if a=52\sqrt{6} then find the value of a^2+\frac{1}{a^2}
97,294 results
math
Find an integer $x$ such that $\frac{2}{3} < \frac{x}{5} < \frac{6}{7}$

algebra
am I right? 1. Simplify radical expression sqrt 50 5 sqrt ^2*** 2 sqrt ^5 5 sqrt ^10 5 2. Simplify the radical expression sqrt 56x^2 28x 2x sqrt 14*** 2x sqrt 7 sqrt 14x2 3. Simplify the radical expression. sqrt 490y^5w^6 2 sqrt 135y^2 2y sqrt 135*** 27

Trig
Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(5,4). (0 is not the number zero I don't know what its called) I have to find r first. r=sqrt x^2+y^2 r=sqrt 5^2+4^2 r=sqrt 41

Math
1. The length of the hypotenuse of a 306090 triangle is 7. Find the perimeter. A) 7/2+21/2 sqrt 3 B) 21+7 sqrt 3 C) 7+21 sqrt 3 D) 21/2 + 7/2 sqrt 3 Could someone please help me, I don't know how to do this. Thank you!

algebra
Simplify: 2 sqrt (3) + 6 sqrt(2)  4 sqrt(3) + sqrt (2) a) 8 sqrt(2)  3 sqrt(3) b) 6 sqrt(2)  8 sqrt(3) c) 5 sqrt(6) d) 7 sqrt(2)  2 sqrt(3) the answer i picked was d

Algebra
Evaluate sqrt7x (sqrt x7 sqrt7) Show your work. sqrt(7)*sqrt(x)sqrt(7)*7*sqrt(7) sqrt(7*x)7*sqrt(7*7) sqrt(7x)7*sqrt(7^2) x*sqrt 7x49*x ^^^ would this be my final answer?

math
1 Esteban drew Triangle JKL on a coordinate plane with J (−3,5), K (−1,−4), and L (2,4). Then he drew J'K'L', the results of the dilation were (x, y) > ( \frac{2}{3} 3 2 x, \frac{2}{3} 3 2 y) What are the coordinates of J'?

math
Let $A$ and $B$ be real numbers such that $\frac{A}{x5}+B(x+1)=\frac{3x^2+12x+22}{x5}$. What is $A+B$?

math;)
Find the unit vector in the direction of u=(3,2). Write your answer as a linear combination of the standard unit vectors i and j. a. u=3[sqrt(13)/13]i+2[sqrt(13)/13]j b. u=3[sqrt(5)/5]i+2[sqrt(5)/5]j c. u=3[sqrt(5)/5]i2[sqrt(5)/5]j d.

Calculus
In these complex exponential problems, solve for x: 1)e^(i*pi) + 2e^(i*pi/4)=? 2)3+3=3i*sqrt(3)=xe^(i*pi/3) MY attempt: I'm not really sure of what they are asking. For the 1st one I used the e^ix=cos(x)+i*sin(x) and got 1+sqrt(2) +sqrt(2)i 2) I solved

Math:)
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12 radians? a.

mathInverse functions
f(x)=4x2 & g(x)=5x6. Find (f*g) and state domain. f(x)x^21 what is the equation for f^1(x)? f(x)=3x+2, find f(f^1(14)). f(x)=4x+7 and g(x)=3x5 find (f*g)(4) f(x)=sqrt x+3 what is equation for f^1(x)? Graph y=sqrt x2 +5 which point lies on graph?

Surds
Solve in the exact form. (sqrt of 4x+1)+(sqrt of x+1)=2 Someone showed me to do this next: Square both sides..so.. 4x+1+2((sqrt of 4x+1)•(sqrt of x+1))=4 I do not understand where the 2 come from ..and why do we need to multiply the sqrt of 4x+1 and sqrt

Math _
For all x in the domain of the function x+1 over x^3x this function is equivalent to \[a)\frac{1}{x^2}\frac{1}{x^3}\\ b)\frac{1}{x^3}\frac{1}{x}\\ c)\frac{1}{x^21}\\ d)\frac{1}{x^2x}\\ e) \frac{1}{x^3}\] This is one of the questions to my math test can

College Algebra. Please Help.
Use the quotient property to simplify roots. \sqrt{\frac{27a^{13}}{b^{12}}}

