Slightly confused at what it wants me to do here?]]>

I used the definition , but I don't know what to do next. Thank you.]]>

Given that the Ferris wheel takes 18 minutes to complete one revolution, how many degrees will each capsule move per minute?

create a table calculating the angle of rotation, vertical leg height and capsule height from the ground for the given 10 interval of time. Calculate in degrees. Assume platform height is 15 meters.]]>

]]>

A. 2

B. 1

C. 0

D. -1

E. -2

What I did:

If \(\displaystyle f(x)=\frac{u}{v}\) then:

u =\(\displaystyle 3x^2-5\) → u' = 6x

v = x + 6 → v' = 1

f'(x) =\(\displaystyle \frac{u'v-uv'}{v^2}\)=\(\displaystyle \frac{6x(x+6)-(3x^2-5)(1)}{(x+6)^2}\)

f(0) + f'(0) = \(\displaystyle \frac{3(0^2)-5}{0+6}\) + \(\displaystyle \frac{6(0)(0+6)-(3(0^2)-5)(1)}{(0+6)^2}\) = \(\displaystyle \frac{3(0)-5}{6}\) + \(\displaystyle \frac{0(0+6)-(3(0)-5)}{6^2}\)= \(\displaystyle \frac{0-5}{6}\) +...

[ASK] Derivative of an Algebraic Fraction find f(0) + f'(0)]]>

What information I have so far is that since the side of the little squares are unknown, I called them "x", and so since the length of the full box is 12 inches, once folded up I'd have 12-2x. One thing I'm having trouble with is setting up my equation. I've done a...

Dimension of the cut-out squares that result in largest possible side area]]>

Any help appreciated]]>

\(\displaystyle \overline{\triangle}=\dfrac{f(b)-f(a)}{b-a} \)]]>

OK I went thru this 3 time and might still have some error ... otherwise typos maybe

I don't think this could be solved by just observation]]>

$|y+3|\le 4$

we don't know if y is plus or negative so

$y+3\le 4 \Rightarrow y\le 1$

and

$-(y+3)\le 4$

reverse the inequality

$ y+3 \ge -4$

then isolate y

$y \ge -7$

the interval is

$-7 \le y \le 1$

which is c

hopefully]]>

Fraction word problem: how many rows are devoted to each plant]]>

After i factor the denominator what do i do next to find A and B?

=(x-3)/(x+3)(x+1)

=A/(x+3)+B/(x+1)]]>

I have to transform the first function which is f(x)=x^3 to the second function. First, I have to find each shift then combine those to make a new function equation. I've used desmos and I know that there is a horizontal shift 3 units to the right. There is a vertical shift up but I don't know how many units. And I believe there is a stretch. There are only 3 transformations. PLEASE HELP!!!]]>

Would anyone be willing to give me an idea?]]>

Would anyone be willing to help?]]>

I don't think this is a super complicated question yet it proves to be too confusing for my brain >_<

Any kind of help would be appreciated, thank you!!]]>

]]>

y^2+12y+16x+68=0

The form we have been using is (y-k)^2=4p(x-h)

Any explanation would help too, I'm really stuck on this one.

Thank you!]]>

equation n = 1 − 7logT/3 , where T is the fraction of visible light that glass transmits.

a. What shade number should a welder use that only transmits ⅛ of the light entering the glass?

b Viewing a solar eclipse through #14 welding glasses is considered safe. What fraction of light do

these glasses transmit.]]>

85 Given $(-1,3),\quad (6,2),\quad (-2,-4)$

since the radius is the same for all points set all cirlce eq equal to each other

$(x_1-h)^2+(y_1-k)^2=(x_2-h)^2+(y_2-k)^2=(x_3-h)^2+(y_3-k)^2$

plug in values

$(-1-h)^2+(3-k)^2=(6-h)^2+(2-k)^2=(-2-h)^2+(-4-k)^2$

from this we get (via W|A)

$h = 2,\quad k = -1$

derive the radius by the distance of the center to one of the points...

85 find circle from 3 points]]>

equation I(x) = I0 (0.8)^x , where x is the thickness of the glass in millimetres and I0 is the intensity of

light entering the glasses. How thick should the glass be so that it will block 25% of the light entering

the sunglasses?]]>

what is the average profit on producing and selling 40 items per day

how many must we sell to get an average daily of $80?]]>

here is my overleaf output

View attachment 9075

I was wondering if this could be solved with a matrix in that it has squares in it

or is there a standard equation for finding the intersection of 3 circles given the centers and radius'

and an assumed intersection]]>

e^(-1) = c]]>

10^(x) = 105

e^(x) = 100

3^(2x) = 50

0.5*e^(-x) = 0.2

ln x^(2) = 6

5 ln 3x = 12]]>

Log(6) 1294 = 4

Log(w) v = t

Ln(1/4) = x

Evaluate

Log(4) 64 = ?

