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2 years ago

A triangle has two angles with measures 43 and 51.

1 answer:

6 0

In Euclidean geometry, the angles of a triangle add to 180, which means the remaining angle has a measure of 86 degrees.

In spherical geometry, it's impossible to know the measure of the remaining angle precisely without knowing any more info about the triangle. The sum of the interior angles is between 180 and 540 degrees, so the missing angle is somewhere between 87 and 445 degrees.

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Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

2 years ago

Http://prntscr.com/lkz30r What is the value of x? 28 20 36 17

ivolga24 [154]

This is a question that can be solved with Pythagorean Theorem since it is a right triangle. The longest side, 29, is the hypotenuse and the sides 21 and x are the legs. So, the Pythagorean Theorem states,

$c^{2}= a^{2}+ b^{2}$

Where,

c is the Hypotenuse, a and b are the legs. Putting the respective values gives us,

$(29)^{2}= (21)^{2} +x^{2} \\841=441+x^{2} \\400=x^{2} \\20=x$

So, 20 is the side length of x.

ANSWER: 20

5 0

2 years ago

Read 2 more answers

Is V 5 rational or irrational

madreJ [45]

Answer:

it's a whole number

Step-by-step explanation:

it's a whole number

4 0

2 years ago

Dream Loan Bank offers loans. Carrie borrows $10,500 to help start a business. The loan must be repaid at 4.5% simple interest o

MaRussiya [10]

$~~~~~~ \textit{Simple Interest Earned Amount}\\\\A=P(1+rt)\qquad\begin{cases}A=\textit{accumulated amount}\\P=\textit{original amount given}\dotfill & \$10500\\r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\t=years\dotfill &10\end{cases}\\\\\\A=10500(1+0.045\cdot 10)\implies \boxed{A=15225}$

7 0

2 years ago

What is the answer to 6+9y-18=-3

lara [203]

6 + 9y - 18 = -3 Combine like terms (6 and -18)
9y - 12 = -3 Add 12 to both sides
9y = 9 Divide both sides by 9
y = 1

7 0

2 years ago