Calculus
Evaluate the indefinite integral: 8xx^2. I got this but I the homework system says its wrong:sqrt((x8)x)/(2*sqrt(x8)*sqrt(x))*(((sqrt(x8)*(x4)*sqrt(x))32*log(sqrt(x8)+sqrt(x))

is this correct? math
find the domain of the real valued function; f(x) = sqrt(5  (sqrtx)) my solution: 5  (sqrt x) >=0 (sqrt x) >= 5 (sqrt x)

Calc I
Find the range of y = (3x1)/(2x^2 + x  6) I was going to take the derivative of the numerator and denomenator and then use the quotent rule to find the derivative of the function and find the critical values but I ran into the imaginary number during the

MATH
I need to simply this equation, but I got stuck. h/(4sqrt(16+h)) = y First, I multiplied (4+sqrt(16+h)/(4+sqrt(16+h) to both sides, and I ended up with h(4+sqrt(16+h)/h. Is this correct? (I tried to graph both equations to see if I would get the same

math,algebra,help
Directions are simplify by combining like terms. x radiacal 18 3 radical 8x^2 can someone show me how to do these types of problems. thanks I cant determine the second term. For the first, I think you meant x sqrt(18) which reduces to x sqrt (9*3) or 3x

math calculus please help!
l = lim as x approaches 0 of x/(the square root of (1+x)  the square root of (1x) decide whether: l=1 or l=0 or l=1 Let me make sure I understand the question. Do we have lim x>0 x/[sqrt(1+x)  sqrt(1x)] ? If so then multiply the expression by

Math
So I am supposed to solve this without using a calculator: Sqrt[20]/10  Sqrt[10]/Sqrt[32]  Sqrt[0.3125] + Sqrt[3 + 1/5] You can put this into WolframAlpha as is to make it prettier. Answer given is 1/2 * SQRT(5) I really don't know where to start here. I

Trignometry
A calculator is broken so that the only keys that still work are the \sin, \cos, \tan, \cot, \sin^{1}, \cos^{1}, and \tan^{1} buttons. The display initially shows 0. In this problem, we will prove that given any positive rational number q, show that

Math
f(x)= 4x^2 and g(x)= sqrt (x) find the implied domain of fg(x) fg(x)= f(sqrt(x)) fg(x)= 4(sqrt(x))^2 fg(x)=4(sqrt x)(sqrt x) fg(x)=4x domain= (x:x=all real numbers) Am I correct?

Math sequence
Let {An} be the sequence defined recursively by A1=sqr(2) and A(n+1) = sqr(2+An) for n is bigger and equal to 1. Show that An < 2. What is An? and how do I find it? Thank you for your time. An is the nth number in the sequence, and is defined by the

Precalculus
The roots of \[z^7 = \frac{1}{\sqrt{2}}  \frac{i}{\sqrt{2}}\]are $\text{cis } \theta_1$, $\text{cis } \theta_2$, $\dots$, $\text{cis } \theta_7$, where $0^\circ \le \theta_k < 360^\circ$ for all $1 \le k \le 7$. Find $\theta_1 + \theta_2 + \dots +

Calculus
Please look at my work below: Solve the initialvalue problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/ Sqrt(4^24(1)(6)))/2(1) r=(16 +/ Sqrt(8)) r=8 +/ Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2

Inequality
When I solve the inquality 2x^2  6 < 0, I get x < + or  sqrt(3) So how do I write the solution? Is it (+sqrt(3),sqrt(3)) or (infinity, sqrt(3))? Why? Thanks. So would this work? abs x < ( sqrt 3 ) or  sqrt 3

Algebra 2
Operations with Complex Numbers Simplify. 1. sqrt(144) 2. sqrt(64x^4) 3. sqrt(13)*sqrt(26) 4. (2i)(6i)(4i) 5. i13 6. i38 7. (5 – 2i) + (4 + 4i) 8. (3 – 4i) – (1 – 4i) 9. (3 + 4i)(3 – 4i) 10. (6 – 2i)(1 + i) 11. (4i)/(3+i) 12. (10+i)/(4i)

algebra,math,help
Use Property 2 to simplify each of the following radical expressions. sqrt (10)/ sqrt(49) My answer: sqrt (10) / (7) THis next one i need help: Use the properties for radicals to simplify each of the following expressions. Assume that all variables

Geometry
What is the minimum distance between any point on the circle x^2 + y^2 = 25 and the line y = \frac{3}{4}x + \frac{75}{4} ?

