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2 years ago

Question 9 of 25

Mathematics

2 answers:

mote1985 [20]2 years ago

5 0

Answer:

Step-by-step explanation:

an arithmetic sequence is B

laila [671]2 years ago

4 0

Answer:0c

Step-by-step explanation:

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Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

$\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\$

$x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\$

$\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]$

4 0

2 years ago

Robbie has 2 times as many apples as Bob. After receiving 35 more, Robbie now has 7 times as many as Bob. How many apples does B

Hoochie [10]

Answer: 18.5 apples

Step-by-step explanation:

7 0

2 years ago

A number,M, is rounded to 1 decimal place. the result is 9.4 complete the error interval for M

ivann1987 [24]

Answer:

$9.35 \le M \le 9.45$

Step-by-step explanation:

Given

$M = 9.4$ to 1 d p

Required

The error interval

The error interval is represented as:

$Lower \le M \le Upper$

Where

$Lower = M - 0.05$

$Upper = M + 0.05$

So, we have:

$Lower = M - 0.05$

$Lower = 9.4 - 0.05$

$Lower = 9.35$

$Upper = M + 0.05$

$Upper = 9.4 + 0.05$

$Upper = 9.45$

Hence, the error interval: $Lower \le M \le Upper$ is:

$9.35 \le M \le 9.45$

3 0

3 years ago

What is 0.0000001 converted to the tenth power

jenyasd209 [6]

this would look like this: 0.0000001^10

If we were to do 0.0000001*0.0000001 it would be 0.00000000000010

We doubled the zeroes and moved the one up. Continue on until you reach the tenth power.

6 0

3 years ago

What should be included ina financial plan to protect assets?

pantera1 [17]

Answer:

Step-by-step explanation:

its important to have a large savings so that if something happens & it's an emergency, you can touch THOSE funds and not your assets, which may lose you money.

5 0

3 years ago

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