Answer:
OPTION A: 2x + 3y = 5
Step-by-step explanation:
The product of slopes of two perpendicular lines is -1.
We rewrite the given equation as follows:
2y = 3x + 2
⇒ y = 
The general equation of the line is: y = mx + c, where 'm' is the slope of the line.
Here, m =
.
Therefore, the slope of the line perpendicular to the line given =
because
.
To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:
y - y₁ = m(x - x₁)
The point is: (x₁, y₁) = (-2, 3)
Therefore, the equation is:
y - 3 =
(x + 2) $
⇒ 3y - 9 = -2(x + 2)
⇒ 3y - 9 = -2x - 4
⇒ 2x + 3y = 5 is the required equation.
Answer:
c = 0.165
Step-by-step explanation:
Given:
f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,
f(x, y) = 0 otherwise.
Required:
The value of c
To find the value of c, we make use of the property of a joint probability distribution function which states that

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)
By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have

Since c is a constant, we can bring it out of the integral sign; to give us

Open the bracket

Integrate with respect to y

Substitute 0 and 3 for y



Add fraction


Rewrite;

The
is a constant, so it can be removed from the integral sign to give


Integrate with respect to x

Substitute 0 and 3 for x




Multiply both sides by 


Answer:
1st question is 1:2
2nd question is 5
Step-by-step explanation:
15 times two is 30, so if you divide both 15 and 30 by 15, you get 1:2
Divide 300 and 60 and you get 5.
Hi there!
Question 1:
For this, we are taking away 1/4 yards of spring from 7/8 yards. This is essentially just subtracting 1/4 from 7/8. This then gives us the equation:

Now, to subtract these, we want to make it so the denominators are the same, or the numbers on the lower half are the same. (One way to explain why this is true is:
). Now, to make it so the denominators are the same, we can multiply the second fraction, 1/4, by 2/2 as 2/2 is essentially 1, and multiplying by 1 will get the same result, just with a denominator switched in this case. Doing this, we get:


Now, subtracting the numerators, we get:
yards of string will remain.
Question 2:
For this, we are combining these two thicknesses, and thus we add 1/4 to 7/12. This gives us the equation:

Now, we again want to make it so the denominators are the same. (Here's a similar proof but for addition this time:
). Now, to make the denominators the same, we can multiply the first fraction, 1/4, by 3/3 (also equivalent to 1). Doing this, we get:


, which is equivalent to (dividing both the top and the bottom by 2)
inches.
Hope this helps!
The answer should be X= 3.60m