Log(16) 4 = ?]]>

Determine if (27/4)/(6.75) is a whole number, natural number, integer, rational or irrational.

I will divide as step 1.

27/4 = 6.75

So, 6.75 divided by 6.75 = 1.

Step 2, define 1.

The number 1 is whole or natural. It is also an integer and definitely a rational number because it can be expressed as 1/1, which is, of course, 1.

I conclude by saying that (27/4)/(6.75) belongs in the set of Z.

What do you say?]]>

A. How much must John pay the bank if he returns the loan in full in 6 months?

B. Same as...

Personal Bank Loan: How much must John pay the bank if he returns the loan in full in 6 months]]>

I know that integers include positive and negative numbers and 0.

Let Z = the set of integers

Z = {. . . -2, -1, 0, 1, 2, . . .}

I also know that any integer Z can be written as Z/1 = Z.

I will conclude by saying the following:

7 = 7/1

So, 7 is a natural number, an integer and a rational number (because it can be written as a fraction over 1).

Does this apply to all integers, Z?]]>

I do not know how to start thinking about part a and then got even more confused when I saw the answer be:

P<x^2-5x.

I ask for your guidance please.]]>

I'm pretty sure 2 cos^-1(x) is the same as cos2x, the doubles formula, but from there I'm completely lost.]]>

I have redone this problem two or three times and all the steps just make my head spin. I've tried looking up tutorials online but they introduce things into the problem that we haven't been taught yet and that just confuses me more. Help!]]>

y=-1/2[cos(x+pi)+cos(x-pi)]]]>

getting really frustrated with my math teacher. gives us forumlas for things but then barely shows us how to use them if at all and then throws problems at that we have to make sense of ourself. why can't math teachers teach?

anyway, the question is express f(x)=sinx+cosx in terms of sin.]]>

Can anybody help me figure this out? There are 2 hints. I am at a loss.]]>

I don't know where to start! Thank you so much!]]>

I always get stuck at this kind of exercises.How to approach an exercise like this?]]>

Also, I know that x1 is the lowest root of this equation.

I need to solve lim (x1) as m->infinity

A. 1

B. 3/2

C. 0

D. -1/2

E. -1

I tried to solve the equation with the discriminant then to calculate the limit but didn't work.

Also, I think that because x1 is the lowest root and the function graphic is a parabola, I tink that -b/2a (the peak of parabola) > x1 but I don't see how this condition would help me.

Some ideas?

Thanks!]]>

vector w=i+3j

vector v=<5, 2>]]>

I know triangle 1 has angles 30 degrees, 60 and 90. So the adjacent side is 4*sqrt(3)

I know triangle 2 has angles 45 degrees, 45 and 90. The adjacent side is 2*sqrt(2)

From here I am stuck as I do not know...

Find the distance between points C and D if the height of the tree is 4m]]>

Find the square roots of 4*sqrt(3)+4(i)]]>

Express cos(2 tan^-1(x/4)) and sin(2tan^-1(x/4) as an algebraic expression in x

I got:

cos(theta)=8*sqrt(x^2+64)/x^2+64

sin(theta)=x*sqrt(x^2+64)/x^2+64]]>

the answer I got was 10*4th root(3)

Is this correct?

I am asking because someone other than my professor wrote the study guid for us for the final and I am not 100% sure what |AC|=|BC| means as my professor never used it. I'm assuming it means side lengths of the triangle.]]>

A=1/2*b*h

I split the triangle in half to find the height. Since the base is 4, that divided the base into 2:

2^2+h^2=6^2

4+h^2=36

h^2=32

h=4*sqrt(2)

===========

1/2*4*4*sqrt(2)=area of 8*sqrt(2)

Did I do this correctly? I do not have an answer key to the study guide I was given.]]>

If tan(theta) = -2[sqrt(2)], and theta is between 270 degrees and 360 degrees, evaluate cos 2(theta) and sin 2(theta).

I got -7/9]]>

The graph of function f(x) = ax + b is transformed by the following sequence:

translation by (1) (meaning 1 horizontal, 2 vertical)

(2)

reflection through y=0

horizontal stretch, scale factor 1/3, relative to x=0

The resulting function is g(x)=4-15x

Find a & b

Thanks for your help.]]>

which passes through points:

(-1,3) and (0,2) and (1,0) and (2,1) and (3,5)

second function is defined: g(x)=2f(x-1)

Calculate g(0)

Calculate g(1)

Calculate g(2)

Calculate g(3)]]>

I have vector U=<1, 3> and vector V=<5, 2>

It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)?

I already know how to find the missing angle for cos(theta) but we never covered how to find the missing angle for sin(theta). It was never in our homework and it's not in my notes but apparently it could be on the test.

