It's not clear from your problem statement if the larger bed is 2 m longer is diameter or in radius. I'm going to assume it's 2 m longer in radius because it works out better. Let r = the radius of the smaller bed. The larger bed has a radius of r+2. Their combined areas...
V(t) = 10ekt
In 2002, t = 2002 - 1975 = 27:
V(27) = 10e27k
20 = 10e27k
2 = e27k
ln(2) = 27k
ln(2)/27 = k
This is the exact answer. If you want an approximate answer, use your calculator to compute the value of ln(2)/27.
The standard form of a quadratic equation is:
y = ax2 + bx + c
where a, b, and c are constant values called coefficients. In your equation,
a = 5, b = -1, and c = 1. If a > 0, then the parabola opens upward. If
In all of these types of problems, you need to draw a diagram and find the right triangle. In this case:
One leg of the triangle runs horizontally from the boat to the base of the cliff and equals 128 feet
The other leg runs vertically from the base to the top of the cliff, so it's...
You don't get the same answer because multiplying 0.23 by 50 is not the right procedure. If you turn 23 into 0.23, you need to divided it by 0.50:
23/50 = 0.23/0.50 = 0.46 = 46%
Another way to think of it is that 0.5 = (1/2):
0.23/0.5 = 0.23/(1/2)...
Assuming the temperature remains constant, you can use Boyle's Law:
P1V1 = P2V2
P1 = starting pressure = 20 atm
V1 = starting volume = 500 ml
P2 = final pressure = 14 atm
V2 = final volume = ? ml
Plug in the numbers and solve for V2.
Draw a picture of the situation.. The ladder makes a 45-45-90 right triangle with the ground and the wall. The ladder is the hypotenuse and equals 10 feet. The two legs are equal,. One leg is the horizontal distance of the foot of the ladder from the wall and the other is...
Let x = the amount you need to earn on day 5:
$170 = ($110+$230+$230+$160+x) / 5
$170 = ($730 + x) / 5
$850 = $730 + x
Solve for x.
! + 3 + 2 = 6, so the sand uses 3/6 = 1/2 of the 30 shovelfuls:
(1/2) (30) = ____?
Let x = the length and x-4 = the width:
Area = (length)(width)
96 = x(x-4)
96 = x2 - 4x
0 = x2 - 4x - 96
0 = (x-12)(x+8)
x = 12 and -8. Since you can't have a negative length, x = 12.
Perimeter = 2(length) + 2(width)
16x2 - 64x + 7y2 = 48
Complete the square on the x terms:
16(x2-4x+4) + 7y2 = 48 + 16·4
16(x-2)2 + 7y2 = 112
Divide by 16·7 (=112):
(x-2)2/7 + y2/16 = 1
This is the equation of an ellipse centered...
f(x) = -13x + 7
-42 = -13x + 7
Solve for x.
You want ax + b = 4/x at x = -1
a(-1) + b = 4/(-1)
-a + b = -4
You also want ax + b = 2/x when x = 1/2
a(1/2) + b = 2/(1/2)
a/2 + b = 4
You need convert meters to miles and minutes to hours. The conversion factors are:
1 mile = 1609.344 meters
1 hour = 60 minutes
(300 m/min)(1/1609.344 mi/m)(60 min/1 hour) ≅ 11.18 ... mph
Not all that fast.
Let r = the radius of circle A. The radius of circle B is twice as big (2r). Their circumferences are:
CA = 2 pi r
CB = 2 pi 2r = 4 pi r
CA + CB = 2 pi r +4 pi r
81 pi = 6 pi r
Solve for r. The diameter of circle...
For (a) just plug in x = -4 into f(x) and compute the answer.
f(x) = -x2 + 5x -2
f(-4) = -(-4)2 - 5(-4) - 2 = ____?
For (b), just replace the x with -b. Some of the signs will change.
x3 + 3x2 = 4
x3+ 3x2 - 4 = 0
To factor, we want three factors of -4 that add to +3: Answer: 2·2·(-1) = -4, 2+2+(-1) = 3.
(x+2)(x+2)(x-1) = 0
(x+2)2(x-1) = 0
x = -2 and x = 1
Since you can't have a negative...
y = 4x · x2
y = eln(4^x) · x2
y = ex ln(4) · x2 [Log Property: ln(ab) = b ln(a)]
Use the Product Rule to find the derivative. Remember that ln(4) is just a constant.
It always helps to draw a diagram and find the right triangle. In this case, the triangle has the loading dock as one leg, the ramp as the hypotenuse, and the distance of the ramp from the loading dock as the other leg. Call that distance x. Use the tangent of 24o to find x.
Since 19 is a prime number, the only possible dimensions for the prism are 19 × 1 × 1; that is , L=19, W = 1, H = 1. That corresponds to lining the 19 cubes up in one long row.
SA = 2(LW + LH + WH) = 2(19 + 19 + 1) = 78 cm2