Answer:
8
Step-by-step explanation:
1) let’s take the original number as “x”
So
3x=28-0.5x
Lol don’t worry I’ll show you how I got that
So it says 3 times a number. That tells me my number, X is multiplied by 3 so I have
3x so far
Next it says “is equal to”, this tells me my number 3x is equal to something so I have this now:
3x=
After that it says “half of a number” so I know I will have 0.5x subtracted from 28. Since it says subtracted from 28 that means my number will be subtracted from 28, not the other way around so
3x=28-0.5X
Now I can solve this by bringing “-0.5” to the left.
3x+0.5x=28
3.5x=28
Divide both sides by 3.5 and
X=8
Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
and dividing everything by 2 to simplify a bit:
. Upon analyzing that equation, it looks like we need values for x, y,
, and
. And here's what we were given:
and
In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find
at the instant that
= .5.
Solving for x and y:
and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
so
and now we can fill in our derivative. Remember the derivative was found to be
so
and
and
and multiplying by the reciprocal of the left gives us:
so

Answer:
The value of x is 84 and the remaining angles are: 76° and 86°
Step-by-step explanation:
Given three angles are
18
x-8
and
x+2
We have to find the angles and for that we have to find the value of x
As we know that the sum of internal angles of a triangle is 180°
So,

And the angles are:
x-8 = 84-8 = 76
x+2 = 84+2 = 86
Hence,
The value of x is 84 and the remaining angles are: 76° and 86°
Geo is
an=a1r^(n-1)
2nd term is 12
4th term is 4/3
a2=a1r^(2-1)=12
a2=a1r=12
a4=a1r^(4-1)=4/3
a4=a1r^3=4/3
we have
a1r=12 and a1r^3=4/3
(a1r^3)/(a1r)=r^2=(4/3)/12=1/9
1/9=r^2
sqrt oth sides
1/3=r
the common ratio is 1/3