Starting at 300 feet away, a car drives towards you. IT then passes you by at a constant speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds is given by the equation d=|300-48t|. AT what times is the car 60 feet from you?

The car is 60 feet away from you after___seconds and after _____ seconds.

Explain what 48t represents in the given equation.

Answer:

i t s C i t h i n k s o i t h i n k t h i s wouod help u

me at 1:36pm: oh no,  i hope he got his answer

Answer:

x = 23

Step-by-step explanation:

all you have to do is follow the rules of PEMDAS and treat it like a normal equation of order of operations;

Answer:

a

Step-by-step explanation:

because all top numbers can go into bottom numbers.

If the function f(x) =(4x² tan x)/sec x , then f'(x) =4( 2x sin(x) + x² cos x) using product rule of differentiation and f'(5) =103.11

Product rule for differentiation states that the differentiation the product of two functions is the product of derivative of first function and second function plus  product of derivative of second function and first function.

If we have consider the differentiation of product of two functions u ,v that we can write product rule as

(u*v)' = u' v  + u v' , where '  represents first derivative  with respect to independent variable

Given f(x) = (4x² tan x)/sec x or we can write it as :

f(x) = (4x² )(sin x) as   1/ sec x is cos x , tan x = sin x / cos x

let u =4x² , v = sin x

Then f(x) =u × v

Using product rule of differentiation:

f'(x) =  u' v + u v'  = (8x sin x) + (4x² cos x) = 4( 2x sin(x) + x² cos x)

To find value of f'(x) at x= 5

f'(5) = 4(10sin5 + 25 cos5) = 103.10569951 = 103.11(rounding off )

Therefore if f(x) = (4x² tan x)/sec x  then f'(x) =4( 2x sin(x) + x² cos x) and f'(5) =103.11

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This is between 2 and 3 seconds, excluding both endpoints.

========================================================

Explanation:

t = elapsed time in seconds

h(t) = height of the ball at time t

Replace h(t) with 100. Then get everything to one side.

[tex]h(t)= -16t^2+80t+4\\\\100= -16t^2+80t+4\\\\0 = -16t^2+80t+4-100\\\\0= -16t^2+80t-96\\\\-16t^2+80t-96 = 0[/tex]

Next, we'll use the quadratic formula to isolate t.

Plug in a = -16, b = 80, c = -96 which are the coefficients of the last equation mentioned above.

[tex]t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\t = \frac{-80\pm\sqrt{(80)^2-4(-16)(-96)}}{2(-16)}\\\\t = \frac{-80\pm\sqrt{256}}{-32}\\\\t = \frac{-80\pm16}{-32}\\\\t = \frac{-80+16}{-32} \ \text{ or } \ t = \frac{-80-16}{-32}\\\\t = \frac{-64}{-32} \ \text{ or } \ t = \frac{-96}{-32}\\\\t = 2 \ \text{ or } \ t = 3\\\\[/tex]

Therefore, the ball's height is greater than 100 ft in the air for the interval [tex]2 < t < 3[/tex]

This is between 2 and 3 seconds, excluding both endpoints.

------------------

Check:

Let's plug in t = 2 to find that...

[tex]h(t)= -16t^2+80t+4\\\\h(2)= -16(2)^2+80(2)+4\\\\h(2)= -16(4)+80(2)+4\\\\h(2)= -64+160+4\\\\h(2)= 100\\\\[/tex]

You should find that h(3) = 100 as well. I'll let you do those steps.

Since h(2) = 100 and h(3) = 100, this confirms the two solutions we found earlier.

The solution to the non-linear inequality 5x² + 3x < 0, in interval notation, is: (-0.6,0).

We have to look at the graph of the function relative to the x-axis, as follows:

The inequality for this problem is:

5x² + 3x < 0.

Meaning that the two bullet points above are relevant as we want to find when the function is negative.

The graph of f(x) = 5x² + 3x is given at the end of the answer, and it is negative for:

(-0.6,0).

Which is the solution set for the inequality, and is painted on the graph.

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Answer:

your answer should be

Step-by-step explanation:

x=2i or like i should say -2i

i hope its right tbh sometimes i make mistakes doing these

Answer:

8

Step-by-step explanation:

Answer:

2/3 = 6/9

3/5 = 12/20

2/10 = 4/20

1/3 = 2/6

4/6 = 8/12

Answer:

8x - 4y + 12

Step-by-step explanation:

-2(-4x + 2y - 6)

(-2)(-4x) + (-2)(2y) + (-2)(-6)

(2 * 4x) - (2 * 2y) + (2 * 6)

8x - 4y + 12

Answer:

Step-by-step explanation:

The answer is 2 because 2 is a prime number

The domain and the range of the function are given as follows:

a) Domain: -3 ≤ x < 4.

b) Range: -4 < y ≤ 5.

In a graph:

Hence, for the graphed function:

a) Domain: -3 ≤ x < 4.

b) Range: -4 < y ≤ 5.

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Step-by-step explanation:

ummmm ok then hahaha :)

Answer:

Area of rectangle OABC = 18 units²

Step-by-step explanation:

From the graph attached,

Vertices of the rectangle are O(0, 0), C(3, 0) and A(0, 6).

Length of side AO = 6 units

Length of side OC = 3 units

Area of the rectangle = Length × Width

                                    = OC × AO

                                    = 3 × 6

                                    = 18 square units

Answer: its actually 900

Step-by-step explanation:

Answer:

y= -2(-6) +5

y= 12+5

y= 17

y= -2(-3) +5

y= 6 +5

y= 11

y= -2(0) +5

y= 0+5

y=5

y= -2(3) +5

y= -6 +5

y= -1

umm

18.00 x 3 = 54

$54.00

Answer: 39.13 for 18 plants

Step-by-step explanation:

120/55.20= 2.17 dollars per plant

18*2.17=39.13

Answer:

The answer is: Use a calculator.

Step-by-step explanation

With the calculator you are able to do ANY problem.

Answer: There is no solution.

Step-by-step explanation:

Simplify both sides of the equation

subtract 3x from both sides

add 6 to both sides

0=10

The answer is - there are no solutions

Answer:

I would C because it is in the middle of 20 and 40

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

y = 46

Step-by-step explanation:

I'm assuming you wanted to solve for y.

x = 5

y = 8(5) + 6

y = 40 +6

y = 46

Answer: 1 10/39

Step-by-step explanation:

The number of adults that are there will be 368 adults.

Let adults = a

Let children = c

The equation to solve the question will be:

a + c = 865 ....... i

30a + 9c = 15513 ...... ii

From equation i, c = 865 - a

Since 30a + 9c = 15513

30a + 9(865 - a) = 15513

30a + 7785 - 9a = 15513

30a - 9a = 15513 - 7785

21a = 7728

a = 7728/21

a = 368

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