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2 years ago

PLEASE HELP!! FAST!!

Mathematics

1 answer:

d1i1m1o1n [39]2 years ago

7 0

Answer:

134

Step-by-step explanation:

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Let a4+a8+a12+a16=224. Find the sum of first 19 term in sequence.

Tomtit [17]

Without knowing anything about the sequence, this is impossible to answer. But suppose the sequence is arithmetic, in which case each term differs by some constant $k$ :

$a_2=a_1+k$

$a_3=a_2+k=a_1+2k$

$a_4=a_3+k=a_1+3k$

$\ldots$

$a_n=a_{n-1}+k=a_1+(n-1)k$

Then we can write

$a_4+a_8+a_{12}+a_{16}=4a_1+36k=224\implies a_1+9k=56$

and from the formula above, we see this means the 10th term in the sequence is $a_{10}=56$ . But that's all the specific info we can gather about such an arithmetic sequence. If we set the first term to be some unknown $a_1=a$ , then the sum of the first 19 terms in the sequence would be

$\displaystyle\sum_{n=1}^{19}a_n=\sum_{n=1}^{19}\big(a+(n-1)k\big)=19a+k\sum_{n=1}^{18}n=19a+171k$

If we knew one more term in the sequence, we could determine the value of $k$ and derive the value of $a$ (if the first term $a_1$ is not immediately given), and then go on to find an exact numeric value for the sum.

7 0

3 years ago

Find the measure of the angle indicated

Grace [21]

Answer:

Step-by-step explanation:

y + 28 + 58 = 180

y + 86 = 180

y = 180 - 86

y = 94

x + y = 180

x + 94 = 180

x = 180 - 94

x = 86

6 0

3 years ago

Find the distance between the points (2, - 5) and ( - 10, - 10).

cestrela7 [59]

Answer: You would use the distance formula to determin the distance between the points

13 would be your answer

Step-by-step explanation:

3 0

3 years ago

Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

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3 years ago

Do 8feet + 10feet + 12feet make a right triangle

bija089 [108]

9514 1404 393

Answer:

Step-by-step explanation:

If triangle side lengths are an arithmetic sequence (have a common difference), they must have the ratios 3:4:5 to make a right triangle. Here, the ratios of the side lengths are 4:5:6, so will not be a right triangle.

4 0

3 years ago