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slamgirl [31]
2 years ago
8

The measures of the three angles of a triangle are given by 1. 3x +1 2. 2x -3, and 9x. What is the measure of the smallest angle

?
A. 13 degrees
B. 23 degrees
C. 29 degrees
D. 40 degrees
Mathematics
1 answer:
nordsb [41]2 years ago
4 0
Since the total measure of all the angles of a triangle is always 180, solve for x with the equation: 3x+1+2x-3+9x=180. x=13. Now plug in x and look for the smallest one, which will be B. 23 degrees.
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“encontrar la integral indefinida y verificar el resultado mediante derivación”
Oliga [24]

I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx

Haz la sustitución:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C

Para confirmar el resultado:

\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}

I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx

Sustituye:

y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx

\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C

(Te dejaré confirmar por ti mismo.)

I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx

Sustituye:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C

I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}

Sustituye:

u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}

\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C

Podemos hacer que esto se vea un poco mejor:

\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}

\implies I=-\dfrac{(t+1)^4}{4t^4}+C

4 0
3 years ago
The ratio of 6th graders to 7th graders in a MATHCOUNTS club is 5:4. The ratio of 8th graders to 7th graders in the same club is
lorasvet [3.4K]
ANSWER
========

Ratio of 8th graders to 7th graders = 3 : 2

Let the number of graders be 3x and 2x

Number of 8th graders = 18

So , 3x = 18

x = 18/3 = 6

Number of 7th graders = 2 × 6 = 12

Ratio of 6th graders to 7th graders = 5 : 4

Let the number of graders be 5a and 4a

Number of 7th graders = 12

So , 4a = 12

a = 12/4 = 3

Number of 6th graders = 5×3 = 15 ANS

_______________________________

#BE BRAINLY
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3 years ago
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Answer:

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Step-by-step explanation:

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2 years ago
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\bf \textit{"The distance around each dot is 24}\pi \textit{ inches."}\\\\
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A. -8
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