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KIM [24]
3 years ago
5

Let csc(x) = Cosecant (x) = StartFraction 14 Over 10 EndFraction, where 0 less-than x less-than StartFraction pi Over 2 EndFract

ion. Which ratio has a value of StartFraction StartRoot 96 EndRoot Over 14 EndFraction?
cos(x)
sin(x)
sec(x)
cot(x)
Mathematics
2 answers:
dedylja [7]3 years ago
4 0

Answer:

First Option: cos(x)

Step-by-step explanation:

What is given is csc(x) = 14/10

The graph lies in the first quadrant since 0 < x < pi/2

Create a triangle:

The length across is 14

The adjacent is 10

The length of the shorter side is root 96

Use the pythagorean theorem

BC^2 = 14^2 - 10^2

BC^2 = 196 - 100, 96

BC^2 = root 96/14

Recall SOH-CAH-TOA

Adjacent over Hypotenuse is cos

That is how the answer is cos(x)

NeTakaya3 years ago
3 0

Answer:

A. cos(x)

Step-by-step explanation:

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(1,10), (18.-10) slope
kobusy [5.1K]

Answer:

I think the slope is -20/17 hope this helps

8 0
3 years ago
four plastic bottles, each with a radius of 2 inches, are packed into a cardboard box. The glasses touch each other and the side
shepuryov [24]

The area of a 2D form is the amount of space within its perimeter. The area of the bottom of the box is 64 square inches.

<h3>What is an area?</h3>

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or other quadrilateral, multiply its length by its width.

Given the radius of the base of the plastic bottle is 2 inches, and there are four bottles arranged as shown below, therefore, the area of the bottom of the box is,

\rm \text{Area of the bottom of the box} = 8 \times 8 = 64\ in^2

Hence, the area of the bottom of the box is 64 square inches.

Learn more about Area:

brainly.com/question/1631786

#SPJ1

7 0
2 years ago
A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min
sesenic [268]
A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})
\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}
A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4

We're given that A(0)=30. Multiply both sides by the integrating factor e^{t/100}, then

e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4
\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4
e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C
A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}

Given that A(0)=30, we have

30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02

so the amount of salt in the tank at time t is

A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}
3 0
3 years ago
Pythagorean theorem. Appreciate the help with this question . Thank you very much who ever help with the question .
NikAS [45]

\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{30}\\ b=\stackrel{opposite}{40}\\ \end{cases} \\\\\\ x=\sqrt{30^2+40^2}\implies x=\sqrt{2500}\implies x=50

5 0
2 years ago
How many solutions does this system of equations have?<br> y = –2x + 3<br> y = –2x – 1
Nadusha1986 [10]

Answer:

Step-by-step explanation:

in y = mx + b form, the slope is in the m position and the y int is in the b position

y = -2x + 3.....slope is -2 and y int is 3

y = -2x - 1...slope is -2 and y int is - 1

same slope, different y int's....means parallel lines...NO SOLUTION

learn this...it helps

same slope, different y int's = no solution

different slopes, different y int's = 1 solution

same slope, same y int's = infinite solutions

6 0
4 years ago
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