3/4 is 1/3 of what number? Write a division expression to match this expression

URGENT HELP PLEASE!

Vaselesa [24]

Answer:

(a) $x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b) $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Step-by-step explanation:

It is given that $0\leq x\leq 2\pi$ .

(a)

$\sqrt{2}\sin 2x=1$

$\sin 2x=\dfrac{1}{\sqrt{2}}$

$\sin 2x=\dfrac{\pi}{4}$

$2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}$ $[\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]$

$x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}$

(b)

$\csc^2 x-\csc x-2=0$

$\csc^2 x-2\csc x+\csc x-2=0$

$\csc x(\csc x-2)+1(\csc x-2)=0$

$(\csc x+1)(\csc x-2)=0$

$\csc x=-1\text{ or }\csc x=2$

$\sin x=-1\text{ or }\sin x=\dfrac{1}{2}$ $[\because \sin x=\dfrac{1}{\csc x}]$

$x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}$

Therefore, $x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}$ .

5 0

3 years ago

Y=? What is Y? Please help me!

kumpel [21]

Answer: y = 6 mi. .
______________________________________________
Explanation:
______________________________________________
Area of a triangle = (½) * (base) * (height) ;

or, A = (½) * b * h ; or, A = b*h / 2 ;
_____________________________________
Given: A = 24.3 mi ² ;
b = 8.1 mi
___________________
Find the height, "h" ; (in units of "miles", or , "mi" ).
__________________________
Plug in the known values into the formula:

24.3 mi ² = (½) * (8.1 mi) *(h) ;
_____________________________
Solve for "h" (height) ;
_____________________________
(½) * (8.1 mi) = 4.05 mi ;
______________________________
Rewrite:
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24.3 mi² = (4.05 mi) *(h) ; Solve for "h" ;
_________________________________________
Divide each side of the equation by "(4.05 mi)" ; to isolate "h" on one side of the equation ; and to solve for "h" ;
__________________________________________
24.3 mi² / 4.05 mi = (4.05 mi) *(h) / 4.05 mi ;

→ 6 mi = h ; ↔ h = 6 mi.

→ h = y = 6 mi.
____________________________________________

7 0

3 years ago

Read 2 more answers

The outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63 degre

Rasek [7]

Answer:

For 124 chirps per minute the temperature is 68 ºF.

For 68 chirps per minute the temperature is 54 ºF.

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form

$f(x)=b+mx$

b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.

m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.

We know that

At 104 chirps per minute, the temperature is 63 ºF.

At 176 chirps per minute, the temperature is 81 ºF.

This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and y = the temperature in ºF.

To find a linear function that let us find the outside temperature from how fast crickets chirp we must:

Find the slope:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{81-63}{176-104}=\frac{1}{4}$

Find the equation:

$81=\frac{1}{4}\cdot 104+b$

Solving for b

$b=81-\frac{1}{4} (176)=37$

Therefore, the linear function is

$y=\frac{1}{4} \cdot x+37$

Now, using this linear function we can know the temperature when we know the chirps per minute:

For 124 chirps per minute the temperature is:

$y=\frac{1}{4} \cdot (124)+37=68$

For 68 chirps per minute the temperature is:

$y=\frac{1}{4} \cdot (68)+37=54$

6 0

2 years ago

batteries which normally sell for $1.89 a pack are on sale for $3.40 for two packs. approximately what percentage markdown does

aev [14]

Normally, two packs of batteries cost $1.89*2=$3.78. The discounted price of $3.40 divided by the standard price of $3.78 for two packs is approximately .9, or 90 percent. Therefore, we have an approximately ten percent discount with the sale.

6 0

3 years ago

Read 2 more answers

You decide that you want to purchase a Tesla SUV. You borrow \$95,000 for the purchase. You agree to repay the loan by paying eq

liraira [26]

Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.

<h3>What is compound interest?</h3>

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$