This is a nice "rates of change" problem from Calculus.
Let the length and width of the rect. be L and W. We are given the following info:
dL/dt = 6 cm/s; dW/dt = 4 cm/s; L = 11 cm and W = 5 cm.
The area of the rect. is A = L*W. Differentiating,
dA/dt = L(dW/dt) + W(dL/dt).
Subst. the given info: dA/dt = (11 cm)(4 cm/sec) + (5 cm)(6 cm/sec).
Just evaluate this to find dA/dt: (44 + 30) cm^2/sec = 76 cm^2/sec
Answer:
4145
Step-by-step explanation:
3x+7x-28+31-8x x=2043
2x+59
4086+59
4145
Step-by-step explanation:
Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.
By interior angle sum postulate of a triangle:
a + b + c = 180°... (1)
Therefore, by remote interior angle theorem:
x = b + c.... (2)
y = a + c..... (3)
z = a + b.... (4)
Adding equations (2), (3) & (4)
x + y + z = b + c + a + c + a + b
x + y + z = 2a + 2b + 2c
x + y + z = 2(a + b + c)... (5)
From equations (1) & (5)
Thus, the sum of exterior angles so formed is equal to four right angles.
Proved.
The system of equation is y = 300 + 3x and y = 250 + 5x and the number of visits is 25
<h3>The system of equations </h3>
The given parameters are:
<u>Jim's Gym</u>
- Initial fee = $300
- Charges = $3 per visit
<u>Sally's Salon</u>
- Initial fee = $250
- Charges = $5 per visit
The equation is calculated as:
Total (y) = Initial * Charges * Number of visits (x)
So, the system of equation is
y = 300 + 3x
y = 250 + 5x
<h3>Number of visits before the plans are equal</h3>
We have:
y = 300 + 3x
y = 250 + 5x
Substitute y = 300 + 3x in y = 250 + 5x
300 + 3x = 250 + 5x
Evaluate the like terms
-2x = -50
Divide by -2
x= 25
Hence, the number of visits is 25
Read more about system of equations at
brainly.com/question/12895249
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Answer: 15.72575
Step-by-step explanation:
Divide 250 over:
40/250=(0.89)^x
Log both sides (easiest with graphing calculator)
Remember exponent comes down in front on a log
Log(0.16) = x log (0.89)
X= Log (.16) / log (0.89)