So if someone could give me the formula and then show a step by...

find the sin angle between two 2d vectors]]>

r= 1/1+sin(theta)

I know the answer is supposed to be:

x^2+y^2=(1-y)^2

I can't figure out the steps to get to the answer.]]>

The equation is:

sec(theta)=2

I am supposed to convert it to a rectangular equation. I know the answer is going to be y^2-3(x)^2=0

I don't know how to get to the answer he gave us.]]>

I think you are supposed to use arc length formula.

This is what I got so far:

s=r(radian symbol) = 3=1(radian symbol)]]>

Solve

i^(-21/2)

Note: i means iota.]]>

A jet flew from Tokyo to Bangkok, a distance of 4800km. On the return trip, the speed was decreased by 200km/h. If the difference in the times of the flights was 2 hours, what was the jets speed from Bangkok to Tokyo?

Just need the formula for the Jets speed and I should be fine with the rest.

This was my guess: 4800 = (x-200)(-2x)]]>

The reflecting telescope is deployed in low earth orbit( 600km) with each orbit lasting about 95 min. use the linear velocity formula to solve the problem.

I did 300 * 95 min = 28500. Can someone check my work please? if someone could check it today hat would be great thanks.]]>

$g(x)=2x^3+5x^2-28x-15$

$\text{synthetic division}$

$\begin{array}{c|rr}

& 2 & 5 &-28 &-15 \\

&&6&33 & 15\\ \hline

3&2&11&5&0

\end{array}$

$\text{thus }\\$

$2x^2+11x+5$

$\text{use quadradic formula}$

$\begin{align*}

x=\frac{-(11)\pm\sqrt{(11)^2-4(2)(5)}}{2(1)}

&=\frac{-11\pm\sqrt{81}}{2}

=\frac{-11\pm9}{2}

\end{align*}$

$x=-10,-1 \quad g(x)=(x+10)(x+1)(x-3)$

hopefully

comment?]]>

$\displaystyle\frac{e^x+e^{-x}}{2}=3$

ok we have the indenty of

$$\displaystyle\cosh{x}=\frac{e^x+e^{-x}}{2}$$

presume then the x can be replaced by 3

$$\displaystyle\cosh{3}=\frac{e^3+e^{-3}}{2}$$

ok $W\vert A$ returns

$x = \ln(3 \pm 2 \sqrt 2)$

ok so how??

]]>

$$\displaystyle\bar{z}u=\bar{z}\bar{u}

\textit{ and }

\displaystyle \left(\frac{z}{u} \right)=\frac{\bar{z}}{\bar{u}}$$

ok couldn't find good example on what this is

and I'm not good at 2 page proof systems

so much help is mahalo

]]>

so expanded

$$x\ln{3}-\ln 7-\ln 2 +x \ln 3=\ln 5$$

ok W|A says the answer is

$$\frac{\ln\left({7}\right)}{\ln\left({3}\right)}$$

don't see the steps how?]]>

f(a+h)=-5(a+h)^2+2(a+h)-1

Please enlighten me]]>

$$

\hspace{0.3cm} \large {\int_{0} ^{\infty} \frac{\frac{1}{x^4} \hspace{0.1cm} e^{- \frac{r}{x^2}}\hspace{0.1cm}e^{- \frac{r}{z^2}} }{ \frac{1}{x^2} \hspace{0.1cm} e^{- \frac{r}{x^2}}+ \frac{1}{y^2} \hspace{0.1cm} e^{- \frac{r}{y^2}}}} dr \hspace{.2cm} ; \hspace{1cm} x>0,y>0,z>0 $$ where $ x $ ,$ y $ and $z $ are constants and independent of $ r $.]]>

$$5+i \quad 4-i$$

ok I did this but don't think this is the final answer

$(x-(5+i))(x-(5-i))=x^2+26$

$(x-(4-i))(x-(4+i))=x^2-17$]]>

$$f(x)=16x^4+3x^2-2$$

ok I presume we can solve this with the quadratic formula even with powers of 4 and 2

by setting $u=x^2$ I was able to get

$$x=\pm\sqrt{-\frac{3}{2}+\frac{\sqrt{137}}{2}}$$

but $W\vert A$ says the answer is

$$x=\pm\frac{1}{4}\sqrt{-\frac{3}{2}+\frac{\sqrt{137}}{2}}$$

where does the $\frac{1}{4}$ come from?

$$\tiny{140.56}$$]]>

express (sqrt(2)/2 + sqrt(2)/2 i)^8 in a+bi form

I know r=1 and tangent=pi/4

Using the theorem i get 1(cos (2pi) +i*sin (2pi)) which becomes 1(1*i)=1*i however WebAssign says this is incorrect. I've also tried "0+1i" and just "i"

