(ECSEPTEMBER 2019) QUESTION 8 8.1 8.2 Determine f'(x) from first principles if f(x) = 3 - 2x² Determine: 8.2.1 D₂[x(x-2)²] 8.2.2 dx MATHEMATICS PI if y = ax 2x √x +3​

Answer:

It takes takes them 31.67 secs to meet after Person A starts walking

OR

34.67 secs after Person B starts walking

Step-by-step explanation:

First, we will find the perimeter of the rectangle

From,

Perimeter of rectangle = 2 (\(l\) + \(b\))

Where \(l\) is the length

and \(b\) is the breadth

From the question, \(l\) = 100m

and \(b\) = 50m

Hence,

Perimeter of the rectangle = 2 (100+50)

= 2(150) = 300m

Hence, the perimeter of the rectangle is 300m

This is the total distance that will be covered by both persons by the time they meet.

Let the distance covered by person A be \(S_{1}\)

and the distance covered by person B be \(S_{2}\)

We can write that

\(S_{1}\) + \(S_{2}\) = 300m

Velocity of person A, \(V_{A}\) = 4 m/s

and velocity of person B, \(V_{B}\) = 5 m/s

From the question, Person A starts walking 3 seconds after person B,

This means, if person A spends \(t\) secs before they meet, then person B would spend (3 + \(t\)) secs.

For Person A,

Velocity = 4 m/s

Time = \(t\) secs

Distance = \(S_{1}\)

From,

\(Velocity = \frac{Distance}{Time}\)

Then,

\(Distance = Velocity \times time\)

\(S_{1} = 4 \times t\)

\(S_{1} = 4t\) ...... (1)

For Person B

Velocity = 5 m/s

Time = (t + 3) secs

Distance = \(S_{2}\)

Also, from

\(Distance = Velocity \times time\)

\(S_{2} = 5 \times (3+t)\)

\(S_{2} = 5(3+t)\) ...... (2)

Recall that, \(S_{1}\) + \(S_{2}\) = 300m

Then, \(S_{2}\) = 300m - \(S_{1}\)

We can then write that,

300m - \(S_{1}\) \(= 5(3+t)\)

Then,

\(S_{1} = 300 - 5(3+t)\) ..... (3)

Equating equations (1) and (3), we get

\(300 - 5(3+t) = 4t\)

\(300 - 15 -5t = 4t\\9t = 285\\t = \frac{285}{9}\\\)

\(t = 31.67 secs\)

This is the time spent by Person A

Hence, it takes takes them 31.67 secs to meet after Person A starts walking OR

34.67 secs after Person B starts walking

Answer:

I mistakenly rated Abdulazeez10's answer 2 stars because I thought he mixed up his variables, but I was actually the one who mixed up my variables.

Step-by-step explanation:

Sorry, Abdulazeez10 :( I can't change my rating, but just so everyone else knows, his answer is 100% correct!

Answer:

I got 192 too

Step-by-step explanation:

Let me know if you need explaining or not

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

0.5x - 0.3 = 0.3

0.5x = 0.3 + 0.3

0.5x = 0.06

x = 0.06/0.5

x = 0.12

here is the value of x

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Substitute sin(x) = tan(t) and cos(x) dx = sec²(t) dt. We want this change of variable to be reversible, so let's assume bot x and t are bounded between 0 and π/2.

Then we have

\(\displaystyle \int \frac{\cos(x)}{\sqrt{1 + \sin^2(x)}} \, dx = \int \frac{\sec^2(t)}{\sqrt{1 + \tan^2(t)}} \, dt\)

Recall the Pythagorean identity,

1 + tan²(t) = sec²(t)

Then

√(1 + tan²(t)) = √(sec²(t)) = sec(t)

and the integral reduces to

\(\displaystyle \int \frac{\sec^2(t)}{\sqrt{1 + \tan^2(t)}} \, dt = \int \frac{\sec^2(t)}{\sec(t)} \, dt = \int \sec(t) \, dt = \ln|\sec(t)+\tan(t)| + C\)

Change the variable back to x, so the antiderivative is

\(\displaystyle \int \frac{\cos(x)}{\sqrt{1 + \sin^2(x)}} \, dx = \ln \left|\sec\left(\tan^{-1}(\sin(x))\right) + \tan\left(\tan^{-1}(\sin(x))\right) \right| + C \)

\(\displaystyle \int \frac{\cos(x)}{\sqrt{1 + \sin^2(x)}} \, dx = \boxed{\ln \left|\sqrt{1+\sin^2(x)} + \sin(x) \right| + C} \)

Answer:

62.16

Step-by-step explanation:

The sample space for the two mornings at the stop light would be D. {red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}.

In probability theory, the sample space constitutes the collection of all potential results that could ensue from an experiment. Symbolized by S, it encompasses every plausible outcome that can arise when such a test is conducted.

The sample space would therefore be :
{red/red, red/yellow, red/green, yellow/red, yellow/yellow, yellow/green, green/red, green/yellow, green/green}

This includes all the possible lights that could be seen on the two mornings by Julie.

