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valina [46]
4 years ago
7

What is the radius for the circle given by the equation x^2+(y-1)^2=12

Mathematics
1 answer:
Naddik [55]4 years ago
3 0
(x-h)^2+(y-k)^2=r^2
r=radius
12=r^2
sqrt12=r
2√3=radius
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550.2cm

Step-by-step explanation:

6 cm x 7 cm x 13.1 cm = 550.2 cm

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In order to evaluate 7 sec(θ) dθ, multiply the integrand by sec(θ) + tan(θ) sec(θ) + tan(θ) . 7 sec(θ) dθ = 7 sec(θ) sec(θ) + ta
Maurinko [17]

Answer:

\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c

Step-by-step explanation:

The question is not properly formatted. However, the integral of \int {7 \sec(\theta) } \, d\theta is as follows:

<h3></h3>

\int {7 \sec(\theta) } \, d\theta

Remove constant 7 out of the integrand

\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta

Multiply by 1

\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta

Express 1 as: \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}

\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta

Expand

\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta

Let

u = \sec(\theta) + \tan(\theta)

Differentiate

\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)

Make d\theta the subject

d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}

So, we have:

\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}

Cancel out \sec(\theta)\tan(\theta) + sec^2(\theta)

\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}

Integrate

\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c

Recall that: u = \sec(\theta) + \tan(\theta)

\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c

8 0
4 years ago
Given: PSTK - trapezoid m∠P = 90°, SK=13 PK = 12, ST = 8 Find: Area of PSTK
bazaltina [42]

Answer:

Area of PSTK = 50

Step-by-step explanation:

△SPK:

SK = 13, PK = 12

13^2 - 12^2 = SP^2

SP = 5

(8 + 12) /2 x 5 = 50  


5 0
3 years ago
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