Answer:
√161 yd
Step-by-step explanation:
Hi there!
We're given a right triangle (notice the right angle), the measure of one of the legs (one of the sides that make up the right angle) as 8 yd, and the hypotenuse (the side opposite to the right angle) as 15 yd.
We need to find x, which is the other leg in the triangle
If we are given 2 sides and need to find a third, we can use Pythagorean Theorem, which states that a²+b²=c² if a and b are legs and c is the hypotenuse
In this case, a=8, b=x, and c=15
So let's substitute those values into the formula
(8)²+x²=(15)²
raise everything to the second power
64+x²=225
subtract 64 from both sides
x²=161
take the square root of both x and 161
x=√161, x=-√161
-√161 cannot work in this case, as distance cannot be negative.
The question asks for the answer to be in simplified radical form, but √161 cannot be simplified down further
so the answer is <u>√161 yd</u>
Hope this helps! :)
Remember the equation to find the circumference?
Equation of circumference: Pi x 2(radius)
Therefore, 3.141592654 x 2(6ft) = 37.7 feet
Answer:
No
Reasoning:
If something is a perfect cube, it is able to be put under a cube root (![\sqrt[3]{..}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B..%7D)
) and will result in an integer (a non-decimal number > 0, basically).
So let's calculate ![\sqrt[3]{48}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B48%7D)
, and see if the result is an integer.
= 3.634.......
As you can see, the result is not an integer, therefore 48 is not a perfect cube.
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
Let
b---------> <span>the cost of one flower bouquet
</span>v--------> <span>the cost of one vase.
we know that
2b+2v=12.50-----> </span>Multiplied by -1------------->-2b-2v=-12.50
8b+2v=29---------------------------------------------> 8b+2v=29
I add the two equations ------------------------
6b=16.50
b=2.75
2*2.75+2*v=12.50---------------> v=(12.50-5.5)/2---------> v=3.5
the answer is
the cost of one flower bouquet is $2.75
the cost of one vase is $3.5
