Assuming the coefficient of kinetic friction is 0.60...
Draw a free body diagram listing all forces (I can't really show that to you on here). Since the speed is constant, the acceleration must be zero and thus the net force must be zero, so the horizontal force F must be equal to...
This question does not make sense: "a body was thrown from certain height and it covered the same distance in the first second and the last three second.what was the time taken by the body to reach the ground?"
Objects accelerate under gravity, so it's not possible for an object to...
First you have to complete the square with both the y and the x. Start by grouping together the x's and y's, and you might as well add 12 to both sides to get:
(x2 - 4x) + (y2 - 6y) = 12
Now complete the square, by dividing the -4 in front of the x by 2, and divide the...
If logab = x
then ax = b
What you have is:
log107 = k so 10k = 7
(the 'standard' logarithm, when no base is shown, is assumed to be base 10)
George is correct. It's a relatively simple integral, you just break it up into two parts (you can use the same method for the integral of any absolute value functions).
You integrate separately for x<0 and x>0:
Using some log laws:
log3(27x)2 = 2(log3(27x)) = 2(log327 + log3x) = 2(log333 + log3x) = ...
22 appears correct. If you let his age be S, then divide by the only even prime (2) and add four, it's equal to the LCM of of 5 and 3 (15), so:
S/2 + 4 = 15
For (i), we can treat the 2 papers as being one item (but they can be arranged in 2 ways), and we have to arrange 5 items. Let's call the math papers A and B so they can be arranged as A,B or B,A, and call the others C, D, E, F. So it can look like this for example:
(A, B) C, D, E, F, ...
Try using this form:
(x - h)2=4p(y - k)
Vertex is (h, k)
Your vertex is (1, 5), so h = 1 and
k = 5
Focus is (h, k+p).
Your focus is (1, -9) which means k + p = -9.
We know k = 5, so 5 + p = -9, which means p = -14.
I think you have the function f(x)= 4 - 2x2 and you want to evaluate it for when x = 4. If so, you're finding
f(4), so you'd plug in 4 as x, like so:
f(4) = 4 - 2*22 = ?
Difference of two squares factors in this way: a2 - b2 = (a + b)(a -b)
You can determine if it's a difference of two squares, by seeing if both terms are perfect squares, and can be written in the form a2 - b2. Michael already showed how to factor it.
eg. 4x2 - 25 can be written...
With inequalities, you mostly treat them the same as an equality, except when multiplying or dividing both sides by a negative number (that changes the direction of the inequality sign).
In this case, treat x + 3 > 2 the same way you'd treat x + 3 = 2. We want to get...
First try FOILing the two sets of parentheses:
x2 + 3x + 6x + 18 - 4 = 0
x2 + 9x + 14 = 0
Now do you know how to factor this? Look for two numbers that multiply to equal 14, and add up to 9, then you can put the factors into the parentheses:
point-slope form is: y = mx + b
We're given the slope, m = 2, so: y = 2x + b
We're also given it goes through (1,
-4) and those are x and
y, since points are given as (x, y).
Replace the y and x in:
y = 2x + b with
-4 and 1:
-4 = 2(1) + b
When you have ax2 + bx + c, the quickest way to factor it is to first multiply
a by c, and then find two factors that will multiply to equal a*c , add up to
b. Then you write (ax + _)(ax + _) with the two factors in the blank spots, then divide it all by
This problem may have been written incorrectly, as it only has complex number solutions (not part of algebra 1).
The exact (complex) solutions are:
x = 8(-1)3/5
x = -8(-1)2/5
Note: if you change the plus sign in 2x5/3 + 64=0 to a minus sign:
2x5/3 - 64=0
You can tell it diverges even before doing the integral, because at x = 2, the denominator of 4x2/(x3 - 8) is zero. There's a vertical asymptote at x = 2 (and that makes it difficult to find the area under the curve!).
Remember that that's the point of integration - to find the area under...
You can also cross multiply the fractions (which is unfortunately awkward to show in this answer box):
1/x + 1/x2 = (x2 + x)/(x*x2) then pull a factor of x from the numerator
x(x + 1)/x3 = (x + 1)/x2
Let's call the number x.
x2 + (x + 5)2 = 157
x2 + (x2 + 10x + 25) = 157
2x2 + 10x + 25 - 157 = 157 - 157
2x2 + 10x - 132 = 0 now divide both sides by 2
x2 + 5x - 66 = 0
You can use the quadratic formula here, but it looks...
Is this problem from a calculus class? Because I think that may be the only way to solve it, and it's a kinda long solution (and I left out a few things)... unless you just graph it and try to estimate.
It's a minimization problem. You need to use the distance formula
D = d2 = (x2...