Answer:
h=404.89
Step-by-step explanation:
We are looking for side h, which is opposite of the observer. We know that the side adjacent to the observer is 500 feet. We also know that the angle from the observer to the bird is 39°. Because we have these values, SOH CAH TOA tells us that we should use tangent, opposite over adjacent.
We can set up our equation as follows:
tan(39°)=h/500
We can then solve for h:
500*tan(39°)=h
h=404.89
You'd fine the unit rate, in the context of the problem it would be how many minutes it takes for 1 pizza to cook
20/4= 5 minutes for 1 pizza
we are finding how long it would take to cook 10
5 times 10= 50, so 50 minutes
Answer:
942 6/7 cm²
Step-by-step explanation:
Since O = Center of bigger circle, OA = Radius of bigger circle.
∴ Area of smaller circle - Area of bigger circle = Area of shaded part.
∴ Area of smaller circle = 22/7 × 10²
= 22/7 × 100
= 2200/7
= 314 2/7 cm²
∴ Area of bigger circle = 22/7 × 20 ²
= 22/7 × 400
= 1257 1/7 cm²
∴ Area of shaded part = 1257 1/7 - 314 2/7
= 942 6/7 cm²
Answer:
k = 8
Step-by-step explanation:
Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.
By the roots of an equation, ax² + bx + c , where its roots are x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.
Comparing both equations, a = 3 b = 2 and c = k.
So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3
x₁ + x₂ = -2/3 and x₁x₂ = k/3
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
3x₁ + (-2x₁) = -2 and x₁(3x₂) = k
3x₁ - 2x₁ = -2 and x₁(3x₂) = k
x₁ = -2 and x₁(-2x₁) = k
x₁ = -2 and -2x₁² = k
Substituting x₁ = -2 into -2x₁² = k, we have
-2x₁² = k
-2(-2)² = k
2(4) = k
8 = k
So, k = 8
Here's are the steps to solving it.
3-a+5-2a=17
-3a=9
a=-3
