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2 years ago

Use the law of sines to find the length of side c (answer as soon as possible)

Mathematics

1 answer:

Serggg [28]2 years ago

7 0

Answer:

Step-by-step explanation:

Using the law of sines in ΔABC, then

$\frac{c}{sinC}$ = $\frac{a}{sinA}$

Substituting in values gives

$\frac{c}{sin31.6}$ = $\frac{25}{sin38}$ ( cross- multiply )

c × sin38° = 25 × sin31.6° ( divide both sides by sin38° )

c = $\frac{25(sin31.6)}{sin38}$ ≈ 21.28 → D

You might be interested in

How many applications of integration by parts are required to evaluate integral (x^7)(e^x) dx?

charle [14.2K]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2860229

_______________

Make it more general, and see what happens when you try to reduce the exponent of x in the following integral:

$\mathsf{\mathtt{I}_0=\displaystyle\int\! x^k\cdot e^x\,dx\qquad\qquad (k\ge 1,~~k\in\mathbb{N})}$

Now, integrate it by parts:

$\begin{array}{lcl}
\mathsf{u=x^k}&\quad\Rightarrow\quad&\mathsf{du=k\cdot x^{k-1}\,dx}\\\\
\mathsf{dv=e^x\,dx}&\quad\Leftarrow\quad&\mathsf{v=e^x}
\end{array}$

$\mathsf{\displaystyle\int\! u\,dv=u\cdot v-\int\! v\,du}\\\\\\
\mathsf{\displaystyle\int\! x^k\cdot e^x\,dx=x^k\cdot e^x-\int\! e^x\cdot k\cdot x^{k-1}\,dx}\\\\\\
\mathsf{\displaystyle\int\! x^k\cdot e^x\,dx=x^k\cdot e^x-k\int\! x^{k-1}\cdot e^x\,dx}\\\\\\
\mathsf{\displaystyle\int\! x^k\cdot e^x\,dx=x^k\cdot e^x-k\cdot \mathtt{I}_1}$

where $\mathsf{\mathtt{I}_1=\displaystyle\int\! x^{k-1}\cdot e^x\,dx.}$

So after one iteration, the exponent of x was decreased by one unit.

The question is: after how many iterations will the exponent of x equals zero?

After exactly k iterations, of course.

Therefore, for k = 7, you have to apply integration by parts 7 times, to get rid of that polynomial factor. Then, there will be one last integral left to evaluate:

$\mathsf{\displaystyle\int\! e^x\,dx}$

But this one doesn't need to be evaluated by parts. You can directly write the result:

$\mathsf{\displaystyle\int\! e^x\,dx=e^x+C}$

Shortly, for the integral

$\mathsf{\mathtt{I}_0=\displaystyle\int\! x^7\cdot e^x\,dx}$

you have to apply integration by parts 7 times (not 8 times).

I hope this helps. =)

Tags: <em>indefinite integral integration by parts reduction formula product polynomial exponential differential integral calculus</em>

8 0

3 years ago

Find the equation of circle touches x axis at 3,0 and through the point 1,2

pickupchik [31]

Let the eq of circle be

x
2
+y
2
+2gx+2βy+c=0

now, x intercept = 2
g
2
−c

But circle touches x axis ∴ x intercept = 0

∴2
g
2
−c

=0∴g
2
=c

∴eq
n
become x
2
+y
2
+3gx+2βy+g
2
=0

Now circle passes through (3, 0) and (1, 4)

∴(3)
2
+(0)
2
+2g(3)+0+g
2
=0

9+6g+g
2
=0

∴g=−3

Also (1)
2
+(4)
2
+2(−3)(1)+2β(4)+9=0

∴1+16−6+8β+9=0

∴20+8β=0 ∴β=
2
5

Hence eq
n
of circle is

x
2
+y
2
−6x−5y+9=

7 0

2 years ago

Explain the steps for 0.000000001 in scientific notation

lawyer [7]

If you count the zeros it’s
one billionth

8 0

2 years ago

Read 2 more answers

Please help me with this please is hard

Elan Coil [88]

Answer:

1. $5

2. $38.4

Step-by-step explanation:

1) $5

2) 120/100 x 32 = $38.4

4 0

2 years ago

Read 2 more answers

A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet. The width is one four t

aliina [53]

We know that area of rectangle its equail A=l*w.
We know that length is 4 times greater than width, so we can say
l=4x and w=x
Knowing that area A=144 we can say
4x*x=144
$4x^2=144 \\ x^2=36 \\ x=6$ -
w=6 - its the width
l=6*4=24 - its the length

3 0

2 years ago