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vlada-n [284]
3 years ago
9

Tom read a novel for 1 1/4 hours and comic books for 1 2/5 hours. How long did Tom read?

Mathematics
1 answer:
Allushta [10]3 years ago
6 0
Tom read a novel for 1 1/4 hours and comic books for 1 2/5 hours.

How long did Tom read?


Tom read a novel for 1 1/4 hr  or 1 hr and 15 min.
Tom read a comic book for 1 2/5 hr  or 1 hr and 24 min.

1:15 + 1:24 = 2 hrs and 39 min.

Hope this helps!
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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)
5 0
3 years ago
business plans are aimed MAINLY at A.Government Regulators B.employees C.marketing firms D.potential investors
Talja [164]
Salutations!

Business plans are mainly aimed at ----

Business plans are mainly aimed at potential investors. You need plan your business so thoroughly to gain the attention of potential investors. Potential investors are people who give you cash (capital) to help invest you in other companies or business.

Thus, your answer is option D.

Hope I helped :D
5 0
3 years ago
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What attributes of a rectangles and rhombuses are also attributes of parallelogram
Scorpion4ik [409]

Answer: rhombus, rectangle, and square — are so-called because they’re special cases of the parallelogram.

Step-by-step explanation:

8 0
3 years ago
PLS help i rly need help ive posted with no help im rly confused
vesna_86 [32]
Asked and answered elsewhere.
brainly.com/question/8666894
8 0
3 years ago
3. Marissa collected 8 seashells. Her sister Emily
eimsori [14]

Answer:

3

Step-by-step explanation:

There are 15 shells all together

there is 5 friends

15 divided by 5 is 3

Therefore  the answer is three

8 0
3 years ago
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