A prism is filled with 44 cubes with 0.5-unit side lengths. What is the volume of the prism in cubic units?
1 answer:
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Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
Answer:
OPTION C: Sin C - Cos C = s - r
Step-by-step explanation:
ABC is a right angled triangle. ∠A = 90°, from the figure.
Therefore, BC = hypotenuse, say h
Now, we find the length of AB and AC.
We know that:
and
Given, Sin B = r and Cos B = s
⇒
⇒
Hence, the length of the side AC = rh
Now, to compute the length of AB, we use Cos B.
⇒
Hence, the length of the side AB = sh
Now, we are asked to compute Sin C - Cos C.
⇒
= s
Sin C = s
⇒ Cos C =
Therefore, Cos C = r
So, Sin C - Cos C = s - r, which is OPTION C and is the right answer.