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3 years ago

Estimate the sum: 1 3/7 + 3 5/9 + 1/2. Show your work.

2 answers:

8 0

Add 1 3/7 and leave it like that, and then do 9x3=27+5=32 so it’s gonna be 32/9 and then calculate the sum into 691/126 or u can divided more into 5 61/126

MakcuM [25]3 years ago

6 0

Answer:

The correct answer is 5 61/126!

Step-by-step explanation:

Leave a fraction alone

1 3/7

Find the Addend

9x3=27+5=32 = 32/9

Find the sum and simplify

1 3/7 + 32/9 = 691/126 = 5 61/126

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3 years ago

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3 years ago

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2 years ago

Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.

Mashcka [7]

Answer:

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Step-by-step explanation:

Integration Rule:

$\int x^n dx= \frac{x^{n+1}}{n+1}+c$
$\int \frac1x dx= ln(x) +c$

Given differential equation is

$x^2 \frac{dw}{dx}= \sqrt{w}(2x+5)$

$\Rightarrow x^2 dw= \sqrt{w} (2x+5) dx$ [ multiplying dx both sides]

$\Rightarrow \frac{dw}{\sqrt w}= \frac{(2x+5)}{x^2} dx$ [ dividing $x^2\sqrt w$ both sides]

Integrating both sides

$\int \frac{dw}{\sqrt w}=\int \frac{(2x+5)}{x^2} dx$

$\Rightarrow \int w^{-\frac12} dw=\int (\frac{2x}{x^2}+\frac{5}{x^2} )dx$

$\Rightarrow \int w^{-\frac12} dw=\int \frac{2}{x}dx +\int\frac{5}{x^2} dx$

$\Rightarrow \frac{w^{-\frac12+1}}{-\frac12+1} =2ln x+5 \frac{x^{-2+1}}{-2+1}+c$ [ c is arbitrary constant]

$\Rightarrow 2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

6 0

3 years ago

Find the interval on which the curve of y equals the integral from 0 to x of 2 divided by the quantity 1 plus 3 times t plus t s

elena-14-01-66 [18.8K]

$y=\displaystyle\int_0^x\frac2{1+3t+t^2}\,\mathrm dt$

By the fundamental theorem of calculus,

$\dfrac{\mathrm dy}{\mathrm dt}=\dfrac2{1+3x+x^2}$

then by standard differentiation,

$\dfrac{\mathrm d^2y}{\mathrm dt^2}=-\dfrac{6+4x}{(1+3x+x^2)^2}$

$y$ is concave upward whenever $\dfrac{\mathrm d^2y}{\mathrm dt^2}>0$ . The denominator is always positive, so the sign is determined by the numerator alone:

$6+4x>0\implies x>-\dfrac32$

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3 years ago