Answer: The first and second angles measure 54 degrees each. The third angle measures 72 degrees.
Step-by-step explanation:
First, I transcribed the sentences into equations.
The first part of the sentence says that "two angles of a triangle have equal measures", and we can use the konwledge that the interioir angle sum of all triangles in 180 degrees to solve this.
Lets call the first and second angles x and the third angle y. Then we can get the equation that 2x + y = 180. You might be asking "where did the 2x come from?", well, we know that if we add all of the angles up we get 180 degrees, and since two of the angles are equal, they can be simplified to 2x.
The second part of the sentence says that "the third angles measure is 36 degrees less than the sum of the other two", which translates to:
y = 2x - 36
Then we can substitute the second equation into the first and solve!
2x + (2x - 36) = 180
4x - 36 = 180
4x = 216
x = 54
Knowing that x = 54, we can substitute back into the first equation to solve for y. 2(54) + y = 180, 108 + y = 180, y = 72.
Answer:
1. C. cylindrical coordinates
2 A. spherical coordinates
3. A. spherical coordinates
4. D. Cartesian coordinates
5 B. polar coordinates
Step-by-step explanation:
USE THE BOUNDARY INTERVALS TO IDENTIFY
1. ∭E dV where E is:
x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0 -- This is A CYLINDRICAL COORDINATES SINCE x>= 0, y>= 0, z>= 0
2. ∭E z^2 dV where E is:
-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2 This is A SPHERICAL COORDINATES
3. ∭E z dV where E is:
1 <= x <= 2, 3<= y <= 4,5 <= z <= 6 -- This is A SPHERICAL COORDINATES
4. ∫10∫y^20 1/x dx ---- This is A CARTESIAN COORDINATES
5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4 This is A POLAR COORDINATES
Answer:
Q1
|a-b| = b-a when a<b
Q2
104159/33000
Step-by-step explanation:
Q1
If a<b then a-b will always be negative. To get the absolute value, we can take -(a-b) = -a+b = b-a.
Q2
Let x = 3.12789789789...
We isolate the repeating decimal to start after the decimal, so we multiply by 100.
100x = 312.789789789...
We want to multiply by 10 for each digit that repeats (in this case 3), to get the repeating part to the left of the decimal.
100000x = 312789.789789
Subtracting the two...
x(100000-100) = 312789.789789 - 312.789789
99900x = 312477
x = 312477/99000 = 104159/33000
Answer:
56 + 7d
Step-by-step explanation:
For using the distributive property, You have to multiply the first number to the rest. So 8 x 7 = 56 and 7 x d = 7d.