If we are to rewrite the equation such that we are able to clearly distinguish the exponents of each of the variables, this is,
-10p²q + 7p³q - 5q
(A) Writing this polynomial in descending order, we properly looked the exponent of the first variable and arrange it from highest to least.
7p³q - 10p²q - 5q
(B) There are three terms in the polynomial given above. Hence, the given is TRINOMIAL.
(C) The degree of the polynomial is 4 since it is the highest exponent of the term in the given.
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
Answer: The volume of given substance is
.
Step-by-step explanation:
Given: Density = 10.7 ![g/cm^{3}](https://tex.z-dn.net/?f=g%2Fcm%5E%7B3%7D)
Mass = 23.54 g
Density of a substance is the mass of substance divided by its volume.
Mathematically, ![Density = \frac{mass}{volume}](https://tex.z-dn.net/?f=Density%20%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D)
Substitute the values into above formula to calculate volume as follows.
![Density = \frac{mass}{volume}\\10.7 g/cm^{3} = \frac{23.54 g}{volume}\\volume = \frac{23.54 g}{10.7 g/cm^{3}}\\= 2.2 cm^{3}](https://tex.z-dn.net/?f=Density%20%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D%5C%5C10.7%20g%2Fcm%5E%7B3%7D%20%3D%20%5Cfrac%7B23.54%20g%7D%7Bvolume%7D%5C%5Cvolume%20%3D%20%5Cfrac%7B23.54%20g%7D%7B10.7%20g%2Fcm%5E%7B3%7D%7D%5C%5C%3D%202.2%20cm%5E%7B3%7D)
Thus, we can conclude that the volume of given substance is
.
Step-by-step explanation:
Given
13 sin θ = 5
sin θ = 5/13 = p/h
p = 5 , h = 13 and b = ?
By using Pythagoras theorem
b = √ h² - p²
= √ 13² - 5²
= √144
b = 12
Now
tan θ
= p / b
= 5 / 12
Hope it will help :)
6 4/5 as improper fraction is 34/5
5 3/4 as improper fraction is 23/4
3 1/3 by 25/4 is 8/15
14/3 by 3 1/2 is 4/3
3 1/4 by 5 1/2 is 13/22