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Veseljchak [2.6K]
3 years ago
5

The ratio of pink roses bushes to white rose bushes in the city Garden is about 12 to 15. If there were 92 pink rose bushes, abo

ut how many white rose bushes with there be?
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
8 0

Answer:

115\ white\ rose\ bushes

Step-by-step explanation:

Let

x------> the number of pink roses bushes

y----> the number of white rose bushes

we know that

\frac{x}{y} =\frac{12}{15}

y=\frac{15}{12}x -----> equation A

x=92

substitute the value of x in the equation A

y=\frac{15}{12}(92)=115\ white\ rose\ bushes


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The following integral requires a preliminary step such as long division or a change of variables before using the method of par
shtirl [24]

Division yields

\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}

Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that

\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}

\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a

which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then

\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}

Now, in the integral we get

\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}

7 0
2 years ago
Can anyone solve this?
erastova [34]
It would be 76 degrees because it’s a vertical angle
4 0
3 years ago
PLEASE HELP ASAP
makkiz [27]

Answer:

5

Step-by-step explanation:

Since the difference in each term number is 5, we put 5 in the place of the star.

Formula for constant difference in a pattern: Tn= an+b

a is the difference while b is the number that comes before the 1st term. So, the equation to find the nth term is Tn=5n+4.

Hope this helps and please give a brainlist, thank you!

5 0
2 years ago
Pheobe Andy and polly share £270 pheobe gets three times the amount of Andy who gets twice as much as polly
Vladimir79 [104]
Hey!!

here is your answer >>>

the total money is 270 , it is shared among three people .

let's take the amount of Polly as X

then, the amount of Andy would be 2x

then, the amount of Phoebe would be 6x

the sum of 6x,2x and x is 270!.

let's add them up,

9x = 270

x = 30!.

Polly = £30

Andy= £60

Phoebe = £180

Hope my answer helps!
6 0
3 years ago
Can someone please help me with this question?
CaHeK987 [17]
No. you need to multiply both sides by 11 which would make it -88 > t. 99 is not less than -88
4 0
3 years ago
Read 2 more answers
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