Steve 2.0

well, there is always at least one real root for a cubic. Just not always rational. Since f(-6) = -24 f(-5) = 30 you know there is a root inside (-6,-5). The work comes in narrowing it down a bit more.

11 years ago

If you want the graph shifted up by 12, then you need to add 12 to all the values of f(x): g(x) = f(x)+12 = x^2+15

11 years ago

well, there are lots of methods. An easy one is bisection. Since you know the root is between -6 and -5, try -5.5 f(-5.5) = 6.625 Now you know that the root r is in (-6,-5.5), so try -5.75 f(-5.75) = -7.73 r is in (-5.75,-5.5) f(-5.625) = -0.322 each time...

11 years ago

no use for derivatives here. 90% of capacity is 7200 fish So, just solve for t when P(t) = 5000 or 7200

11 years ago

(1/2)^t/5730 = .16 t/5730 = log(.16)/log(.5) t = 5730*log(.16)/log(.5) t = 15149 makes sense. 12.5% left would be three half-lives, or 17190 years

11 years ago

degree of a polynomial is the highest power of x. in this case, 2.

11 years ago

The slant height of the cone is the original radius of the paper circle. So, r = 10 The new circumference of the base is .6 of that, so 40% of the circle was lost. 40% of 360° is 144°.

11 years ago

there is no common denominator. π is irrational! That means it cannot be expressed as a ratio of two integers.

11 years ago

looks good to me

11 years ago

yes, if you lose the space. More common would be 3A.

11 years ago

Hmmm. z - 1/5 > 1/4 z > 1/4 + 1/5 z > 9/20 You don't swap direction unless multiplying or dividing by a negative value. Addition and subtraction do not affect the sense of the inequality.

11 years ago

well, just plug in n=9 A(9) = -14 + (9-1)(2) = 2

10 years ago

correct

10 years ago

Or, you can reason that since y=kx, y/x is constant. So, 14/-4 = y/-6 y=21 And you don't even have to figure out what k is.

10 years ago

First, it's "heading" or "course," <b>not</b> "bearing." Just figure the x- and y-displacements for each leg of the trip. Add them up for a final location. Then figure the distance and (yes) <u>bearing</u> of the port from there. What do you get? I'll che...

10 years ago

The population by 4000 for 15 years, or 60,000 So, it must have been 450,000-60,000 = 390,000 in 2010 p(x) = 390 + 4x

10 years ago

64 = 4^3 so log_4(64) = 3log_4(4) = 3*1 = 3

10 years ago

If you mean |x|-15 then as usual, the graph is shifted down 15 units. It's a lot easier to figure out what you mean if you just use proper notation. If you meant |x-15| then none of the choices is correct.

10 years ago

any line y = -1/12 x + c will be parallel to that line, for any value of c that you like.

10 years ago

4s+6h = 52 2h = s+1 Now you can find both costs.

10 years ago

For x people, we have A: 50+25x B: 130+20x So, you want 50+25x = 130+20x

10 years ago

v = 2pi*r*w just watch the units: w = /min r = ft, so c=2pi*r = ft

10 years ago

figure the length of the diameter d, using your distance formula. Then the area of the circle is A = πd^2/4

10 years ago

-(13x)^0 y^-7 z anything^0 = 1, so -z/y^7

10 years ago

(-2)^-3 (-24) = 1/(-2)^3 * (-24) = -24/-8 = 3

10 years ago

x/2 + 1 < 5/2 x/2 < 3/2 x < 3

10 years ago

t <= 9

10 years ago

∫te^at dt needs to be done with integration by parts, with u = t, du = dt dv = e^at dt, v = 1/a e^at Do all that and you have ∫0.02te^(-0.05t) dt = -(0.4t+8)e^(-0.05t) now just plug in the numbers

10 years ago

#1 any rational function with vertical asymptotes will do this: 1/(x-1)(x+1) #2 f(x) = x+1 for x <= 1 x-1 for x > 1 just any function where there is a finite break at some x value

10 years ago

if all you have is angles, there is no way to find the sides. All similar triangles have the same angles, but different sides. However, you do know that X/sin40 = Y/sin80 what's the stuff about a plane on top? What does that have to do with anything?

