Answer:
The beam should be placed 8 feet from the center.
Step-by-step explanation:
The struts are y = √(x + 8) and y = √(x − 4). The struts are 2 feet apart at the location of the beam:
√(x + 8) − √(x − 4) = 2
Solving:
√(x + 8) = 2 + √(x − 4)
x + 8 = 4 + 4√(x − 4) + x − 4
8 = 4√(x − 4)
2 = √(x − 4)
x − 4 = 4
x = 8
Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
tan(x)/sec(x) = sin(x)
Hint: | Eliminate the denominator on the left hand side.
Multiply both sides by sec(x):
tan(x) = ^?sec(x) sin(x)
Hint: | Express both sides in terms of sine and cosine.
Write secant as 1/cosine and tangent as sine/cosine:
sin(x)/cos(x) = ^?1/cos(x) sin(x)
Hint: | Come to a conclusion.
The left hand side and right hand side are identical:
Answer: (identity has been verified)
First, we can use the slope formula to find the slope of the two points.
For points in the form of (x1, y1), (x2, y2). Plug in the points:
Subtract:
Divide:
So the slope is 3, we can plug this and one of the points into point-slope form first, and then convert it to slope-intercept form.
Where 'm' is the slope and (x1, y1) is a point on the line. Let's use (2, 4):
Now convert to slope-intercept form:
Distribute 3 into the parenthesis:
Add 4 to both sides:
Hello!
You can make this into two expressions based on what you know
let x stand for Devaughn's age
let y stand for Sydney's age
x = y + 10
x + y = 64
You can put x into the second equatoin
y + 10 + y = 64
Combine like terms
2y + 10 = 64
Subtract both sides by 10
2y = 54
Divide both sides by 2
y = 27
You can put y into the first equation
x = 27 + 10
combine like terms
x = 37
Devaugn is 37 and Sydney is 27
Hope this helps!
Y = mx+b
y - b = mx
(y - b)/x = m