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aleksley [76]
3 years ago
6

Circle A has a center at the origin and a point M located on the circle at (1,0). Circle B has a center at (-2,1) and point N lo

cated on a circle at (3,1).
Mathematics
1 answer:
kvasek [131]3 years ago
5 0
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3x+3y+6z=9<br> 2x+y+3z=7<br> x+2y-z=-10 <br> any one know the answer
kati45 [8]
3x + 3y + 6z = 9
2x + 1y + 3z = 7    ⇒ 6x + 6y + 8z = 6
1x + 2y  - 1z = -10                                   6x + 6y + 8z = 6
                                                                                4z = 12 
3x + 3y + 6z = 9                                                       4      4
2x + 1y + 3z = 7    ⇒  0x + 0y + 4z = 12                    z = 3
1x + 2y  - 1z = -10                                             2x + y = -2
                                                                      2x + (-4) = -2
                                                                          2x - 4 = -2
                                                                              + 4  + 4
                                                                               2x = 2
                                                                                2     2
                                                                                 x = 1
                                                                       (x, y, z) = (1, -4, 3)
7 0
3 years ago
Find approximate solution for the equation in the interval -π tan x= 2 csc x
tresset_1 [31]

Answer:

The angle in the 1st quadrant is 1.144 and in the 4th quadrant is -1.144

∴ The answer is (a)

Step-by-step explanation:

* The domain of the function is -π < x < π

- Then the angle is in the 1st or 4th quadrant

∵ tan(x) = 2 csc(x)

∵ tan(x) = sin(x)/cos(x)

∵ csc(x) = 1/sin(x)

∴ sin(x)/cos(x) = 2(1/sin(x)) = 2/sin(x) ⇒ using cross multiplication

∴ sin²(x) = 2cos(x)

∵ sin²(x) = 1 - cos²(x) ⇒ substitute it in the last step

∴ 1 - cos²(x) = 2cos(x) ⇒ arrange the terms in one side

∴ cos²(x) + 2cos(x) - 1 = 0

* Lets factorize it using the formula

∵ a = 1 , b = 2 , c = -1

∵ x = [-b ± √(b² - 4ac)]/2(a) ⇒ formula of quadratic equation

∵ b² - 4ac = 2² - 4(1)(-1) = 4 - -4 = 4 + 4 = 8

∵ √8 = 2√2

∴ cos(x) = [-2 ± 2√2]/2(1) = [-2 ± 2√2]/2 ⇒ ÷ 2 up and down

∴ cos(x) = -1 ± √2

* cos(x) = -1 + √2 ⇒ positive value and cos(x) = -1 - √2 ⇒ negative value

∵ x lies on 1st or 4th quadrant

∴ cos(x) must be positive according to the ASTC rule

∴ We will rejected the negative value

* Now lets find the values of angle x

∵ cos(x) = -1 + √2

∴ x = cos^-1(-1 + √2) = 1.1437 ≅ 1.144 ⇒ approximated to the nearest

  3 decimal place

* The angle in the 1st quadrant is 1.144 and in the

  4th quadrant is-1.144

∴ The answer is (a)

4 0
3 years ago
The coordinate of A is -3, and the coordinate of B is 0.5  Find AB ..please explain answer 
vesna_86 [32]
A = (-3)
B = (0.5)

|AB| = |0.5 - (-3)| = |0.5 + 3| = |3.5| = 3.5
3 0
3 years ago
Can anyone help me with trig identities?
nevsk [136]

Answer:

cosA = √(21/25)

Step-by-step explanation:

We know

sin²(A) + cos²(A) = 1

Next, we know that sin(A) = 2/5. Plugging that into our equation, we get

(2/5)² + cos²A = 1

4/25 + cos²A = 1

subtract 4/25 from both sides to isolate cos²A

cos²A = 1 - 4/25 = 25/25-4/25 = 21/25

square root both sides to get

cosA = √(21/25)

We do not include -√(21/25) in our possible answer for cosA because this is in quadrant 1, so cosA must be positive.

6 0
3 years ago
5. David Read's the problem:
vladimir1956 [14]

Answer:

No, David's answer does not seem reasonable.

Let x= original purchase amount

25x = $10.25, so solve for x by dividing both sides by .25, and you get x = $41.

If the shirt was $18, the shorts must have been $41-$18 = $23 NOT $41.

Step-by-step explanation:

7 0
3 years ago
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