physics
How can the alternative definition of power: P = \frac{w}{\Delta t} = F \frac{d}{\Delta t} ... can be derived by substituting the definitions of work and speed into the standard definition of power, P =\frac{W}{\Delta t}. (Equations written without latex

math
The figure below shows the ellipse $\frac{(x20)^2}{20}+\frac{(y16)^2}{16}=2016$. [asy] defaultpen(linewidth(0.7)); pair c=(20,16); real dist = 30; real a = sqrt(2016*20),b=sqrt(2016*16); xaxis("x",c.xadist,c.x+a+3*dist,EndArrow);

some algebra help (radicals)
I hope I am writing this down right.. I am trying to do some practice questions to learn 10^5 (sqrt)2y  4^5 (sqrt)2y I am trying to figure out how to solve this They gave us some answers to choose from, but I am clueless on how to solve this 6y ^5 (sqrt)2

Calculus (Area Between Curves)
Find the area of the region bounded by the curves y=x^(1/2), y=x^(2), y=1 and y=3. You get: a.) 1/2(sqrt(3)) + 4/3 b.) 2(sqrt(3))  8/3 c.) 1/2(sqrt(3)  32/3 d.) 2(sqrt(3))  32/3 e.) 8/3  2(sqrt(3))

Quantum Physics
I try to make a Quantum Fourier Transformation with N=6: w=e^(2*pi*7/6) so we have 6th roots: 1,w,w^2,1,w,w^2 My matrix is QFT6= 1/sqrt(6)* (1 1 1 1 1 1 ) (1 w w^2 1 w w^2) (1 w^2 w 1 w^2 w ) (1 1 1 1 1 1 ) (1 w w^2 1 w w^2 ) (1 w^2 w 1

horizontal tangent
f(x) = sqrt(x^2 + 0.0001) At x = 0, which of the statements is true. a)f is increasing b)f is discontinuous c)f has a horizontal tangent d)f' is undefined Answer is c but why? f(x,y) = sqrt(x^2 + y) g(x,y) = df/dx = 1/(2*sqrt[x^2 + y]) * 2x = x/sqrt[x^2 +

precal
Find the roots of the function f(x)= x^2+2x+2 Determine f(x) a) (x+1i)(x+1+i) b)(x+1i sqrt of 2)(x+1+i sqrt of 2) c)x1+i)(x1i) d)x1+i sqrt of 2) (x1i sqrt of 2) Please Help! For all of these, use the rule [f(x) + ai]*[(f(x)  ai} = [f(x)]^2 + a^2

subscripts and superscripts enabled
Examples: The water molecule: H20 Quadratic: ax2 + bx + c = 0 Just like you would use the b tag for bold or the i tag for italic, use the sub and sup tags for subscript and superscript. that's great...but what do you mean "b tag" and "i tag" ?? the b tag

Physics
The equation describing the (r, \theta ) coordinates of points along a single field line of a magnetic dipole is r=R_0 \sin ^2(\theta ) where \theta =0 is in the direction of the dipole moment and R_0 is a constant which is different for each field line.

math please help!!
For what values of x is the graph of y = 8e^−x^2 concave down? (Enter your answer using interval notation.) I started by finding the second derivative and factoring and ended up getting 16e^x^2 (2x^21) and I know up till this part that I'm doing the

Calculus (please check my answer)
Find the Avrage value of the function i=15(1e to the power of 1/2 t) from t=0 and t=4? A.7.5 sqrt 1+4e^2 e^4

Algebra
a and b are positive numbers that satisfy the equation \frac {1}{a}  \frac {1}{b} = \frac {1}{a+b} . Determine the value of \frac {a^6}{b^6} + \frac {b^6} {a^6} .

math
Let k be a positive integer and let X be a continuous random variable that is uniformly distributed on [0,k]. For any number x, denote by ⌊x⌋ the largest integer not exceeding x. Similarly, denote frac(x)=x−⌊x⌋ to be the fractional part of x. The

Math Advanced Functions
1) what kind of functions are the following equations: a) x12.4=\left(0.5y0.8\right)^{2}\left\{12.307\le x\right\}\left\{1.6153\le y\right\} b) x13.54=0.38\sin\left(1.1y6\right)\left\{11.306\le y\le12.66\right\} c)

Simple Calculus
Evaluate \displaystyle \lim_{x \to 0} \frac{\sqrt{2}x}{\sqrt{2+x}\sqrt{2}}.

math
if a=52\sqrt{6} then find the value of a^2+\frac{1}{a^2}

Precalculus
The roots of \[z^7 = \frac{1}{\sqrt{2}}  \frac{i}{\sqrt{2}}\]are $\text{cis } \theta_1$, $\text{cis } \theta_2$, $\dots$, $\text{cis } \theta_7$, where $0^\circ \le \theta_k < 360^\circ$ for all $1 \le k \le 7$. Find $\theta_1 + \theta_2 + \dots +

