[/tex]

where height is in meters and time is in seconds. And t is the time in seconds passed from the point of time when the bullet was fired.

Finding its first and second rate with respect to the variable 't', we get:

[tex]\dfrac{d(h(t))}{dt} = h'(t) = -32t + 200\\\\\dfrac{d^2(h(t))}{dt^2} = h''(t) = -32 < 0[/tex]

Thus, the second rate is negative no matter what the value of 't' is. So all the critical points would be corresponding to maxima.

Now, finding the critical points by equating the first rate = 0, we get:

[tex]h'(t) = 0\\\\-32t + 200 = 0\\\\t = \dfrac{200}{32} = 6.25 \: \rm sec.[/tex]

Due to only one critical point, and that each critical point is maxima, we have the value of h(t) globally maximum when t = 6.25

Putting t = 6.25 in the function h(t), we get the maximum height achieved by the bullet as:

[tex]h(t) = -16t^2 + 200t + 3\\h(6.5) = -16(6.5)^2 + 200(6.5) + 3 = 627 \: \rm ft[/tex]

When the bullet will fall on the ground, the value of h(t) would be 0.

Putting h(t) = 0, and finding the values of 't' for which this is true, we get:

[tex]h(t) = -16t^2 + 200t + 3\\0 = -16t^2 + 200t + 3\\\\16t^2 -200t -3 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(-3)}}{2(16)}\\\\t \approx \dfrac{200 \pm 200.479}{32}\\\\t \approx -0.0149 \: \rm sec., t \approx 12.51 \: sec.[/tex]

Bullet will fall only after it is shot, so time taken for the bullet to fall compared to the time when its shot would be greater, so time passed (t here) would be positive.

Thus, at approx t = 12.51 sec, the bullet will fall on the ground.

At  t = 0, bullet was at 3 ft, and therefore, whenever bullet will reach 400 ft, the time t would be > 0.

Putting h(t) = 400, we get:
[tex]h(t) = -16t^2 + 200t + 3\\400 = -16t^2 + 200t + 3\\\\16t^2 -200t +397 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(397)}}{2(16)}\\\\t \approx \dfrac{200 \pm 120.797}{32}\\\\t \approx 2.475\: \rm sec., t \approx 10.02\: sec.[/tex]

These both values are true. The time when t = 2.475 approx, the bullet would be going up, passing by 400 ft height, and when t = 10.02 approx, the bullet would be coming down, passing by 400 ft height.

Thus, the maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.

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Answer:

See below ~

Step-by-step explanation:

Question 1

5/6 _ 10/12

Question 2

12/100 _ 10/12

y=x-50

[tex]\huge\mathfrak\colorbox{white}{}[/tex][tex]\huge\mathfrak\colorbox{white}{}[/tex]

Answer:

8

Step-by-step explanation:

HOPE THIS HELPS! PLS GIVE ME BRAINILIEST PLSSSSSSSSSSSSSSSSSSS!

Answer:

Step-by-step explanation:

3.088 x [tex]10^{-5}[/tex]

scientific notation requires one number before the decimal, moving the decimal place to the right requires counting down.  

Answer:

Both figures have an area of (6hl) by Cavalieri's Principle for two-dimensional figures.

Step-by-step explanation:

Answer:

option a

Step-by-step explanation:

because of his province duh

The volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.

We have given that, the radius of the sphere is 9.1ft.

We have to determine the volume of the sphere

The volume of the sphere  is given by

[tex]V=\frac{4}{3}\pi r^3[/tex]

r is the radius of the sphere

V- is the volume of the sphere

So use the given value in the formula so that,

[tex]V=\frac{4}{3}\pi (9.1)^3[/tex]

[tex]V=3156.55082 ft^3[/tex]

Therefore the volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.

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Answer:3156.6

Step-by-step explanation:

Answer:

64 feet squared

Step-by-step explanation:

Since it's a square, all sides have a length of 8 ft. Area is length x width, so simply multiply 8 by itself. 64 feet squared is therefore the answer.

Answer: answer below

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the slope formula.

