33.3..........................................
Answer:
Algebra book weighs 24 oz
Grammar book weighs 15 oz
Step-by-step explanation:
algebra = x and grammar = y
x = 2y-6
5x = 8y
5(2y-6) = 8y
10y - 30 = 8y
2y - 30 = 0
2y = 30
y = 15
x = 2(15)-6
x = 30-6
x = 24
Answer:
Area covered by the fences will be 16.1 unit²
Step-by-step explanation:
Let the first parabola is represented by the function f(x) = 6x²
and second parabola by g(x) = x² + 9
point of intersection of the graphs will be determined when f(x) = g(x)
6x² = x² + 9
5x² = 9
x² = 1.8
x = ± 1.34
Now we will find the area between these curves drawn on the graph.
Area = ![\int_{-1.34}^{1.34}[f(x)-g(x)]dx=\int_{-1.34}^{1.34}[6x^{2}-(x^{2}+9)]dx](https://tex.z-dn.net/?f=%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5Bf%28x%29-g%28x%29%5Ddx%3D%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5B6x%5E%7B2%7D-%28x%5E%7B2%7D%2B9%29%5Ddx)
= 
= ![[\frac{5}{3}x^{3}-9x]_{-1.34}^{1.34}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7Dx%5E%7B3%7D-9x%5D_%7B-1.34%7D%5E%7B1.34%7D)
= ![[\frac{5}{3}(-1.34)^{3}-9(-1.34)-\frac{5}{3}(1.34)^{3}+9(1.34)]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7D%28-1.34%29%5E%7B3%7D-9%28-1.34%29-%5Cfrac%7B5%7D%7B3%7D%281.34%29%5E%7B3%7D%2B9%281.34%29%5D)
= ![[-4.01+12.06-4.01+12.06]](https://tex.z-dn.net/?f=%5B-4.01%2B12.06-4.01%2B12.06%5D)
= 16.1 unit²
Again using the Pythagorean Theorem:
h^2=x^2+y^2, where h is the hypotenuse of a right triangle and x and y are the side lengths. You are given that the hypotenuse is 34 ft and the base side is 16ft. Let h=34, x=16, and y=height, then you have:
34^2=16^2+y^2
y^2=34^2-16^2
y^2=1156-256
y^2=900
y=√900
y=30 ft
So the ladder will reach a spot 30 feet high on the building.
Answer:
Natural numbers are the counting numbers, meaning that they make up the set {1,2,3,4,5,...} So , 4/5 is belong to natural number
