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2 years ago

Solve the equation: 1. |x-7|=8 2. |x-9|=-14

Mathematics

2 answers:

Lyrx [107]2 years ago

5 0

Answer:

1. $x=-1; x=15$
2. Impossible

Step-by-step explanation:

About #1.

There are two ways of reasoning.

Algebrically, you split the absolute value in two based on the sign of the quantity $x-7$

$x-7 = 8; x\ge7\\x=15\\x-7=-8; x < 7\\x=-1$

Geometrically, and it's a personal preference of mine, you're asking to find the numbers that are 8 units away from 7. One is to the right (15), and the other is to the left (-1).

#2 is impossible. The modulus of a number is by definition non negative, so it can never be equal to a negative number.

Alecsey [184]2 years ago

4 0

1. x=-1 or x=15
2. no sol

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All possible solutions for 6sin^2(3x)=-3

vova2212 [387]

Answer:

Please check the step-by-step explanation for the answer.

Step-by-step explanation:

Considering the trigonometric expression

$6sin^2\left(3x\right)=-3$

Steps

$\mathrm{Let:\:}\sin \left(3x\right)=u$

$6u^2=-3$

$\mathrm{Divide\:both\:sides\:by\:}6$

$\frac{6u^2}{6}=\frac{-3}{6}$

$u^2=-\frac{1}{2}$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$u=\sqrt{-\frac{1}{2}},\:u=-\sqrt{-\frac{1}{2}}$

$\mathrm{Simplify}\:\sqrt{-\frac{1}{2}}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}$

$=\sqrt{-1}\sqrt{\frac{1}{2}}$

$\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i$

$=i\sqrt{\frac{1}{2}}$

Similarly,

$-\sqrt{-\frac{1}{2}}=\quad -i\sqrt{\frac{1}{2}}$

So,

$u=i\sqrt{\frac{1}{2}},\:u=-i\sqrt{\frac{1}{2}}$

$\mathrm{Substitute\:back}\:u=\sin \left(3x\right)$

$\sin \left(3x\right)=i\sqrt{\frac{1}{2}},\:\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}$

So,

$\sin \left(3x\right)=i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}$

and

$\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}$

$\mathrm{Combine\:all\:the\:solutions}$

$\mathrm{No\:Solution\:for}\:x\in \mathbb{R}$

Keywords: trigonometric equation, solution

Learn more about trigonometric equation solution from brainly.com/question/1687218

#learnwithBrainly

5 0

4 years ago

danica purchased a pair of jeans for $24. she had a 15% coupon. she then had to pay 6% sales tax. what was her final price for t

dexar [7]

Answer:

$18.96

Step-by-step explanation:

Multiply 24 by 0.15= 3.6

Multiply 24 by 0.06= 1.44

Add 3.6 and 1.44= 5.04

Subtract 5.04 from 24= $18.96

4 0

3 years ago

you have $47 to spend at the music store. Each cassette tape costs $5 and each CD cost $10. write a linear inequality that repre

Tamiku [17]

Answer:

47 is greater than or equal to 5x+10y

Step-by-step explanation:

you can't spend more than $47 but you can spend less than or equal to that amount.

8 0

3 years ago

Read 2 more answers

Suppose m= 7, t = 20 and r = 35. what is t(m ÷ r)?

kow [346]

The answer is 4.
Here's how to solve it.

Remove parentheses:
=20 × 7/35
7/35 = 1/5

Cancel the common factor 7:
=1/5
=20 × 1/5

Multiply fractions:
1·20/5

Simplify:
20/5

Divide
20/5=4

Hope this helped! :)

7 0

4 years ago

A scrap metal buyer pays $2.79 per square foot of steel.

RUDIKE [14]

Answer:

a. You can earn about $245

b. You will earn about $35 less if the lid is missing

Step-by-step explanation:

a. To solve this we first need to calculate the surface area of the drum, which has a cylinder shape, therefore it's surface area is given by:

surface area = 2*(pi*r² + pi*r*h)

r = d/2 = 4/2 = 2 ft

surface area = 2*(pi*2² + pi*2*5)

surface area = 2*(4*pi + 10*pi) = 2*14*pi = 28*pi ft²

surface area = 87.96 ft²

Since each square foot pays $2.79, then the total value of the drum is:

value = surface area * 2.79 = 87.96*2.79 = $245.42

b. If the lid of the drum is missing, then the surface area is given by:

area drum with no lid = surface area - lid area

area drum with no lid = 87.96 - pi*(2)² = 87.96 - 12.566 = 75.394 ft²

value = area drum with no lid * 2.79

value = 75.394 * 2.79 = 210.35

loss value = 245.42 - 210.35 = $35.07

7 0

3 years ago