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3 years ago

Can I get step by step explanation and answer on numbers 2,4,14, and 36 please

Mathematics

1 answer:

neonofarm [45]3 years ago

7 0

answer for 2nd is Constant.

answer for 4th is Evaluate.

answer for 14th is one subtracted from a number w.

answer for 36th is a number n is divided by 2.4

hope it helps you mate thanks for the question and if possible please mark it as brainliest

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3 years ago

Find the number of elements in A1 ∪A2 ∪A3 if there are 100 elements in A1, 1000 in A2, and 10,000 in A3 if a) A1 ⊆ A2 and A2 ⊆ A

Stella [2.4K]

Answer:

Step-by-step explanation:

Given that there are 3 sets such that there are 100 elements in A1, 1000 in A2, and 10,000 in A3

a) If A1 ⊆ A2 and A2 ⊆ A3

then union will contain the same number of elements as that of A3

i.e. $n(A1 ∪A2 ∪A3)=n(A3) =10000$

b) If the sets are pairwise disjoint.

union will contain the sum of elements of each set

$n(A1 ∪A2 ∪A3) = 100+1000+10000=11100$

c) If there are two elements common to each pair of sets and one element in all three sets

We subtract common elements pairwise and add common element in 3

i.e. $n(A1 ∪A2 ∪A3) = 100+1000+10000-2-2-2+1\\= 10995$

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3 years ago

Solve y′′=sin(x) if y(0)=0 and y′(0)=5. y(x)=?

Ksenya-84 [330]

Answer:

$y(x)=6x-sin(x)$

Step-by-step explanation:

Rewrite the differential equation as:

$\frac{d^{2} y }{dx^{2} } =sin(x)$

Integrate both sides with respect to x:

$\int\ \frac{d^{2} y }{dx^{2} } dx = \int\ sin(x) dx$

$\frac{dy}{dx} =-cos(x)+C_1$

Integrate one more time both sides with respect to x:

$\int\ \frac{dy}{dx} = \int\ -cos(x)+C_1 dx$

$y(x)=-sin(x)+C_1x+C_2$

Now that we find the solution, let's find its derivate:

$y'(x)=C_1-cos(x)$

Evaluating the initial conditions:

$y(0)=C_1(0)+C_2-sin(0)=0\\C_2=0$

$y'(0)=C_1-cos(0)=5\\C_1=5+1=6$

Replacing the value of the constants that we found in the differential equation solution:

$y(x)=6x-sin(x)$

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3 years ago