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3 years ago

Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants.

Mathematics

2 answers:

Mazyrski [523]3 years ago

3 0

Answer:

Step-by-step explanation:

sin x=a+b

cos x=a-b

sin²x+cos²x=(a+b)²+(a-b)²=2a²+2b²

or 2a²+2b²=1

a²+b²=1/2 which is constant for all values of x

(ii)

$\frac{\sin x}{\cos x}=\frac{a+b}{a-b}\\\tan x=\frac{a+b}{a-b}=2\\a+b=2a-2b\\b+2b=2a-a\\or a=3b$

trasher [3.6K]3 years ago

3 0

Answer:25

Step-by-step explanation:

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At her birthday party, Ms. Willow would not give her age directly. She said, 'If you add the year of my birth to this year, s

Nimfa-mama [501]

Answer:

69 years

Step-by-step explanation:

Given that:

Let year of birth = x

This year = 2020

Year of 25th birthday = x + 25

Year of 55th birthday = x + 55

Present age = 2020 - x

Hence,

x + 2020 - (x + 25 + x + 55) + (2020 - x) = 58

x + 2020 - (2x + 80) + (2020 - x) = 58

x + 2020 - 2x - 80 + 2020 - x = 58

-2x + 4040 - 80 = 58

-2x + 3960 = 58

-2x = 58 - 3960

-2x = - 3902

x = 1951

Birth year = 1951

Hence, age =

2020 - 1951 = 69 years

5 0

2 years ago

A car salesperson earns a $500 fee per car she sells. If She sells 4 cars in one day,

Semmy [17]

You would have to do 500x 4 which is 2000

7 0

3 years ago

Read 2 more answers

Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

1 year ago

Lisa wants to buy material for her dress. If she buys 7metres, she is 1 dollar short. If she buys 5metres, 5 dollars is left ove

Ede4ka [16]

Answer:

She has 15 dollar.

Explanation

If every meter costs 2 dollars, then 5 meter would cost 10 dollars and 7 meter would cost 14 dollar. Now we take a number when subtracted from 10, we get 5 dollar and when the same number subtracted from 14 we get 1 dollar left. Now if we take 15 dollar, you'll see that when you subtract 10 from it you get 5 dollar and when you subtract 14 from it you get 1 dollar. Therefore 15 satisfies the given condition in the question.

$15 - $10 = $5

$15 - $14 = $1

4 0

2 years ago

Myra can fill 18 glasses with 2 container of ice tea. How many glasses can she fill with 3 container of tea?

OLga [1]

She can fill 24 glasses with 3 containers of tea

6 0

2 years ago

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