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3 years ago

What is the answer to this in cm

Mathematics

1 answer:

jasenka [17]3 years ago

5 0

The hardest part is finding the length of the curve at the top. To find arc length, multiply the circumference by the arc angle divided by full angle (360°) in a circle. Or:
$s = (2\pi r)( \frac{x}{360})$
x, the arc angle in a semicircle, is 180°.
r, the radius is 7/2 = 3.5.
Now just plug the numbers in and solve for arc length, s.

s = 2π(3.5)(1/2) ≈ 11.00

Now just add up all the sides. 11cm + 10cm + 10cm + 7cm = 38 cm.

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If w = 5 cos (xy) − sin (xz) and x = 1/t , y = t, z = t^3 ; then find dw/dt

Scrat [10]

In this question, we find the derivatives, using the chain's rule.

Doing this, the derivative is:

$\frac{dw}{dt} = \frac{5}{t}(\sin{1} - \cos{1}) - 2t\cos{t^2}$

Chain Rule:

Suppose we have a function $w(x,y,z), x = x(t), y = y(t), z = z(t)$ , and want to find it's derivative as function of t. It will be given by:

$\frac{dw}{dt} = \frac{dw}{dx}\frac{dx}{dt} + \frac{dw}{dy}\frac{dy}{dt} + \frac{dw}{dz}\frac{dz}{dt}$

Thus, we have to find the desired derivatives, which are:

w of x:

$\frac{dw}{dx} = -5y\sin{(xy)} - z\cos{(xz)}$

Considering $x = \frac{1}{t}, y = t, z = t^3$

$\frac{dw}{dx} = -5t\sin{(1)} - t^3\cos{(t^2)}$

w of y:

$\frac{dw}{dy} = -5x\cos{(xy)}$

Considering $x = \frac{1}{t}, y = t$

$\frac{dw}{dy} = -\frac{5}{t}\cos{1}$

w of z:

$\frac{dw}{dz} = -x\cos{(xz)}$

Considering $x = \frac{1}{t}, z = t^3$

$\frac{dw}{dz} = -\frac{1}{t}\cos{(t^2)}$

Derivatives of x, y and z as functions of t:

$\frac{dx}{dt} = -\frac{1}{t^2}$

$\frac{dy}{dt} = 1$

$\frac{dz}{dt} = 3t^2$

Derivative of w as function of t.

Now, we just replace what we found into the formula. So

$\frac{dw}{dt} = \frac{dw}{dx}\frac{dx}{dt} + \frac{dw}{dy}\frac{dy}{dt} + \frac{dw}{dz}\frac{dz}{dt}$

$\frac{dw}{dt} = (-5t\sin{(1)} - t^3\cos{(t^2)})(-\frac{1}{t^2}) - (\frac{5}{t}\cos{1}) - (\frac{1}{t}\cos{(t^2)})3t^2$

Applying the multiplications:

$\frac{dw}{dt} = \frac{5}{t}\sin{1} + t\cos{t^2} - \frac{5}{t}\cos{1} - 3t\cos{t^2}$

Applying the simplifications:

$\frac{dw}{dt} = \frac{5}{t}(\sin{1} - \cos{1}) - 2t\cos{t^2}$

Which is the derivative.

For more on the chain rule, you can check brainly.com/question/12795383

8 0

3 years ago

Solve the equation 10=1/3s+1

Gnom [1K]

Is 1/3 a fraction or division?
If division then the answer would be s= 1/27 (a fraction)

6 0

3 years ago

Read 2 more answers

y = 2 x x 2 + 1 between x = 0 and x = 6 for n 1 = 6 and n 2=12. This means you will be doing two estimates for the area under th

ANEK [815]

Answer:

For n = 1, 150

for n = 2, 1164

Step-by-step explanation:

The answer for n = 1, is,

$\int_{0}^{6}(2 \times x^{2} + 1)\times dx$

= $[2 \times \frac {x^{3}}{3} + x]_{0}^{6}$

=150

The answer for n = 2 is,

$\int_{0}^{12}(2 \times x^{2} + 1)\times dx$

= $[2 \times \frac {x^{3}}{3} + x]_{0}^{12}$

= 1164

3 0

3 years ago

Find the inverse function of m(x) = 5x - 5

sleet_krkn [62]

Answer:

5(x−1)

Step-by-step explanation:

3 0

3 years ago

I WILL GIVE BRAINLIEST ANSWER TO FIRST/CORRECT PERSON

kupik [55]

From the data we are given that:

People who bought CD = 290

People who bought CD alone = 290 – 220 = 70

Therefore the number of people who download music alone is:

People who download music alone = 410 – 220 – 70 = 120

Therefore the total number of people who download music is:

People who download music = 120 + 220 = 340

Answer:

340 people

3 0

4 years ago

Read 2 more answers