3.4k+(0.63−0.81k)÷0.9=5.7

Mathematics

2 answers:

Monica [59]3 years ago

5 0

The answer is k = 2

iren2701 [21]3 years ago

5 0

Answer:

k = 1.93 which can be rounded up to 2

Step-by-step explanation:

3.4k + (0.63 − 0.81k) ÷ 0.9 = 5.7 You don't need parentheses because you can't distribute

3.4k + 0.63 − 0.81k ÷ 0.9 = 5.7 Combine like terms

2.59k + 0.7 = 5.7

- 0.7 - 0.7 Subtract 0.7 from both sides

2.59k = 5 Divide both sides by 2.59

k = 1.93 which can be rounded up to 2

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Evaluate the difference quotient for the given function.

kherson [118]

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f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)

Then the difference quotient of f is

$\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}$

Recall the angle sum identity for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

Then we can write the difference quotient as

$\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}$

$\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}$

(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)

7 0

2 years ago

Try this, please!

mestny [16]

Check the picture below.

the triangle is an isosceles, so it has twin legs, and a base bottom.

the twin sides stem from the "vertex", and we know the vertex is 120°, and since the triangle is inscribed in a circle, because the circle is "circumscribing" it, then the base side of the triangle will be the diameter of it.

if we run a perpendicular line to the base from the vertex, we'll split the vertex in two 60° angles, as you see there, giving us a 30-60-90 triangle on each side.

so, anyhow, the rest is just a matter of using the 30-60-90 rule.

that's the diameter, and as you know, the radius is just the length of the base, or half the diameter.