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2 years ago

Evaluate the expression below for s=2 and t=7

1 answer:

6 0

First replace the letters with the numbers it gave so you have 3(2)(7)^2-(2)^2

multiply the 3 and 2 together to make 6(7)^2-(2)^2

do seven to the second power (7x7) so you get 6(49)-(2)^2

-(2)^2 is the same as -1(2)^2, so that can just become -2^2. so you now have 6(49)-2^2

multiply 6x49 so you have 294-2^2

do two to the second power (2x2) so you get 294-4

294-4=290

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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

1 year ago

Ruth Ann wants to research two different careers, medical doctor and astronaut.

elixir [45]

Answer: visit the US Bureau of Labor Statistics website to find information on both careers

The career section

hope this helped :)

Step-by-step explanation: there is none

3 0

2 years ago

Read 2 more answers

The second side of a triangle is 4cm longer than the first, The third side is 1 less than twice the first, The perimeter is 55cm

lisov135 [29]

Answer:

13 , 17 and 25 cm.

Step-by-step explanation:

Let the length of the first side be x cm.

Then the second is x+4 and the third is 2x-1 cm long.

As the perimeter = 55 cm we have the equation:

x + x + 4 + 2x - 1 = 55

4x + 3 = 55

4x = 52

x = 13 cm.

7 0

2 years ago

Read 2 more answers

What is 1/2 divided by 4?

Natasha_Volkova [10]

1/2/4=1/2 x 1/4 = 1/8

8 0

2 years ago

Read 2 more answers

Caden exercises daily by walking on a treadmill. He sets the machine so that he will walk at a steady rate of 3.6 miles per hour

babunello [35]

Answer:

a) d = 3.6t

b) 10.8 miles

c) 1.2 hours

Step-by-step explanation:

For part a:

Slope of a line: y = mx + b

In this case, the equation would be: d = mt,

where m represents the speed Caden is walking at.

Note: b = 0 in this case because when Caden starts walking on the treadmill, he hasn't really covered any distance yet.

Therefore, plugging in a speed of 3.6 miles per hour, the equation is:

d = 3.6t

For part b:

This is a simple instance of plugging in 3 hours for our t value.

Therefore, d = 3.6 (3)

d = 10.8 miles

For part c:

In this case, we are given that d = 4.32 miles.

Therefore, 4.32 = 3.6t

Dividing both sides by 3.6, we get

t = 1.2 hours

5 0

2 years ago