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3 years ago

What is the measures of angle ECD? Please show work.

Mathematics

2 answers:

bazaltina [42]3 years ago

6 0

The anser is 40

the resense is verticle angle are congrounent.

madreJ [45]3 years ago

4 0

The answer is D. 80°. Angle B is 60 because the angle is adjacent. That makes 60 the vertical angle for the second angle in the triangle with the 40. Since we know two of the angles, we add them together to get 100. 180-100 is 80°

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a cup was filled at a constant rate. it started empty. after 2 seconds, it held 70 cm cubes of water. the radius is 4 and te hei

Viktor [21]

Answer:

89.51%

Step-by-step explanation:

Assuming given units are in cm

Tge rate of filling the cup is 70/2= 35 cm3/s

Volume of the cup is $\pi r^{2}\frac {h}{3}$ and replacing r with 4 cm and h with 7 cm then the volume is equivalent to

$\pi*4^{2}*\frac {7}{3}= 117.3 cm^{3}$

Volume filled after 3 seconds will be 3*35=105 cm3

Percentage filled is $\frac {105}{117.3}\times 100\approx 89.51$

8 0

3 years ago

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x

Lady_Fox [76]

By Stokes' theorem, the line integral of $\vec F$ over $C$ is given by the surface integral of the curl of $\vec F$ over $S$ , where $S$ is the region of intersection of the plane $z=y+6$ and the cylinder $x^2+y^2=1$ with $S$ having positive/upward orientation.

Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+6)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

The curl of $\vec F$ is

$\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-2)\,\vec k$

Then the line integral is equivalent to

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\bigg((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+4)\,\vec k\bigg)\cdot\bigg(-u\,\vec\jmath+u\,\vec k\bigg)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(5u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{5\pi}$

4 0

3 years ago

What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79

Julli [10]

Answer:

Tn = Tn-1 + 2(n-1) + 5

Kindly note that Tn-1 means T subscript n-1

Step-by-step explanation:

Here, we want an expression for the nth term.

First term is 7

Then first common difference is 7

second common difference is 7 + 2

Third common difference is 9 + 2

So within the common differences, the nth term is 7 + (n-1) 2

Now, the nth term of the series would be;

Tn = Tn-1 + 7 + 2(n-1)

Tn = Tn-1 + 7 + 2n -2

Tn = Tn-1 + 2n + 5

Now there is a fix to this,

n for the term is not the same n for the common difference.

the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.

So we might need to rewrite the final expression as follows;

Tn = Tn-1 + 2(n-1) + 5

6 0

3 years ago

If 24x = 2.4, what is 12x? <br> F) 0.2<br> G) 1.2<br> H) 4.8<br> J) 2

dem82 [27]

<h3>We have to add decimal after one place so the value of 12 will become 1.2 hence option G is correct.</h3>

3 0

3 years ago

(2x-3)(3x+4) expand and simplify

elixir [45]

Answer:

6x² - x - 12

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor.

(2x - 3)(3x + 4)

= 2x(3x + 4) - 3 (3x + 4) ← distribute both parenthesis

= 6x² + 8x - 9x - 12 ← collect like terms

= 6x² - x - 12 ← in expanded form

5 0

3 years ago