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3 years ago

Please answer this in two minutes

Mathematics

2 answers:

Ipatiy [6.2K]3 years ago

7 0

Answer: 9.9

Step-by-step explanation:

SINE RULE:

7/sin(31) = q / sin(47)

Therefore q = 7 / sin(31) * sin(47)

which equals: 9.9 to the nearest tenth.

natima [27]3 years ago

5 0

Answer:

q = 9.9

Step-by-step explanation:

We can use the rule of sines

sin R sin Q

------------- = ------------

PQ PR

sin 31 sin 47

------------- = ------------

7 q

Using cross products

q sin 31 = 7 sin 47

Divide by sin 31

q = 7 sin 47 / sin 31

q =9.939995043

To the nearest tenth

q = 9.9

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Z^4-5(1+2i)z^2+24-10i=0

mixer [17]

Using the quadratic formula, we solve for $z^2$ .

$z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2$

Taking square roots on both sides, we end up with

$z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}$

Compute the square roots of -171 + 140i.

$|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221$

$\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)$

By de Moivre's theorem,

$\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i$

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

$t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}$

as well as the fact that

$0$

$\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}$

(whose signs are positive because of the domain of $\frac t2$ ).

This leaves us with

$z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}$

Compute the square roots of 5 + 12i.

$|5 + 12i| = \sqrt{5^2 + 12^2} = 13$

$\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)$

By de Moivre,

$\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i$

and its negative, -3 - 2i. We use similar reasoning as before:

$t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}$

$1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4$

$\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}$

$\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}$

Lastly, compute the roots of -2i.

$|-2i| = 2$

$\arg(-2i) = -\dfrac\pi2$

$\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i$

as well as -1 + i.

So our simplified solutions to the quartic are

$\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}$

3 0

1 year ago

On average a herd of elephants travels 10 miles in 12 hours (picture included)

Tema [17]

For the first Q the answer is the first square on the left 10 miles divided by 12 hours = 0,83 miles

And the second Q goes with the last square 12 hours divided by 10 miles = 1.2 h which in minutes is 72 minutes or 1h and 12 minutes.

4 0

3 years ago

Read 2 more answers

Two other forms of 32,005,008

MaRussiya [10]

3.2005008 x 10^7

Thirty-two million five thousand eight.

6 0

3 years ago

shen's mother gave him $10 to go buy groceries. he picked up a gallon oh milk for $3.49,tree pounds of oranges that cost $1.14 p

bekas [8.4K]

Answer:

He didn’t have enough money for the groceries