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2 years ago

Which ordered pair is a solution of the equation 2x-3y=19

Mathematics

2 answers:

goldenfox [79]2 years ago

7 0

D because 5 times 2 is 10 and - cuts off - so -3 times -3 would be 9 so 10+9 is 19 :)

Dafna1 [17]2 years ago

5 0

The answer is D. 2x5 is 10 and -3x-3 is 9. 10+9=19

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P and q are two arithmetic sequences. The first four terms of sequence P are 2,6,10,14. The nth term of sequence Q is 145-3n. Th

Tomtit [17]

Answer:

r = 21

Step-by-step explanation:

nth of sequence P :

$T_{n} = 4n -2$

$r^{th} term$ : $4r-2=145-3r\\4r+3r=145+2\\7r=147\\r=21$

5 0

1 year ago

"find the reduction formula for the integral" sin^n(18x)

dexar [7]

Let

$I(n,a)=\displaystyle\int\sin^nax\,\mathrm dx$
For demonstration on how to tackle this sort of problem, I'll only work through the case where $n$ is odd. We can write

$\displaystyle\int\sin^nax\,\mathrm dx=\int\sin^{n-2}ax\sin^2ax\,\mathrm dx=\int\sin^{n-2}ax(1-\cos^2ax)\,\mathrm dx$
$\implies I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$

For the remaining integral, we can integrate by parts, taking

$u=\sin^{n-3}ax\implies\mathrm du=a(n-3)\sin^{n-4}ax\cos ax\,\mathrm dx$ $\mathrm dv=\sin ax\cos^2ax\,\mathrm dx\implies v=-\dfrac1{3a}\cos^3ax$

$\implies\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx=-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{a(n-3)}{3a}\int\sin^{n-4}ax\cos^4ax\,\mathrm dx$

For this next integral, we rewrite the integrand

$\sin^{n-4}ax\cos^4ax=\sin^{n-4}ax(1-\sin^2ax)^2=\sin^{n-4}ax-2\sin^{n-2}ax+\sin^nax$
$\implies\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx=I(n-4,a)-2I(n-2,a)+I(n,a)$

So putting everything together, we found

$I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$
$I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)$
$I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$
$\dfrac n3I(n,a)=\dfrac{2n-3}3I(n-2,a)-\dfrac{n-3}3I(n-4,a)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$

$\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax$

7 0

2 years ago

Which equation is equivalent to log^x36=2?

Dennis_Churaev [7]

The equation which is equivalent to $\log _{x} 36=2$ is $x^{2}=36$ or x = 6 ( $\log _{6} 36=2$ ).

<u>Step-by-step explanation:</u>

Given Equation:

$\log _{x} 36=2$

As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:

$b^{y}=a$

Then, the base b logarithm of x is equal to y

$\log _{b}(x)=y$

Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,

$b^{y}=a$

$x^{2}=36$

When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as $\log _{6} 36=2$

8 0

2 years ago

Read 2 more answers

Automobile tires can have a symmetric tread or an asymmetric tread. An experiment is to be conducted to determine whether the st

Genrish500 [490]

Answer:

Hello your question lacks the required options here are the options

By blocking on stopping distance

By blocking on tire tread type

By blocking on automobile type

By blocking on automobile size

Without blocking

Answer : By blocking on automobile size

Step-by-step explanation:

The experiment can best be conducted by blocking on the automobile and this is because the Automobile size and the stopping distance are proportionally related (associated ) as seen from the previous experiments hence the best experiment is By blocking on the size of the automobile is very crucial .

we can have a symmetric tread tire or an asymmetric tires fixed on the different types of Automobiles simultaneously and see if the stopping distance will be affected when we change the tires that way we are blocking on the Automobile size the same type of tires will be fixed at the same time on each automobile size

8 0

2 years ago

1. A ladder that has a length of 50 ft leans

ddd [48]

35 ft is the answer

7 0

2 years ago