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2 years ago

∆ABC ~ ∆WXY. What is the value of x? (show work)

Mathematics

1 answer:

brilliants [131]2 years ago

4 0

You need to set up ratios to solve for x. It's all about proportions here. I'm going to set up the ratio with the smaller triangle stuff (the one on the left) on top and the larger triangle stuff on bottom. Corresponding sides rule the day. $\frac{8}{12}= \frac{x}{18}$ . Cross-multiply to solve for x. 12x=144 and x = 12.

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First change to standard form of first order linear differential equation and then by finding the appropriate integrating factor

Leokris [45]

Answer:

Step-by-step explanation:

Given is a Differential equation as

$xy' + y = lnx ; y(e)=1$

To bring it to linear form we can divide the full equation by x

$y'+\frac{y}{x} =\frac{ln x}{x}$

This is of the form

y'+p(x) *y = q(x)

p(x) = 1/x

So find

$e^{\int\limits{\frac{1}{x} } \, dx } = e^{ln x} = x$

Solution is

$xy = \int {x*lnx /x } \, dx =xln x -x +C$

Use the initial value as y(e) =1

$e= eln e -e+C\\C=e$

So solution is

$xy =xln x -x+e$

5 0

3 years ago

Which of the following is NOT one of the three major credit bureaus?

vovangra [49]

What are the options ?

3 0

3 years ago

The area A (in square feet) of the rectangular shed is given by

a_sh-v [17]

This question is incomplete.

Complete Question

The area A (in square feet) of the rectangular shed is given by 6x³+7x²+11x+21.And one side of the rectangular is 2x+3. Use polynomial long division to find an expression for the length (in feet) of the shed.

Answer:

3x² - x +7

Step-by-step explanation:

Using the long division method:

We have :

Divisor : 6x³+7x²+11x+21

Dividend : 2x+3

Quotient : the length (in feet) of the shed = ???

Hence, we solve below

6x³+7x²+11x+21 ÷ 2x + 3

3x² -x + 7

______________________

2x+3 l 6x³+7x²+11x+21

6x³+9x²

__________

-2x²+11x

-2x²-3x

__________

14x+21

_______

Therefore, an expression for the length (in feet) of the shed is 3x² - x +7

8 0

2 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

zalisa [80]

Answer: 272

Step-by-step explanation:

Let a1=11

a2=20

a3=29

Formula for sequence=

an=a1+(n-1)d

an = nth term

a1= first term

n= nth position

d= common difference

We are looking for the 30th term,so our n=30

d= a2-a1

d= 20-11

d= 9

Using the formula

an= a1+(n-1)d

a30= 11+(30-1)9

a30= 11+(29)9

a30= 11+(29×9)

a30= 11+261

a30= 272

Therefore, the 30th term is 272

8 0

3 years ago

Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1

sleet_krkn [62]

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}$

From Left side:

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)$

$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$

NOTE: sin²θ + cos²θ = 1

$\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}$

$\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}$

$\dfrac{2sec^2\theta}{tan^2\theta-1}$

Left side = Right side <em>so proof is complete</em>

8 0

3 years ago

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