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2 years ago

Solve the system of equations - 6x + 8y = –10 and - 4x + y = –11 by combining the equations.

1 answer:

5 0

Answer: (3, 1) :)

Explanation:
-6x + 8y = -10
-4x + y = -11
-32x + 8y = -88
26x = 78
x = 3
-18 + 8y = -10
8y = 8
y = 1

(Also, can I have brainliest please?)

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If cos θ = .62 and if 0<θ<90 what is the approximate value of sin θ to the nearest hundredth

Deffense [45]

$\cos\Theta=0.62\\\\\text{Use:}\ \sin^2\alpha+\cos^2\alpha=1\\\\\sin^2\Theta+(0.62)^2=1\\\\\sin^2\Theta+0.3844=1\ \ \ |-0.3844\\\\\sin^2\Theta=0.6156\to\sin\Theta=\pm\sqrt{0.6156}\\\\\sin\Theta_1\approx-0.78\ \vee\ \sin\Theta\approx0.78\\\\\Theta\in(0^o;\ 90^o),\ therefore\ \sin\Theta \ \textgreater \ 0\to\boxed{\sin\Theta\approx0.78}$

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2 years ago

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

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2 years ago

g Nationwide, a certain disease occurs only a small proportion of people (.000215). A certain town has 74,000 residents. Use the

Andrei [34K]

Answer:

The probability that the town has 30 or fewer residents with the illness = 0.00052.

Step-by-step explanation:

So, we have the following set of data or information or parameters given from the question above and they are; the number of people living in that particular society/community/town = 74,000 residents and the proportion of people that the diseases affected = .000215.

The first step to do is to determine the expected number of people with disease. Thus, the expected number of people with disease = 74,000 × .000215 = 15.91.

Hence, the probability that the town has 30 or fewer residents with the illness = 1.23 × 10^-7 × 15.91^30/ 2.65253 × 10^-32 = 0.00052.

Note the formula used in the calculating the probability that the town has 30 or fewer residents with the illness = e^-λ × λ^x/ x!

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2 years ago

What greater than 1/3

Sholpan [36]

I think the The answer 1/1 or1/2! If it is not correct then ask some one else

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3 years ago

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