10 years ago

the radius is 60 135-60 = ?

10 years ago

well, now you know that d = p-3 - (p-5) = 2 2p-15 - (p-3) = 2, so p=14 so, a = p-5 = 9 n/2 (2*9 + (n-1)*2) = 180 n = 10

10 years ago

recall the chain rule fy/fx = dy/du du/dx #1: u=3x^3 dy/dx = -sin(u) (9x^2) = -9x^2 sin(3x^3) #2: u = x^4 + e^2x) dy/dx = 1/u du/dx = (4x^3 + 2e^2x)/ln(x^4+e^2x)

10 years ago

oops #2 is (4x^3 + 2e^2x)/(x^4+e^2x)

10 years ago

and it is correct or, as we usually write it, 1.25x10^-4 or 1.25 * 10^-4

10 years ago

well, what is (20x)^2 - pi(4x)^2 ?

10 years ago

since time = distance/speed, Mrs Healthy took 800m/(2400 m/hr) = 1/3 hr = 20 min So, Mrs Wise's speed = 800m/16min = 50m/min = 3000m/hr

10 years ago

6d^4+9d^3-12d^2 first, factor out the d^2 d^2(6d^2+9d-12) Now, how about a 3? 3d^2(2d^2+3d-6) Now, note that the discriminant is 57, so the roots will contain √57. No rational roots exist. Can't factor it any further using integers.

10 years ago

you are correct

10 years ago

right on

10 years ago

nope. There are exactly as many roots as the degree of the polynomial. In this case, 2, since the highest power is x^2. There are three terms, but only two solutions. Recall your quadratic formula. It only produces two values.

10 years ago

since the period is proportional to r^(3/2), replacing r with (9r) produces a period 9^(3/2) = 27 times longer.

10 years ago

me too.

10 years ago

42

10 years ago

max distance is when θ=45° so, use that to figure x- and y-components of initial velocity,

10 years ago

right on

10 years ago

pick one of the acute angles. Call it t. Label the opposite side x, and the hypotenuse h. Then sin(t) = x/h Do the same for the other angle and side, or use the Pythagorean Theorem to find the other side.

10 years ago

well, sin x = 12/37 cos x = 35/37 so, x is close to zero either (b) or (c) push the buttons and find out

10 years ago

tan 29.3° = 9/16, so width = diagonal * sin 29.3° length = diagonal * cos 29.3°

10 years ago

linear pairs add to 180, so (assuming the usual typos) x-30 + x+76 = 180 x = 77 Now you can figure the two angles.

10 years ago

since LMO+NMO = LMN, x+34 + NMO = 6x-28 But, MO bisects LMN, so LMO=NMO x+34 + x+34 = 6x-28 2x+68 = 6x-28 4x = 96 x = 24 Now you can figure the actual degree measures.

10 years ago

Good catch.

10 years ago

well, the distance between those points is the radius of the circle.

10 years ago

you can find the radius: it's the distance between the points.

10 years ago

f◦g = √(g-1) = √(x^2-1) You know that √n has domain n>=0. SO, you need (x^2-1) >= 0. g◦f = f^2 = (√(x-1))^2 = x-1 I'm pretty sure you can handle that one, right?

9 years ago

Find the lowest common denominator. The just sort the numerators. For example, 5/8,11/12,7/4,9/16 = 30/48, 44/48, 84/48, 27/48 Now you just have to sort 30,44,84,27 do the others in like wise.

9 years ago

AcTuAlLy if you BoThEreD to do WERK (sis) then you might know der!v@t!ve$

6 years ago

Yo I think that answer was wrong :skull:

2 years ago