For this case, what we must do is solve the following system of equations: tan (50) = h / x tan (40) = h / (x + 50)
Solving the system we have: (x + 50) * tan (40) = h (x) * tan (50) = h
Matching: (x + 50) * tan (40) = (x) * tan (50)
Rewriting: x (tan (50) - tan (40)) = 50 * tan (40) x = 50 * tan (40) / (tan (50) - tan (40)) x = 118.9692621
Substituting: h = (x) * tan (50) h = (118.9692621) * tan (50) h = 141.7820455
B. 141.8ft
The dimensions of the rectangle are determined by setting up and solving a quadratic equation using the Pythagorean theorem, based on the provided conditions; the width of the rectangle is 'w', its length is 'w + 3', and the length of the diagonal is 15 inches.
In this problem, we are exploring the dimensions of a rectangle. Let's represent the width of the rectangle as 'w'. Then its length, according to the problem, is 'w + 3'. Next, we will apply the Pythagorean theorem because we are told the length of the diagonal is 15. In a rectangle, the diagonal, the length, and the width form a right triangle.
Applying the Pythagorean theorem, we get: (w)^2 + (w + 3)^2 = (15)^2. Solving this quadratic equation will give us the values for w and consequently for the length.
Take into account that the unit for these measures is in inches.
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The value of diameter is,
⇒ d = 16 mm
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
A cylinder has surface area of 256 π square millimeters and a height of 8 millimeters.
Since, We know that;
Surface area of cylinder is,
SA = 2πrh + 2πr²
Here, We have;
SA = 256π
h = 8 mm
Hence, We get;
256π = 2π × r × 8 + 2π × r²
128 = 8r + r²
r² + 8r - 128 = 0
r² + 16r - 8r - 128 = 0
r (r + 16) - 8 (r + 16) = 0
(r - 8) (r + 16) = 0
r = 8 mm
Hence, The value of diameter is,
d = 2 x 8
d = 16 mm
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Answer:
I believe the answer is 32.
Answer:
see below
Step-by-step explanation:
You solve an equation by undoing what is done to the variable. When the variable is squared, as here, you undo the squaring by taking the square root. Any operation you do on one side of the equation must also be done on the other side. Hence, you take the square root of both sides of the equation.
As per the concept of unitary method, Aaron collected 7 shells.
Let's assume that Aaron initially collected "A" shells, and Maria initially collected "M" shells.
According to the first piece of information, Maria had three times as many shells as Aaron: M = 3A.
Now, according to the second piece of information, if Aaron had found 8 more shells and Maria had found 6 fewer shells, their final shell counts would have been the same. So, Aaron's final count would be A + 8, and Maria's final count would be M - 6.
Given that the final counts are equal, we can set up an equation:
A + 8 = M - 6.
Now, we can substitute the value of M from the first piece of information (M = 3A) into the equation above:
A + 8 = 3A - 6.
Next, let's solve for A:
8 + 6 = 3A - A,
14 = 2A.
Finally, we can find the value of A by dividing both sides of the equation by 2:
A = 14/2,
A = 7.
So, Aaron collected 7 shells.
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