8 times 9 - 7 + 4 times 5
Use PEMDAS. Parentheses, Exponent, Multiply, Divide, Add, Subtract
Multiply:
8 times 9 = 72
4 times 5 = 20
72 - 7 + 20
Add:
72 + 20 = 92
Subtract:
92 - 7 = 85
8 times 9 - 7 + 4 times 5 is equal to 85.
as you already know, the slope of the tangent line is simply the derivative of the function, so
![r=2cos(3\theta )\implies \cfrac{dr}{d\theta }=2\stackrel{chain~rule}{\left[ -sin(3\theta )\cdot 3 \right]} \\\\\\ \left. \cfrac{dr}{d\theta }=-6sin(3\theta ) \right|_{\theta =\frac{\pi }{6}}\implies -6sin\left( 3\cdot \frac{\pi }{6} \right)\implies -6sin\left( \frac{\pi }{2} \right)\implies -6](https://tex.z-dn.net/?f=r%3D2cos%283%5Ctheta%20%29%5Cimplies%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D2%5Cstackrel%7Bchain~rule%7D%7B%5Cleft%5B%20-sin%283%5Ctheta%20%29%5Ccdot%203%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft.%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D-6sin%283%5Ctheta%20%29%20%5Cright%7C_%7B%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7D%5Cimplies%20-6sin%5Cleft%28%203%5Ccdot%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%5Cright%29%5Cimplies%20-6sin%5Cleft%28%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%5Cright%29%5Cimplies%20-6)
Answer:
$4,160,000
Step-by-step explanation:
First, find the length of the new road in km using Pythagorean Theorem.
According to Pythagorean Theorem:
c² = a² + b²,
Where, c is the longest leg, which is the hypotenuse, a and b are the 2 other legs of the ∆.
Since we are calculating the lenght in km, convert each lenght of the two legs of the ∆ into km.
1 km = 1,000 m
10,000 m = 10 km
24,000 m = 24 km
c² = 24² + 10²
c² = 576 + 100
c² = 676
c = √676
c = 26 km
Lenght of the new road = 26 km
If cost of construction is $160,000 per kilometer, therefore, cost of constructing 26 km road = 160,000*26 = $4,160,000
Simplify the Integer part of the SQRT
Step-by-step explanation:
Factor 200 into its prime factors
200 = 23 • 52
My work for your question
