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There is a perfectly good calculator on the home page.

Find (LCD) of 56 and 78 .

I think you really want the HCF   Highest common factor    

I'll use the web2 calc to help

factor(56) = 2^3*7       =2     *2*2*7

factor(78) = (2*3)*13  = 2      *3*13

The only common factor other than one is 2 so 2 is the highest one.

Here is why

\(\begin{align}\frac{1}{7}&:\frac{1}{8}\\~\\ \frac{1}{7}\times \frac{56}{1}&:\frac{1}{8}\times \frac{56}{1}\\~\\ \frac{1}{1}\times \frac{8}{1}&:\frac{1}{1}\times \frac{7}{1}\\~\\ 8&:7 \end{align} \)

A clock that loses 10 minutes every hour is set correctly at 10:00. What is the correct time when the clock next reads 10:00? Thanks.

I decided to do it the super long way :)

Oops!  Careless of me.  Thank you Guest.

With x = -3, then y = -2, so the distance between (5,2) and (-3,-2) is:

\(\sqrt{(-2-2)^2+(-3-5)^2}\rightarrow4\sqrt5\)

Intersection is at x = -3 Alan.

"Determine the shortest distance from the point H(5, 2) to the line through points J(-6, 4) and K(-2, -4)"

I get the following:

.

Assuming the skier is travelling in the positive x-direction and the 22.5° angle is measured from the x-axis, then:

Fx = 105*cos(22.5°) - 74.8 N  ≈ 22.2 N

Fy = 105*sin(22.5°) N ≈ 40.2 N

.

"how do you simplify problems such as (1+sqrt(3)/3)/(1-sqrt(3)/3)"

.

12x^6-4x^4=3x^2*4x^4-4x^4=4x^4(3x^2-1)

That is easy.

The third of an imperial AU mouthful plus half a flipped bottle.

Desculpe, mas isso não se traduz muito bem.

Talvez você poderia reformular isso?

Simplify the following:
(1 + (sqrt(3))/(3))/(1 - (sqrt(3))/(3))

Put each term in 1 - (sqrt(3))/(3) over the common denominator 3: 1 - (sqrt(3))/(3) = 3/3 + (-sqrt(3))/(3):
(1 + (sqrt(3))/(3))/(3/3 + (-sqrt(3))/(3))

3/3 - (sqrt(3))/(3) = (3 - sqrt(3))/(3):
(1 + (sqrt(3))/(3))/((3 - sqrt(3))/(3))

Put each term in 1 + (sqrt(3))/(3) over the common denominator 3: 1 + (sqrt(3))/(3) = 3/3 + (sqrt(3))/(3):
(3/3 + (sqrt(3))/(3))/((3 - sqrt(3))/(3))

3/3 + (sqrt(3))/(3) = (3 + sqrt(3))/(3):
((3 + sqrt(3))/(3))/((3 - sqrt(3))/(3))

Multiply the numerator by the reciprocal of the denominator, (3 + sqrt(3))/(3 (3 - sqrt(3))/(3)) = (3 + sqrt(3))/(3)×3/(3 - sqrt(3)):
((3 + sqrt(3))×3)/(3 (3 - sqrt(3)))

((3 + sqrt(3))×3)/(3 (3 - sqrt(3))) = 3/3×(3 + sqrt(3))/(3 - sqrt(3)) = (3 + sqrt(3))/(3 - sqrt(3)):
(3 + sqrt(3))/(3 - sqrt(3))

Multiply numerator and denominator of (3 + sqrt(3))/(3 - sqrt(3)) by 3 + sqrt(3):
((3 + sqrt(3)) (3 + sqrt(3)))/((3 - sqrt(3)) (3 + sqrt(3)))

(3 - sqrt(3)) (3 + sqrt(3)) = 3×3 + 3 sqrt(3) - sqrt(3)×3 - sqrt(3) sqrt(3) = 9 + 3 sqrt(3) - 3 sqrt(3) - 3 = 6:
((3 + sqrt(3)) (3 + sqrt(3)))/(6)