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Her score in computer to get a proportionally weighted average of 46% will be 134.

The total score for both subjects = 200 + 300 = 500

Since the proportionally weighted average is 46%, then her score will be:

= 46% × 500

= 0.46 × 500

= 230

Since she had 32% for her statistics test, which was out of a total of 300. Her score will be:

= 32% × 300

= 0.32 × 300

= 96

Therefore, her score in computer will be:

= 230 - 96

= 134

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Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

Answer:

12.4

Step-by-step explanation:

to get radius divide diameter by 2

Answer:

D

Step-by-step explanation:

Because 12 is greater than -5 and when you divide a postive and a negative you get a negative number. And negative numbers are less than 0 .

Answer:

$35

Step-by-step explanation:

All you have to do is subtract 10 from 45 because it was $10 off and the original price was $45.

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

90

Step-by-step explanation:

i think

Answer:

37.17 grams

Step-by-step explanation:

59% of 63 grams = 0.59 × 63 grams = 37.17 grams

Answer:

16 slices of pizza without 2 olives

Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

r1 should be twice the value of r2.

Circuit a and circuit b are shown in the figure below, where r1 and r2 are the resistance values of the resistors.

The power dissipated by the resistor of resistance r2 in circuit a is given by:

\(Pa = V^2 / (r1 + r2)\)

Similarly, the power dissipated by the resistor of resistance r2 in circuit b is given by:

\(Pb = V^2 * r2 / (r1 + 2*r2)\)

For these two powers to be equal, we can equate them:

\(V^2 / (r1 + r2) = V^2 * r2 / (r1 + 2*r2)\)

Simplifying this equation, we get:

\(r1 = 2*r2\)

For the power dissipated by the resistor of resistance r2 to be the same for circuit a and circuit b, the ratio of r1 and r2 should be 2:1.

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Approximately 456.3 feet of fence to surround the entire circular yard.

Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.

Since, The circumference of a circle is,

⇒ C = πd,

where, C is circumference, d is diameter,

Here, the diameter of the circular yard is 145 feet,

So the radius is half of that,

r = 145/2 = 72.5 feet.

So, Using the formula, we can calculate the circumference as:

C = πd

C = 3.14 x 145

C = 456.3 feet

Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.

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Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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Answer:

Step-by-step explanation:

c^2 = a^2 - b^2

13^2 - 5^2 = -12

Answer:

Step-by-step explanation:

Answer:

The answer is -2/3

Step-by-step explanation:

17 - 6/x = 21

subtract 17 from each side

-6/x = 4

then multiply each side by 1/6

-x = 4/6

simplify.

-x = 2/3

divide -1 to each side

X = -2/3

Answer:

The figure is attached and the total distance is 1031 feet.

Step-by-step explanation:

The graph is indicated in the attached figure.

For calculation of distance consider following

Point Flagpole is (0,0)

Point Clue1 is (0,5)

Point Clue2 is (6,0)

Point Clue3 is (0,-5)

So the distance is calculated as follows

\(d_{T}=[d_{FP\ to\ Clue1}+d_{Clue1\ to\ Clue2}+d_{Clue2\ to\ Clue3}]*distance\ per\ unit\\d_{T}=[\sqrt{(Clue1_x-FP_x)^2+(Clue1_y-FP_y)^2}+\sqrt{(Clue2_x-Clue1_x)^2+(Clue2_y-Clue1_y)^2}+\sqrt{(Clue3_x-Clue2_x)^2+(Clue3_y-Clue2_y)^2}]**distance\ per\ unit\\\)Substituting the values

\(d_{T}=[\sqrt{(0-0)^2+(5-0)^2}+\sqrt{(6-0)^2+(0-5)^2}+\sqrt{(0-6)^2+(-5-0)^2}]*50 \text{ feet}\\d_{T}=[\sqrt{(0)^2+(5)^2}+\sqrt{(6)^2+(-5)^2}+\sqrt{(-6)^2+(-5)^2}]*50 \text{ feet}\\d_{T}=[\sqrt{0+25}+\sqrt{36+25}+\sqrt{36+25}]*50 \text{ feet}\\d_{T}=[\sqrt{25}+\sqrt{61}+\sqrt{61}]*50 \text{ feet}\\d_{T}=[5+7.81+7.81]*50 \text{ feet}\\d_{T}=[20.62]*50 \text{ feet}\\d_{T}=1031 \text{ feet}\\\)

So the total distance travelled is 1031 feet.

Answer:

x = 5

Congruent sides = 13 cm each

3rd side = 2(5) = 10 cm

Step-by-step explanation:

2(2x+3)+2x = 36

4x+6+2x = 36

6x = 36-6

x = 30/6

x = 5

Congruent sides = 2(5)+3 = 13

Answer:

3/8

Step-by-step explanation:

hope it helps :)

We can write that -

An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.

Given are the numbers to be verified as rational or irrational.

Therefore, we can write that -

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The normal price is $25, we need to find the 40% of $25.

40% = 0.4

So if we multiply $25 by 0.4