SLOPE FORMULA:

[tex]\Rightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]:\Longrightarrow \sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}}[/tex]

Solve.

[tex]\sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}=\dfrac{-6+4}{-4+3}=\dfrac{-2}{-1}=2}[/tex]

The slope is 2.

Use the slope-intercept form.

SLOPE-INTERCEPT FORM:

[tex]\sf{y=mx+b}[/tex]

y=2x+2

I hope this helps, let me know if you have any questions.

[tex]\text{Given that,}\\\\(x_1,y_1) =(-3,-4)~~ \text{and}~~ (x_2,y_2) = (-4,-6)\\\\\text{Slope,}~m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{-6+4}{-4+3} = \dfrac{-2}{-1} =2\\ \\\text{Equation of line,}\\\\~~~~~y-y_1 = m(x-x_1)\\\\\implies y+4=2(x+3)\\\\\implies y =2x+6-4\\ \\\implies y= 2x+2[/tex]

Answer:

B = 21.4°

Step-by-step explanation:

Using the Law of Sines.

[tex]sin(42)/22=sin(B)/12[/tex]

Cross Multiply

[tex]12*sin(42)=22sin(B)[/tex]

Get Sin(B) by itself.

sin(B)= 12*sin(42°) / 22

B° = sin^-1((12*sin(42°))/22)

B = 21.4°

Answer:

16 is definitely a

17 is c

Step-by-step explanation:

an app that I use that helps a lot is desmos u should try it out

hope this helps :)

can i get brainliest?

Answer:

176/317

Step-by-step explanation:

The formula for slope is [tex]\frac{y2 - y1}{x2 - x1}[/tex], which means you have to subtract the second point's y coordinate (286) minus the first point's y coordinate (110).

Now you have [tex]\frac{286-110}{x2 - x1}[/tex] or [tex]\frac{176}{x2 - x1}[/tex].

Now you have to do the same for x.

446 - 129 = 317, which gives you the final answer of

[tex]\frac{176}{317}[/tex], or about 0.555.

Hope this helps :)

jp524

Answer:

pentagon

Step-by-step explanation:

it has 5 sides

Answer:

The 2 dimensional shape that is formed by the cross section below is a triangle.

Check the picture below.

Answer:

-1

Step-by-step explanation:

The slope is the change in the Y value divided by the change in the X value. Therefore, the slope of this line is:

(-17-[-18])/(-7-[-6) = (-17+18)/(-7+6) = (1)/(-1) = -1

Answer:

11 1/4

Step-by-step explanation:

2 5/4 = 3 1/4

3 5/1 = 8

8 + 3 1/4 = 11 1/4

180

Step-by-step explanation:

9:40

?:800

9×20=180

40×20=800

it is a ratio. 9 oranges to 40 people. 40 times 20 is 800 so you do the same to 9 (which gives you 180)

Answer:

180/800

Step-by-step explanation:

if you multiply the numbers by 20 you can get your answer

Answer:

Slope : 1, Intercept- 3, equation: y = 1x + 3

Step-by-step explanation:

slope is the change of rate and it can be observed that the rate of change from each square is 1

y intercept is the spot where the line intersects with the y axis

equation format: y = mx + b where mx is slope and b is the y intercept

the answer is 82 million

Answer:

∆The lateral surface area of cylinder =417.62 mm²

Step-by-step explanation:

Diameter = 7

Radius = 7/2

Lateral Surface Area of cylinder = 2πrh

=> 2× π × 7/2 × 19

=> 38 × 7/2 × π

=> 133 × π { taking π as 3.14}

=> 133× 3.14

=> 417.62 mm²

To make a triangular prism we need cardboard, glue and scissors.

A triangular prism is a geometric shape characterized by:

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Answer:

1/2, or around 9 times

Step-by-step explanation:

since a fair coin has 2 sides, that makes you have 2 possible outcomes. Heads and tails, 2 sides, makes it 50-50 so you would expect to get around 9 heads because 50% or 1/2 of 18 is 9. Hope this helps

Answer:

100 degrees

Step-by-step explanation:

650$ was the amount of money that was taken away

Step-by-step explanation: