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Dominik [7]
3 years ago
14

PLz help.

Mathematics
2 answers:
Ahat [919]3 years ago
5 0

Answer:

a=6cm

Step-by-step explanation:

Semmy [17]3 years ago
4 0

Answer:  6\ cm

Step-by-step explanation:

Given : The formula for the volume of a cube is :

V=s^3

The volume of a cube = 216\ cm^3

Substitute V= 216 in the above formula , we get

216=s^3

Taking cube root on both the sides , we get

\sqrt[3]{216}=s\\\\\Rightarrow\ s= \sqrt[3]{6^3}=6

Hence, the side length of cube= 6\ cm

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Help with this question (100 points)
Masteriza [31]

Answer:

y = \frac{\pi}{3}

Step-by-step explanation:

using the addition formula for sine

sin(x + y) = sinxcosy + cosxsiny

then

sinxcosy + cosxsiny = \frac{1}{2} sinx + \frac{\sqrt{3} }{2} cosx

for the 2 sides to be equal , then

cosy = \frac{1}{2} and siny = \frac{\sqrt{3} }{2}

then

y = cos^{-1} (\frac{1}{2} ) = \frac{\pi }{3}

and

y = sin^{-1} ( \frac{\sqrt{3} }{2} ) = \frac{\pi }{3}

thus y = \frac{\pi }{3}

6 0
2 years ago
According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and 238U at the creation of the
FromTheMoon [43]

Answer:

6 billion years.

Step-by-step explanation:

According to the decay law, the amount of the radioactive substance that decays is proportional to each instant to the amount of substance present. Let P(t) be the amount of ^{235}U and Q(t) be the amount of ^{238}U after t years.

Then, we obtain two differential equations

                               \frac{dP}{dt} = -k_1P \quad \frac{dQ}{dt} = -k_2Q

where k_1 and k_2 are proportionality constants and the minus signs denotes decay.

Rearranging terms in the equations gives

                             \frac{dP}{P} = -k_1dt \quad \frac{dQ}{Q} = -k_2dt

Now, the variables are separated, P and Q appear only on the left, and t appears only on the right, so that we can integrate both sides.

                         \int \frac{dP}{P} = -k_1 \int dt \quad \int \frac{dQ}{Q} = -k_2\int dt

which yields

                      \ln |P| = -k_1t + c_1 \quad \ln |Q| = -k_2t + c_2,

where c_1 and c_2 are constants of integration.

By taking exponents, we obtain

                     e^{\ln |P|} = e^{-k_1t + c_1}  \quad e^{\ln |Q|} = e^{-k_12t + c_2}

Hence,

                            P  = C_1e^{-k_1t} \quad Q  = C_2e^{-k_2t},

where C_1 := \pm e^{c_1} and C_2 := \pm e^{c_2}.

Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition

                                 P(0) = Q(0) = C

Substituting 0 for P in the general solution gives

                         C = P(0) = C_1 e^0 \implies C= C_1

Similarly, we obtain C = C_2 and

                                P  = Ce^{-k_1t} \quad Q  = Ce^{-k_2t}

The relation between the decay constant k and the half-life is given by

                                            \tau = \frac{\ln 2}{k}

We can use this fact to determine the numeric values of the decay constants k_1 and k_2. Thus,

                     4.51 \times 10^9 = \frac{\ln 2}{k_1} \implies k_1 = \frac{\ln 2}{4.51 \times 10^9}

and

                     7.10 \times 10^8 = \frac{\ln 2}{k_2} \implies k_2 = \frac{\ln 2}{7.10 \times 10^8}

Therefore,

                              P  = Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} \quad Q  = Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}

We have that

                                          \frac{P(t)}{Q(t)} = 137.7

Hence,

                                   \frac{Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} }{Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}} = 137.7

Solving for t yields t \approx 6 \times 10^9, which means that the age of the  universe is about 6 billion years.

5 0
3 years ago
27&lt; 3+5x+4<br><br> “With a step-by-step explanation be specific”
Nataly [62]

Answer:

27 < 3 + 5x + 4 \\ 27 < 7 + 5x \\ 27 - 7 < 5x \\ 20 < 5x \\5x > 20 \\ x >  \frac{20}{5}  \\  \boxed{x > 4}

<h3><u>x>4</u> is the right answer.</h3>
4 0
3 years ago
Read 2 more answers
Find the value of x in the triangle (not drawn to scale.)
AlekseyPX

Your answer would be 29

Why?

Because that is a right angle. They always have to be 90° so 90-61=29

6 0
3 years ago
Which of the following represents the zeros of f(x) = x3 − 3x2 − 2x + 6?
Mrac [35]
D. {3, √ 2, -√ 2}. 
<span>The cubic factors- (x - 3)(x² - 2) = 0.</span>
6 0
3 years ago
Read 2 more answers
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