Algebra 1B
How do I solve \sqrt{\frac{33xy^{3}}{\sqrt{3x}}}? I am getting so confused and I need help please!

trig
{Given: cos(A)=\frac: sqrt{203}/{18} {Find: tan(A) Find the positive value of the above in simplest radical form.

math
If x= \frac{ \sqrt{a+2b} + \sqrt{a2b} }{ \sqrt{a+2b}  \sqrt{a2b} } Show that: bx^2ax+b=0

Math
How do you find a square root of a number that's not a perfect square? I'm very confused. The book doesn't explain it too well. You can approximate it or simplify it in terms of (products of) square roots of smaller numbers. E.g. consider sqrt[117] The

Math Help please!!
Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine them. sqrt 3* sqrt 15=

Algebra
How many ordered pairs of solutions (a, b) are there to \frac{a}{b}  \frac{b}{a}  \frac{2}{a}  \frac{2}{b} = 0, where a and b are integers from 100 \leq a,b \leq 100?

Calculus
"Leave the answer as a definite integral, but indicate how it could by evaluated by using the fundamental theorem of calculus." I solved the problem to a definite integral. Proceeding via the fundamental theorem, would involve finding the indefinite

Algebra
Rationalize the denominator. frac{4}{\sqrt[3]{100x}}

Math(Roots)
sqrt(24) *I don't really get this stuff.Can somebody please help me? The square root of 24 is 4.898979485566356 I know that..lol,but it says not to use decimals.Here is an example they gave me. Ex.sqrt(18)=sqrt(2*3*3)=3sqrt(2) sqrt[24] = sqrt[4*2*3] =

calculus, help!
Evaluate the definite integral: int_{1}^{e^9} \frac{dx}{x \sqrt{\ln x}} = i gt my answer as 1^(e^9) but it's saying it's wrong

Math/Calculus
Solve the initialvalue problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? Thanks. y''+4y'+6y=0, y(0)=2, y'(0)=4 r^2+4r+6=0, r=(4 +/ sqrt(164(1)(6))/2 r=2 +/ sqrt(2)*i , alpha = 2, beta = 2(sqrt(2))

MATH
For each set of numbers, draw your own number line on a piece of paper, taking care to plot each pair of irrational numbers. Then write a statement comparing the position of the two given numbers on a number line. Also write an inequality comparing the two

Engineering Math, Newtons Cooling Method
Newton's equation for a free falling object with air resistance of mass m kilograms says that its velocity v(t) satisfies the DE mv'(t) = mg  kv(t) where g = 9.8 \frac{m}{s^2} and v(t) is measured in \frac{m}{s}. Suppose that k=2 \frac{kg}{sec} and that a

Algebra 2: Radicals URGENT!!
Could some kind, saintly soul help me solve this problem? Simplify: 8w sqrt(48w^5)  x^2 sqrt(3xw^2) . . =8w(√16)(√3)(√w^4)(√w)  x^2(√3)(√x)(√w^2) =32w^3(√3w)  wx^2(√3x) not much of a "simplification" really 8w sqrt(16*3w^5)  x^2 w

Calculus  Second Order Differential Equations
Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initialvalue problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/ Sqrt(4^24(1)(6)))/2(1) r=(16 +/ Sqrt(8)) r=8 +/ Sqrt(2)*i,

Calulus
Given \displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a  \frac{b\pi^2}{c}, where a, b and c are positive integers and b and c are coprime, what is the value of a + b + c?

mathematics
Add. Express the answer in simplest form. 2\frac{2}{3} 4\frac{5}{12}

Geometry
What is the minimum distance between any point on the circle x^2 + y^2 = 25 and the line y = \frac{3}{4}x + \frac{75}{4} ?

Mathematics
sqrt 6 * sqrt 8 also sqrt 7 * sqrt 5 6.92820323 and 5.916079783 So you can see the steps — sqrt 6 * sqrt 8 = sqrt 48 sqrt 7 * sqrt 5 = sqrt 35 I hope this helps a little more. Thanks for asking.

