20 points

Evaluate the function graphically find f(-6)

Answer:

12000 rad/min

Step-by-step explanation:

One formula we can use here is that the linear speed is the same, and the linear speed is equal to the angular speed multiplied by the radius.

Therefore, 2400π rad/min* 35 cm = 7 cm* x, with x representing the angular speed of the smaller wheel in radians per minutes. Dividing both sides by 7 cm, we get

2400π rad/min * 35 cm / 7 cm = x

2400 π rad/min * 5 = 12000 rad/min = x as our answer

Answer:

Step-by-step explanation:

From the information given:

Tank's Capacity = 600 gal

Original content of water = 200 gal

Salt solution = 100 lb

In the tank:

Suppose x(t) = amount of salt at time (t); &

V(t) = volume of water

Then,

V(t) = 200 + t

and [tex]x'(t) = 3 - \dfrac{2x(t)}{200+t}[/tex]

From the above linear equation, the integrating factor can be computed as:

[tex]x(t) = \Bigg(e^{\int \dfrac{2}{200+t}} \Bigg)^{dt}[/tex]

[tex]= e^{2 \ log (200+t)}[/tex]

= (200 + t)²

The general solution can now be expressed as:

[tex]x(t) = \dfrac{1}{(200+t)^2}\Bigg( \int 3(200+t)^2 \ dt +C\Bigg)[/tex]

We know that C = integrating factor, thus taking the integral:

[tex]x(t) = \dfrac{(200+t)^3 +C}{(200+t)^2}[/tex]

At the initial condition, x(0) = 100

∴

[tex]100= \dfrac{(200)^3 +C}{(200)^2}[/tex]

C = ((200)²×100) - 200³

C = -4 × 10⁶

Hence, at any time t, the amount of salt is:

[tex]x(t) = \dfrac{(200+t^2) - 4\times 10^6}{(200+t)^2}[/tex]

Answer:

See below.

Step-by-step explanation:

Alternate Interior Angles - 1

Alternate Exterior Angles - 2

Corresponding Angles - 4

Same-side Exterior Angles - 5

Same-side Interior Angles - 3

Answer:38292

A

Step-by-step explanation:w

jkwlw44444

Answer:

-2i - 3

I can't see a simpler way to explain it. You just have to work your way through each step.

Step-by-step explanation:

The question is what is i^303?

Remember that when the power is divisible by 4 the expression changes to 1

i^1 = i

i^2 = i * i = sqrt(-1)*sqrt(-1) = - 1

i^3 = i^2 * i = - i

i^4 = i^2 * i^2 = -1 * - 1 = 1

So what does i^303 =

i^300 * i^3

But 300 is evenly divisible by 4. (300 / 4 = 75) so i^300 = 1^75

i^3 = -i

So now you are ready to do the question

(2 - 3i) * -i

2*-i - 3i(-i)

-2i - 3(i^2 * - 1)

-2i - 3(-1 * - 1)

-2i - 3(1)

-2i - 3

Answer:

(x, y) = (-5, 5)

Answer:

Step-by-step explanation:

5x+2y=-15

Step 1: Add -2y to both sides.

5x+2y+−2y=−15+−2y

5x=−2y−15

Step 2: Divide both sides by 5

[tex]\frac{5x}{5}[/tex]=[tex]\frac{-2y-15}{5}[/tex]

x=[tex]\frac{-2-15}{5}[/tex]

x+2y=5

Step 1: Add -x to both sides.

x+2y+−x=5+−x

2y=−x+5

Step 2: Divide both sides by 2.

[tex]\frac{2y}{2}[/tex]=[tex]\frac{-x+5}{2}[/tex]

y=[tex]\frac{-x+5}{2}[/tex]

Jessica left her running shoes at school yesterday. Today she walked 4 miles to school to get her shoes, she ran home along the same route, and the total time for both trips was 2 hours. Jessica walked and ran at constant speeds, and she ran 3 miles per hour faster than she walked.

What was Jessica's walking speed in miles per hour?

Answer:

A. -8

B. 23

C. 3

D. 5

Step-by-step explanation:

Answer:

The answer is 5184. Hope it helps luv

Answer:

[tex]area = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 2.9 \times 2.6 \\ = 3.77 \: ft {}^{2} [/tex]

Answer:

3.77 ft²

Step-by-step explanation:

Area of a triangle is half base length multiplied by the height.

0.5(2.9 × 2.6) = 3.77 ft²

Answer:

[tex]y=-3x+4[/tex]

Step-by-step explanation:

To get the equation in the slope-intercept form first, put the equation in slope-point form using the information given. The slope-point form is [tex]y-(-2)=-3(x-2)[/tex]. Then solve for y.

Distribute -3 to [tex](x-2)[/tex],

[tex]y-(-2)=-3x+6[/tex]

Then, add -2 to both sides,

[tex]y=-3x+4[/tex]

This is your final answer; the slope is -3 and the y-intercept is 4. There are also a few other ways to solve but I find this the easiest.

Answer:

9

Step-by-step explanation:

3 - ( -6 ) = 9

Hope this helps! Brainliest?

Answer:

9

Step-by-step explanation:

the other answer is right.

to add a little bit of explanation :

you need to calculate the difference between -6 and +3.

and we are looking on the number line only for a distance and not for a direction, as the distance (or simple difference) between -6 and +3 is the same as between +3 and -6.

so, whatever we get as difference, we need to treat that result as positive number.

so, we get the difference between two numbers by subtracting one from the other.

either 3 - (-6), or -6 - 3

you do know that subtracting a negative number is the same as adding the same positive number ?

e.g. 3 - (-6) = 3 + 6 = 9

as for the other direction -6 - 3 = -9

but again, we have to take this in this context as a positive number.

in math we call this the absolute value of a number.

so, the answer is always 9.

