Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
Answer:
Step-by-step explanation:
On the right side of the = multiply -4 through
add 28a and add 4 to both sides
divide both sides by 22
We know that
[lateral surface area of a regular triangular pyramid]=3*[area of one <span>equilateral triangle]
so
[area of one </span>equilateral triangle]=lateral surface/3-----> 81/3-----> 27 ft²
[<span>surface area of the regular triangular pyramid]=lateral area+area of the base
area of the base is equals to the area of the lateral sides because are </span>equilateral triangles
therefore
area of the base=27 ft²
[surface area of the regular triangular pyramid]=81+27----> 108 ft²
the answer is
<span>the surface area of the regular triangular pyramid is 108 ft</span>²
To answer this problem, you should know the formula that we will be using and this would be:
Angle of elevation = arc tan( (vertical height)/(length of the shadow)).
Plugging in the values in the formula. Here, this angle is:
arc tan (12.5/18) = <span>34.78 degrees</span>
The answer would be approximately 34.78 degrees
Answer:
X = 0, π/2 in the interval [0, 2pi).
Step-by-step explanation:
Use the auxiliary angle method:
R sin(x + a) = Rsin x cos a + Rcos x sin a = 1
sin x + cos x = 1
Comparing coefficients:
R cos a = 1 and R sin a = 1, so
tan a = R sin a / R cos a = 1
So a = π/4 radians.
Also R^2(sin^2 a + cos^2 a) = 1^2 + 1^2 = 2
Therefore R = √2.
So √2 sin (x +π/4 = 1
sin x + π/4 = 1/√2
x + π/4 = π/4
x = 0 radians
Also
x = 0 + π/2 = π/2.