What am I doing wrong?]]>

1) cosW=sin20

2) sinW=cos(-10)

3) sinW< 0.5

4) 1<tanW]]>

Convert r=7cos(theta) into a rectangular equation. Use x and y values. I know how to convert when it's x=r*cos(theta) or y=r*sin(theta) and r and theta is given. But this is different and I don't know how to do it.]]>

f(X) = 2 x2 - 8x and g(x) = x2-3x+ 6 the points (-1,10) and (6,24)]]>

I have so far:

(r^2)cos^(theta)+(r^2)sin(theta)=4

Idk what I'm supposed to do from here]]>

8x=8y

I thought it would be

8*r*cos(theta)=8*r*sin(theta)

Said it was incorrect

then I thought I needed to divide by 8 to remove it, giving me:

r*cos(theta)=r*sin(theta)

But that was also incorrect and now I am stuck]]>

The question is

sec 3(theta)-2=0]]>

cos(2*theta)+sin^2=0]]>

cos(1/2*cos^-1*x)

This is due tonight online and would like help please.]]>

Prove by induction that 3 raised to 2n+1 + 2 raised to n-1 is divisible by 7 for all numbers greater than/or equal to 1. How do you do the inductive step?]]>

]]>

I was using the computer in order to plot the graph of

\[y=x^{\frac{1}{3}}=\sqrt[3]{x}\]

and two different plotters gave two different results. I don't understand why. Can you kindly explain ?

The results are:

Thank you !]]>

I need to find the domain for \(\displaystyle f(x) = ln(x^2-5x)\)

What's confusing me is how to deal with the exponent. I can't think of a way to get around it.]]>

]]>

I am not sure if I could find this by doing a inequality equation, but I think my professor wants us to do it on a number-line anyway. I'm sorry, but I am not sure where to start.]]>

]]>

Can anyone recommend a competitor to ALEKS, which I used to use but gave up on when they revamped the lay out

(besides which, I have reason to believe that ALEKS may not be best value in town)

Hello to everyone on my friend list!

I'm back to have my bi-decennial crack at math mastery.

This time I hope I have all the life "parameters" set to the right frequencies and who knows, maybe this will be "The...

AI-assisted math learning for adult (long-term) beginner]]>

$$\begin{vmatrix}-2 & 0 & 1 \\ 1 & 2 & 0 \\ 4 & 2 & 1 \end{vmatrix}$$

I am going to guess that I need to look at each number in the second horizontal row to see what i and j are for finding the cofactors of the elements. I am a bit confused as to where to start this problem at. I am familiar with evaluating a 2X2 determinant but finding a cofactor of an element, evaluating a determinant, and understanding Cramer's...

The cofactors of elements for every determinant]]>

We can find the exact volume of any shape using:

V= \(\displaystyle int[a,b] A(x) dx\)

Where,A(x)is the cross-sectional area at height x

and [a,b] is the height interval

We know that the horizontal cross-sections are hexagonal

\(\displaystyle ∴A=(3√3)/2 a^2\)

Where a,is the length of a side

Write the side length a,at height x

a= s

\(\displaystyle ∴A=(3√3)/2 s^2\)

\(\displaystyle V= int[0,h](3√3)/2 x^2 dx\)

\(\displaystyle V= (3√3)/2 int[0,h]x^2...\)

Riemanns Sum Problem: Find the exact volume]]>

https://imgur.com/a/NvzxFcS]]>

So, my problem is with a degree 3 complex polynomial. I'm given one zero of the equation, but since it is a complex zero, I can use the conjugate too. So, I already have two of the zeros for the polynomial, and since according to the fundamental theorem of algebra, it should only have one more. Because complex roots also have a conjugate, this...

Complex polynomial zeros]]>

I explain in my class a way to take a function and change it to implict function as:

y - f(x) = 0

I see that way in Wikipedia, so I used it the class.

But my students ask me question that I don't know to answer:

1. Are there more ways to take a function and change it to implict function?

2. Are there infinte ways or a finite ways to do it?

Thanks, for one that answer.]]>

sqrt(x + 15) + sqrt(x) = 15

Any suggestions are appreciated how to approach the solution for this equation.]]>

Thank you in advance.

Yeny]]>

My Effort:

The needed function is

a_n = a_1•r^(n-1), n is the 23rd term, r is the common ratio and a_1 is the initial value.

a_23 = 25•(1.8)^(23 - 1)

Is this correct?]]>

I have to find the values of the 6 trig functions if the conditions provided hold

cos2(theta)=3/5

90 degrees is less than or equal to theta, and theta is also less than or equal to 180 degrees

THANK you so much.]]>

sketch the graph of y=g(x)

I don't know how the [0,5] \implies R changes the graph.]]>