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3 years ago

If y⁻⁴ = 256 then y will be

Mathematics

1 answer:

kvasek [131]3 years ago

4 0

Answer:

y = 1/4

Step-by-step explanation:

y⁻⁴ = 256

(1/y)⁴ = 256

y⁴ = 1/256

y = ⁴√1/256

y = 1/4

Thus, The value of y is 1/4

-<u>TheUnknownScientist</u>

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The angles of a triangle are 80º, 2x + 2º, and 5xº. What is the value of x?

Gekata [30.6K]

Since the sum of the angles of a triangle = 180°

Then <span>80º + (2x + 2)º + 5xº = 180</span>°
82° + (7x)° = 180°
(7x)° = 180° - 82°
x = 98° ÷ 7
∴ x = 14

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4 years ago

Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate

Harman [31]

Answer:

Yes

Step-by-step explanation:

Given that Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes.

When both machines work for 20 minutes

Machine A would produce = $\frac{20}{4} =5$ widget and

Machine B would produce = $\frac{20}{5} =4$ widgets

So we can say that Machine A would produce more widgets than Machine N at that time.

Answer is Yes

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3 years ago

Which of the following represents the factorization of the binomial below ? x^2 - 144

Dima020 [189]

It factors to (x+12)(x-12)

This is the same as (x-12)(x+12) as we can multiply two expressions in any order we want. This is like saying 7*5 is the same as 5*7

I used the difference of squares rule to factor x^2 - 144. It might help to write x^2 - 144 as x^2 - 12^2, then compare it to a^2 - b^2 = (a-b)(a+b)

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3 years ago

A particle moves along the x-axis so that at any time t, t ≥ 0, its acceleration is a(t) = -4sin(2t). If the velocity of the par

sasho [114]

The velocity of the particle is given by

$v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du$

Since $a(t)=-4\sin2t$ and $v(0)=7$ , we get

$\displaystyle\int_0^ta(u)\,\mathrm du=\int_0^t-4\sin2u\,\mathrm du=2\cos2u\bigg|_0^t=2\cos2t-2$

$\implies v(t)=2\cos2t+5$

Similarly, the position function is obtained via

$x(t)=x(0)+\displaystyle\int_0^tv(u)\,\mathrm du$

We know $v(t)$ and we're told that $x(0)=0$ , so

$\displaystyle\int_0^tv(u)\,\mathrm du=\int_0^t(2\cos2u+5)\,\mathrm du=\sin2u+5u\bigg|_0^t=\sin2t+5t$

$\implies x(t)=\sin2t+5t$

making the answer A.

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3 years ago

Imagine a pond. In it sits one lilypad, which reproduces once a day. Each of its offspring also reproduces once a day, doubling

sergeinik [125]

Answer: On the 29th day

Step-by-step explanation:

According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.

On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.

The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are $2^{30}$ lilypads on the 30th, and $2^{29}$ lilypads on the 29th. This can be deduced multiplying succesively by 2.

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3 years ago