Answer:

try 492.43, this should be correct if I did this right

Answer:

31 and a half

Step-by-step explanation:

not sure tho_____________

Answer:

31.5 is ur answer

Step-by-step explanation:

so what you have to do is add up 5.5 + 5.5 + 6+ 7 +7.5 which gives u 31.5

Answer:

A-10

B- -12

C-3.6

If you cant understand B is -12

Answer:

In the problem, the value of x is equal to 6a.

Step-by-step explanation:

For this equation, we are to solve for x.  

11ax + 12ax = 13ax + 60

Add together 11 and 12 because they have like terms.

23ax = 13ax + 60

Substract 13ax on both sides.

10ax = 60

Now, we divide by 10 on both sides.

ax = 6

In order to see what x is, divide a on both sides.

x = 6a

Answer:

Option B. 489.8 ft²

Step-by-step explanation:

From the question given above, the following data were obtained:

Height (h) = 13 ft

Radius (r) = 6 ft

Pi (π) = 3.14

Lateral surface area (Aₗ) =?

The lateral surface area of the cylinder can be obtained as follow:

Aₗ = 2πrh

Aₗ = 2 × 3.14 × 6 × 13

Aₗ = 489.8 ft²

Therefore, the lateral surface area of the cylinder is 489.8 ft²

Answer:

-22 and -23

hope this helped :D

Answer:

- 23 & - 22

Step-by-step explanation:

Let one integer be x, so the other integer is x + 1

x + x + 1 = - 45

2x + 1 = - 45

2x = - 46

x = - 23

The integers are - 23 and - 22.

Answer:

∠ Y ≈ 32.7°

Step-by-step explanation:

Using the law of Cosines

cosY = [tex]\frac{x^2+z^2-y^2}{2xz}[/tex]

with x = 90, y = 55, z = 50

cosY = [tex]\frac{90^2+50^2-55^2}{2(90)(50)}[/tex] = [tex]\frac{8100+2500-3025}{9000}[/tex] = [tex]\frac{7575}{9000}[/tex] , then

∠ Y = [tex]cos^{-1}[/tex] ([tex]\frac{7575}{9000}[/tex] ) ≈ 32.7° ( to the nearest tenth )

Answer:

She wrongly added the equations

Step-by-step explanation:

Given

[tex]-3x + y = 8[/tex]

[tex]-3x + y = -4[/tex]

Required

Her mistake

The mistake is when she added the equations.

When both equations are added, the result is:

[tex]-3x -3x + y+y=8-4[/tex]

[tex]-6x +2y=4[/tex]

and not

[tex]2y = 4[/tex]

The suggestion to avoid such mistake is for the student to check the appropriate signs of each term before adding/subtracting.

Answer:

Her grant in four years time will be of $13108.

Step-by-step explanation:

Exponential equation:

An exponential equation has the following format:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial value and r is the growth rate, as a decimal.

A student get a grant of $10000 a year assuming her grant is increased by 7% each year

This means that [tex]A(0) = 10000, r = 0.07[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 10000(1+0.07)^t[/tex]

[tex]A(t) = 10000(1.07)^t[/tex]

What will her grant be in four years time?

This is A(4). So

[tex]A(t) = 10000(1.07)^t[/tex]

[tex]A(4) = 10000(1.07)^4 = 13108[/tex]

Her grant in four years time will be of $13108.

Answer:

$4800

Step-by-step explanation:

SI=PRT DIVIDED BY 100..

So it is going to be 400×2×6 divided by 100 which will be 4800

Answer:

5.5 hours

Step-by-step explanation:

Since every house has an initial charge of $50, we can begin with that

($50)

Then, let's define h as the number of hours. We know every hour is $70, although the hours is yet unknown so that can be

($70 * h) or simply ($70h)

Now, we know the total should end up to be $435, so after PEMDAS the equation will be

($70h + $50 = $435).

We subtract 50 from both sides so now we have $70h = $385.

Now we divide both sides by 70, giving us h = 5.5. Hope it helped!

The number of hours that the plumber work on the house calls should be 5.5.

Given that,

Based on the above information, the equation is as follows:

70h + 50 = 435

70h = 385

h = 5.5 hours

Therefore we can conclude that the number of hours that the plumber work on the house calls should be 5.5.

Learn more: brainly.com/question/3530056

Answer:

1. 2 is the correct answer

Step-by-step explanation:

24+67-67+78 = 102

102 /2+6-89-4​

= 1. 2

I am sure about my answer , trust me.

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

9:42

Step-by-step explanation:

First, convert his second run into minutes so its easier to simplify

than divide both the timings by 5

to get the answer as 9:42 as the simplest ratio form

Answer: A. 30 students in the lunchroom.

Step-by-step explanation:

A representative sample simply refers to the sample that has same characteristics just like the population.

A random-based selection is regarded as a representative of the population. In this case, the random sample that represents a representative sample of the number of students who enjoy science class is "30 students in the lunchroom".

When the students in the lunchroom are chosen, then it's a representation of the entire students in the school. This is the best option when compared to other options as they don't represent the students entirely.

Answer:

30 students in the lunchroom

Step-by-step explanation:

Got it right on the test.

Answer:

-3 1/2 or -3.5

Step-by-step explanation:

* means multiply

just put 3 where the x is

so

f(x) = -2 ( 1 - 1/4 x )

f( -3) = -2 ( 1 - 1/4 * -3 )

f( -3) = -2 ( 1 3/4 )

f( -3) = - 3 1/2