Answer:n = 209
Step-by-step explanation:
6/11 = 114/n
Find the LCM of the expression
LCM = 11n
Multiply both sides of the equation by the LCM
11n x 6/11 = 11n x 114/n
6n = 1254
n = 1254/6
n = 209
Answer:
Step-by-step explanation:
![\red{ \boxed{ \bold{\overline{AB} \cong \overline{DB} \:\: and \:\: \overline{AC} \cong \overline{DC}}} }\\ \overline{BC} \cong \overline{BC}... (common\: side) \\](https://tex.z-dn.net/?f=%20%5Cred%7B%20%5Cboxed%7B%20%5Cbold%7B%5Coverline%7BAB%7D%20%5Ccong%20%5Coverline%7BDB%7D%20%5C%3A%5C%3A%20and%20%5C%3A%5C%3A%20%5Coverline%7BAC%7D%20%5Ccong%20%5Coverline%7BDC%7D%7D%7D%20%7D%5C%5C%20%20%20%5Coverline%7BBC%7D%20%5Ccong%20%5Coverline%7BBC%7D...%20%28common%5C%3A%20side%29%20%20%5C%5C%20)
Answer:
5^3
Step-by-step explanation:
125= 5*25
25=5*5
5 is a prime number and there are 3 of them so the answer in index notation will be 5^3
Answer:
i-2.4j
Step-by-step explanation:
Given that,
The surface of a mountain is modeled by the equation as follows :
![h(x,y)=5000 -0.001x^2-0.004y^2](https://tex.z-dn.net/?f=h%28x%2Cy%29%3D5000%20-0.001x%5E2-0.004y%5E2)
A mountain climber is at the point (500, 300, 4390).
We need to find the direction in which he should move in order to ascend at the greatest rate.
To find direction, first finding the gradient of h as follows :
![\nabla h(x,y)=-0.002xi-0.008yj](https://tex.z-dn.net/?f=%5Cnabla%20h%28x%2Cy%29%3D-0.002xi-0.008yj)
Now put x = 500 and y = 300
So,
![\nabla h(x,y)=-0.002(500)i-0.008(300)j\\\\\nabla h(x,y)=i-2.4j](https://tex.z-dn.net/?f=%5Cnabla%20h%28x%2Cy%29%3D-0.002%28500%29i-0.008%28300%29j%5C%5C%5C%5C%5Cnabla%20h%28x%2Cy%29%3Di-2.4j)
The direction of the climber is i-2.4j