Hello :
calculate the slope :
<span>2x + 5y = 10
5y = -2x +10
y = (-2/5)x +2
the slope is (-2/5)... (</span><span> parallel so : same slope )
an equation is : y - (-5) = (-2/5)(x-1)</span>
Answer:
Weight of the solution = 250 grams
Step-by-step explanation:
1) Consider the weight of solution as x grams.
32 % solution = 80 grams salt
32% of x = 80
(32/100)*x = 80
Solving for x:
x = (80*100) / 32
x = 250 grams
Let R = 250 ft. & r = 200 ft.
Now, Area of Gravel Path =
= πR² - πr²
= π(R²-r²)
Area of Gravel Path =
π ( 250² - 200² )
π ( 62500 - 40000 )
π ( 22500 )
Taking π as 3.14
As Option is nearest to our answer,
that means it will be right.
So,
Answer will be (c) 70686 ft.²
Answer:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
<h2>
Step-by-step explanation: PHEW THAT TOOK A WHILE LOL IM A FAST TYPER</h2>
Let's use common denominator. In this case, our common denominator would be 40.
3/5 = 24/40.
6/8 = 30/40
6/10 = 24/40.
So 3/5 and 6/10 are the same.