Calculus
a and b are integers that satisfy: \displaystyle \lim_{x \to 1} \frac{x1}{x^2ax+b} = \frac{1}{3}. What is the value of a+b?

math
How many pairs of integers $(b,c)$ satisfy the equation \[\frac{b + 7}{b + 4} = \frac{c}{9}?\]

algebra
How many pairs of integers $(b,c)$ satisfy the equation \[\frac{b + 7}{b + 4} = \frac{c}{9}?\]

Math
Find of g(f(x)) when f(x)=sqrt(x+3) and g(x)=(x^2+2)/x. a. g(f(x))=(x^2+2)(sqrt(x+3))/x b. g(f(x))=(x+5)/(sqrt(x+3)) c. g(f(x))=(x^2+6x+11)/(sqrt(x+3)) d. g(f(x))=(sqrt(((x^2+2)/x)+3) Every time I work this problem, I get some crazy answer. Can someone

Calculus
An object's movement has a velocity given by v(t) = t^25t+5 A) What is the position function for the particle at any time t≥0? For this section I calculated the anti derivative, which is \frac{1}{3}t^3\frac{5}{2}t^2+5t+C (At least I think it is) And

Advanced Math
Can someone check these for me? Please? Use halfangle identity to find the exact value of cos165 degrees. (1/2) sqrt(2+sqrt(3)) Write the equation 2x+3y5=0 in normal form. (2sqrt(13)/13)x (3sqrt(13)/13)y+ (5 sqrt (13)/13) = 0 Find the distance between

Precalculus
I really need help on this as I have tried multiple times and my answers are none of these. Please help 1. Find (f*g)(x) where f(x)=1/(x^2+3) and g(x)=sqrt(x2). a. (f*g)(x)=1/x2 b. (f*g)(x)=1/sqrt(x2)+3 c. (f*g)(x)=1/x+1 d. (f*g)(x)=sqrt(2x^25/x^2+3)

math
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y= \cos(x), x = \frac{\pi}{2}, x = 0 about the axis y= 3 You might need to use the identity: cos^2(x) = \frac{1}{2}(cos(2x) + 1).

Calculus
Given f(x) = \frac{x^32x+5}{x+4} and f’(3) = \frac{a}{b}, where a and b are coprime positive integers, what is the value of a+b?

Algebra
Solve for s: h=(square root of 3)times s/2 and solve for h V= (pi)r squared h / 3 Solve for s: h=(square root of 3)times s/2 Multiply both sides by 2. 2h = (sqrt 3)*s*2/2 which cancels the 2 on the right. 2h = (sqrt 3)*s Now divide the right side by

Math:)
1. Evaluate tan[sin^1(a)]. a. [sqrt(1a^2)]/1a^2 b. [sqrt(1a^2)]/a c. sqrt(1a^2) d. {a[sqrt(1a^2)]}/1a^2 I do not know the steps to find this answer and am not provided with a textbook. I have researched online some what, but I cannot seem to

Chemistry problem
The formula for the MaxwellBoltzmann distribution is given below,where y is proportional to the fraction of particles of molecular mass m at temperature T traveling at speed u. The expression frac(u1,u2) gives the fraction of particles between speeds of

math help
15sqrt8x^15/5sqrt2x^4 remember that sqrt(a)/sqrt(b) = sqrt(a/b) simplify the inside. also notice that sqrt(x^11) = sqrt(x^10) * sqrt(x) = x^5 * sqrt(x)

Algebra
Multiplying sq rts sqrt18a^7b times sqrt27a^8b^6 Jake 1214 18 = 9 * 2 then sqrt 18 = 3sqrt2 sqrt a^7 = a^3 * sqrt a 27 = 9 * 3 then sqrt 27 = 3 sqrt3 sqrt a^8 = a^4 sqrt b^6 = b^3 Now just multiply the liketerms together. 3sqrt6 and sqrt2a^4?

linear algebra check
Use the GramSchmidt process to transform the basis [1 1 1] , [0 1 1] , [2 4 3] for the Euclidean space R3 into an orthonormal basis for R3. (Enter each vector in the form [x1, x2, ...]. Enter your answers as a commaseparated list.) so i went through the

math
how would you simplify this equation: y = (x+3)/[(4sqrt(16+h))] please help me! you have three variables. I am not certain "simplify" is an appropriate term here. ohhhh it was my mistake. I meant: y = h/[(4sqrt(16+h))] y = h/[(4sqrt(16+h))] rationalize

