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GuDViN [60]
2 years ago
9

(PLEASE HELP) The height of a plants increase in the ratio 4 : 6. The height at present is 280 cm, what is new height?

Mathematics
1 answer:
sleet_krkn [62]2 years ago
5 0

Answer:

see photo for your analysis

Step-by-step explanation:

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PLS ANSWER ASAP 30 POINTS!!! CHECK PHOTO! WILL MARK BRAINLIEST TO WHO ANSWERS
Sveta_85 [38]

I'll do Problem 8 to get you started

a = 4 and c = 7 are the two given sides

Use these values in the pythagorean theorem to find side b

a^2 + b^2 = c^2\\\\4^2 + b^2 = 7^2\\\\16 + b^2 = 49\\\\b^2 = 49 - 16\\\\b^2 = 33\\\\b = \sqrt{33}\\\\

With respect to reference angle A, we have:

  • opposite side = a = 4
  • adjacent side = b = \sqrt{33}
  • hypotenuse = c = 7

Now let's compute the 6 trig ratios for the angle A.

We'll start with the sine ratio which is opposite over hypotenuse.

\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(A) = \frac{a}{c}\\\\\sin(A) = \frac{4}{7}\\\\

Then cosine which is adjacent over hypotenuse

\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(A) = \frac{b}{c}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\

Tangent is the ratio of opposite over adjacent

\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(A) = \frac{a}{b}\\\\\tan(A) = \frac{4}{\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{(\sqrt{33})^2}\\\\\tan(A) = \frac{4\sqrt{33}}{33}\\\\

Rationalizing the denominator may be optional, so I would ask your teacher for clarification.

So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.

  • cosecant, abbreviated as csc, is the reciprocal of sine
  • secant, abbreviated as sec, is the reciprocal of cosine
  • cotangent, abbreviated as cot, is the reciprocal of tangent

So we'll flip the fraction of each like so:

\csc(\text{angle}) = \frac{\text{hypotenuse}}{\text{opposite}} \ \text{ ... reciprocal of sine}\\\\\csc(A) = \frac{c}{a}\\\\\csc(A) = \frac{7}{4}\\\\\sec(\text{angle}) = \frac{\text{hypotenuse}}{\text{adjacent}} \ \text{ ... reciprocal of cosine}\\\\\sec(A) = \frac{c}{b}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(\text{angle}) = \frac{\text{adjacent}}{\text{opposite}} \ \text{  ... reciprocal of tangent}\\\\\cot(A) = \frac{b}{a}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\

------------------------------------------------------

Summary:

The missing side is b = \sqrt{33}

The 6 trig functions have these results

\sin(A) = \frac{4}{7}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\\tan(A) = \frac{4}{\sqrt{33}} = \frac{4\sqrt{33}}{33}\\\\\csc(A) = \frac{7}{4}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\

Rationalizing the denominator may be optional, but I would ask your teacher to be sure.

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1 year ago
How to solve by elimination
natka813 [3]
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5 0
3 years ago
exam p A drawer contains four pairs of socks, with each pair a different color. One sock at a time is randomly drawn from the dr
Marta_Voda [28]

Answer:

The probability that the maximum number of draws is required is 0.2286

Step-by-step explanation:

The probability that the maximum number of draws happens when you pick <em>different colors in the first four pick</em>.

Assume you picked one sock in the first draw. Its probability is 1, since you can draw any sock.

In the second draw, 7 socks left and you can draw all but the one which is the pair of the first draw. Then the probability is \frac{6}{7}

In the third draw, 6 socks left and you can draw one of the two pair colors which are not drawn yet. Its probability is \frac{4}{6}

In the forth draw, 5 socks left and only one pair color, which is not drawn. The probability of drawing one of this pair is \frac{2}{5}

In the fifth draw, whatever you draw, you would have one matching pair.

The probability combined is 1×\frac{6}{7} ×\frac{4}{6}× \frac{2}{5} ≈ 0.2286

5 0
3 years ago
If m = 16 and n = 4, what is the value of the following expression?<br> m - 2 • n + 2
Elan Coil [88]

Answer:

10

Step-by-step explanation:

Use PEMDAS to rewrite the equation as:

m - (2 * n) + 2 =

16 - (2 * 4) + 2 =

16 - 8 + 2 =

10

7 0
3 years ago
Read 2 more answers
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