Answer:
69.01 m
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The tangent function is useful for problems like this. Let the height of the spire be represented by h. The distance (d) across the plaza from the first surveyor satisfies the relation ...
tan(50°) = (h -1.65)/d
Rearranging to solve for d, we have ...
d = (h -1.65)/tan(50°)
The distance across the plaza from the second surveyor satisfies the relation ...
tan(30°) = (101.65 -h)/d
Rearranging this, we have ...
d = (101.65 -h)/tan(30°)
Equating these expressions for d, we can solve for h.
(h -1.65)/tan(50°) = (101.65 -h)/tan(30°)
h(1/tan(50°) +1/tan(30°)) = 101.65/tan(30°) +1.65/tan(50°)
We can divide by the coefficient of h and simplify to get ...
h = (101.65·tan(50°) +1.65·tan(30°))/(tan(30°) +tan(50°))
h ≈ 69.0148 ≈ 69.01 . . . . meters
The tip of the spire is 69.01 m above the plaza.
Answer:
262 books sold
Step-by-step explanation:
This is a very vague word problem, but if it truly is just asking the amount of books sold (regardless of music or science), here's how to get the answer:
1. 287+134=421 - first you want to add together the two types of books to get the total amount of books in the store
2. 421-x=159 - create an equation and solve.
3. -x=-262 - follow order of operations and subtract 421 on both sides in order to isolate the variable
4. x=262 - divide each side by -1 to make the variable positive.
If you'd like an easier way, you can just:
1. 421-159=262 - it's easier, but my math teacher would count us wrong if we didn't do equations a specific way. Good luck!
Answer:
the value of the smallest number is 3
Step-by-step explanation:
The computation of the value of the smaller number is shown below:
Given that
y = 4x + 2
y = 2x + 8
Now equate these two equations
4x + 2 = 2x + 8
4x - 2x = 8 - 2
2x = 6
x = 3
Hence, the value of the smallest number is 3
The same is to be considered
2/13_
Step-by-step explanation:
6/39_=
_6÷39/3
=2/39_
=11÷2/39_
=2/13_
(x^4)(3x^3-2)(4x^2+5x)
=(3x^7-2x^4)(4x^2+5x)
=12x^9+15x^8-8x^6-10x^5
answer: 12x^9+15x^8-8x^6-10x^5