Math
For f(x) = 2sinx + (sinx)^3 + tanx find f'(pi/3). Ok, so what I tried was... f'(x) = 2cosx + cosx(3(sinx)^2) + (sinx/cosx) pi/3 = (1/2, sqrt(3)/2) therefore, 2(1/2) + 1/2(3(sqrt(3)/2)(sqrt(3)/2) + (sqrt(3)/2 (2/1)) 1 + .5(3 (3/4)) + sqrt(3) 1 + .5(9/4) +

Calculus
Graph the curve and find its exact length. x = e^t + e^t, y = 5  2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t  e^t, correct? dy/dt = t^2  5t, correct? So: Integral from 0 to 3 of Sqrt[(e^t  e^t)^2 +

calculus
At a summer campfire, the radius of a marshmallow on a stick expands at the rate of \ {r ' (t)} = \frac{2.1 }{1 t + 5} mm/s where t is the time of heating in seconds. Initially the radius was 3.8 mm. Find the radius after 27 seconds using the following

Math
Use a halfangle identity to find the exact value of tan 15° a. √ 7+4 sqrt 2 b. √ 7+4 sqrt 3 c. √ 74 sqrt 2 d.√ 74 sqrt 3

physics
Two speakers emit sounds, the one with an intensity of 3.19 x 10^{7} \frac{W}{m^2} and the other 8.64 x 10^{8} \frac{W}{m^2}. What is the difference in their intensity level? \Delta \beta =

Trigonometry
Given \tan \theta = \frac{4}{3}, where \frac{\pi}{2} < \theta < \pi, what is the value of \frac{1}{\sin \theta + \cos \theta}?

Algebra
If a, b and c are nonzero reals such that a + b + c = 11 and \frac {1}{a} + \frac {1}{b} +\frac {1}{c} = 0, what is the value of a^2 + b^2 + c^2?

Algebra
If a, b and c are nonzero reals such that a + b + c = 11 and \frac {1}{a} + \frac {1}{b} +\frac {1}{c} = 0, what is the value of a^2 + b^2 + c^2?

calculus
At a summer campfire, the radius of a marshmallow on a stick expands at the rate of \ {r ' (t)} = \frac{2.4 }{3 t + 6} mm/s where t is the time of heating in seconds. Initially the radius was 3.8 mm. Find the radius after 16 seconds using the following

calculus
prove that d/dx 4x .√(x + √x) = 6x+5 (x)1/2/√(x + √x) solution is d/dx 4x.[x+(x)1/2]1/2 = d/dx 4x.[x+(x)^1/2]^1/2 d/dx 4x.[x+(x)^1/2]^1/2 Product Rule = 4x[1/2(x+(x)^1/2)^1/2 * (1+1/2x^1/2) +[x+(x)^1/2]^1/2*4 d/dx(4 x sqrt(x+sqrt(x))) = (2 (1/(2

Algebra
In a certain positive fraction \frac{a}{b} , the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by 1 \frac{1}{15} . Find a + b .

mathematics,
Zoey made 6\frac{1}{2}6 1 2 cups of trail mix for a camping trip. She wants to divide the trail mix into \frac{3}{4}3 4 cup servings. Thirteen people are going on the camping trip. Can Zoey make enough \frac{3}{4}3 4 cup servings so that each person on the

Calculus check
Given f(x)=x^4(2x^215). On what interval(s) is the graph of f concave upwards? A. (0, sqrt(3)) B. (sqrt(3), 0) C. (sqrt(3), 0) and (0, sqrt(3)) D. (sqrt(3), sqrt(3)) E. (Negative infinity, sqrt(3)) and (sqrt(3), infinity) I got E

Trigonometry
ABC is a right triangle with AB = 2, BC = 3\sqrt{5}, AC = 7 and \angle ABC = 90^\circ. If \cos \angle BAC = \frac{a}{b}, where a and b are coprime positive integers, what is the value of a + b?

Calculus
Find d/dx integral(with upper bound of 4x and lower bound of 1) of square root of t^2 +1 dt. A. sqrt(4x+1) B. sqrt(16x^2+1) + sqrt(2) C. 4 sqrt(16x^2+1) D. sqrt(16x^2+1)

Calculus
so we are doing integrals and I have this question on my assignment and I can't seem to get it, because we have the trig substituion rules, but the number isn't even so its not a perfect square and I just cant get it, so any help would be greatly

Calculus
I need to find the exact solution to: 2sin2x = sqrt(x)on the interval (0,pi) This is how I started it, but I don't think it's correct. sin2x = sqrt(x)/2 2sinxcosx = sqrt(x)/2 sinxcosx = sqrt(x)/4 What do I need to do now? need to find the exact solution