We know that
1) Sandra can run a mile in 6 minutes-------> 6*60-----> 360 sec
2) 4 laps around the track equals 1 mile
so
4 laps around the track in 360 sec
1 lap in 360/4--------> 90 sec
3) the position of Sandra for t=90 sec must be equal to the point S (0,56)
I proceed to analyze each case for t=90 sec
case a) x(t)=-140 cos(pi*t/45) y(t)=112 sin(pi*t/45)
x(t)=-140 cos(pi*90/45)------> -140
y(t)=112 sin(pi*90/45)-------> 0
the position is the point (-140,0)------> is not the point S
case b) x(t)=140 sin(pi*t/90) y(t)=-112 cos(pi*t/90)
x(t)=140 sin(pi*90/90)------> 0
y(t)=-112 cos(pi*90/90)-------> 112
the position is the point (0,112)------> is not the point S
<span>
case c) x(t)=-70 sin(pi*t/45) y(t)=56 cos(pi*t/45)
</span>x(t)=-70 sin(pi*90/45)------> 0
y(t)=56 cos(pi*90/45)
-------> 56
the position is the point (0,56)------> is equal to the point S----> is the solution
case d) x(t)=70 cos(pi*t/90) y(t)=-56 sin(pi*t/90)
x(t)=70 cos(pi*90/90)------> -70
y(t)=-56 sin(pi*90/90)-------> 0
the position is the point (-70,0)------> is not the point S
therefore
the answer is the option C
x(t)=-70 sin(pi*t/45) y(t)=56 cos(pi*t/45)
1/3 because there's 4 blue marbles in a bag of 12 marbles so as a fraction that would be 4/12 cancelled down = 1/3
Answer:
7.9 ft
Step-by-step explanation:
The hypotenuse is the side opposite of the right angle, hence the hypotenuse for this triangle is 11 ft.
Side 
is adjacent to the angle given. So we need adjacent and we have hypotenuse. Which trigonometric ratio relates adjacent and hypotenuse? It is COSINE.
<em>Thus, we can write:</em>
<em>Cross multiplying, we can solve for :</em>
Rounding to nearest tenth, we have 
ft.
By definition of <em>surface</em> area and the <em>area</em> formulae for squares and rectangles, the <em>surface</em> area of the <em>composite</em> figure is equal to 166 square centimeters.
<h3>What is the surface area of a composite figure formed by two right prisms?</h3>
According to the image, we have a <em>composite</em> figure formed by two <em>right</em> prisms. The <em>surface</em> area of this figure is the sum of the areas of its faces, represented by squares and rectangles:
A = 2 · (4 cm) · (5 cm) + 2 · (2 cm) · (4 cm) + (2 cm) · (5 cm) + (3 cm) · (5 cm) + (5 cm)² + 4 · (3 cm) · (5 cm)
A = 166 cm²
By definition of <em>surface</em> area and the <em>area</em> formulae for squares and rectangles, the <em>surface</em> area of the <em>composite</em> figure is equal to 166 square centimeters.
To learn more on surface areas: brainly.com/question/2835293
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