Combine powers. ((3 + sqrt(3)) (3 + sqrt(3)))/(6) = ((3 + sqrt(3))^(1 + 1))/(6):
((3 + sqrt(3))^1 + 1)/(6)

1 + 1 = 2:
((3 + sqrt(3))^2)/(6)

(3 + sqrt(3))^2 = 9 + 3 sqrt(3) + 3 sqrt(3) + 3 = 12 + 6 sqrt(3):
(12 + 6 sqrt(3))/(6)

Factor 6 out of 12 + 6 sqrt(3) giving 6 (2 + sqrt(3)):
(6 (2 + sqrt(3)))/(6)

(6 (2 + sqrt(3)))/(6) = 6/6×(2 + sqrt(3)) = 2 + sqrt(3):
Answer: |2 + sqrt(3)

What is the parent function of y= -3 cos (2(x - pi/4))-1 

I am not so sure about this parent function term.  I am not at all sure that there is a definative answer.

If I was going to 'grow' this graph I would do it in this order.

1) cos(x)                             

2) cos(x-pi/4)                 graph moved pi/4 units to the right         

3) cos(2(x-pi/4))             Graph wavelength halved   (now pi units)

4) -cos(2(x-pi/4))            Graph turned upside down - reflected across the y=0

5) -3cos(2(x-pi/4))          amplitude increased from 1 to 3

6) -3cos(2(x-pi/4))-1       whole graph dropped one unit.

4 and 5 could be done in either order or both together.

So my lay use of the term would call all of the ealier functions parent functions....

Here is how I could build the graph.

Click on the circles at the side of the graph one at a time to see what is happening.

I know this is not much of an answer, I just thought you mjight find it interesting or helpful.

Thanks solver

It is handy to know that th co in front of sine stands for complementary and that complementary angles add to 90 degrees    (pi/2 radians)

so

\(cosine(\theta)=sine(90-\theta)\\ cotangent(\theta)=tangent(90-\theta)\\ cosecant(\theta)=secant(90-\theta)\)

The best way to approach this problem is to think about the polar form representation. So a complete circle is 2PI. In your case 

you have to find the tan inverse of the given value and then add 2PI to the angle value you obtain. 

use the identity \(cos(x) = sin(90-x)\)

Hence we can write this as

\(k(x) = 5sin(3\pi/4 - 2x) -3\)

So the parent function basically means the simplest mathematical equation to represent a curve. 

In this case its a sine curve. Now if you were to replace x with 2x, physically you are increasing the frequrency of the curve and by using the scalar -3 you are scaling and limiting it to the amplitude range of +3 and -3 instead of -1 to 1. This basically implies that the form remains the same in all cases as they all belong to the same family of cosine curves. 

for better understanding: 

http://fooplot.com/

Plot your cosine functions to see the change!

Statistical file:
{1.4, 4.3, 4.3, 0.7, 0.7}


Average (mean): μ=2.28
Absolute deviation: 8.08
Mean deviation: 1.616
Minimum: 0.7
Maximum: 4.3
Variance: 2.7856
Standard deviation σ=1.6690116836
Corrected sample standard deviation s=1.86601178989
Coefficient of variation cV=0.818426223635
Mode: {0.7, 4.3} - multimodal
Geometric mean: 1.66208107832
Harmonic mean: 1.23868312757
Sum: 11.4
Sum of absolute values: 11.4
Average absolute deviation: 1.616
Range: 3.6
 

So it wouldnt be y= -3 cos 2x ??

jk i know its obvious

no idea lol

visit my website

https://instabooknew.yooco.org/

The missing number is 53. 

\(4{sin}^{2}(x) =3\)

\(x= {sin}^{-1}(\sqrt{3} \div 2) \)

using standard value tables for sine

\(x= 60 deg\)