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3 years ago

Find the value of each trigonometric ratio

Mathematics

1 answer:

Mila [183]3 years ago

8 0

$27)\\sine=\dfrac{opposite}{hypotenuse}\\\\\text{We have:}\\opposite=40\\hypotenuse=50\\\\\sin C=\dfrac{40}{50}=\dfrac{4}{5}\\\\29)\\\\tangent=\dfrac{opposite}{adjacent}\\\text{We have:}\\opposite=18\\adjacent=24\\\\\tan C=\dfrac{18}{24}=\dfrac{18:6}{24:6}=\dfrac{3}{4}$

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Why does no one love me

Mariana [72]

Sometimes we start to lose faith, in those moments we think that no one loves us when they do, they care about us too. It's just your head messing with you. It's like saying "I'm depressed" but you're really not. it's just that you keep saying is that your brain starts believing it. Most of the time it's you losing faith. Which is completely normal and everyone in their life will once feel that way. That's why people often decide to end life way too soon. They don't know it's only going to last some time. It's going to be hard of course but it will soon have to come to an end, and when it does you will feel free and you will be able to enjoy life the way you are supposed to.

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8 0

2 years ago

A boat travels 8 miles upstream in the same amount of time it can travel 12 miles downstream. In still water the speed of the bo

Anastaziya [24]

Answer:

1 mi/hr

Step-by-step explanation:

Given that:

Speed in still water, s = 5 mi/hr

Let speed of current = x

Time = distance /speed

Upstream (subtract speed of current) = 5 - x

Upstream time = 8 / 5 - x - - - (1)

Downstream (add speed of current) = 5 + x

Downstream time = 12 / 5 + x - - - (2)

Equate (1) and (2)

8 / (5 - x) = 12/ (5 + x)

8(5 + x) = 12(5-x)

40 + 8x = 60 - 12x

40 - 60 = - 12x - 8x

-20 = - 20x

x = 1

Spwed of current = 1 mi/hr

7 0

3 years ago

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

pashok25 [27]

Answer with Step-by-step explanation:

We are given that

$f(x,y,z)=10x+10y+3z$

$g(x,y,z)=5x^2+5y^2+3z^2=43$

We have to find the extreme values of the function.

$f_x(x,y,z)=10,f_y(x,y,z)=10,f_z(x,y,z)=3$

$g_x(x,y,z)=10x,g_y(x,y,z)=10y,g_z(x,y,z)=6z$

$\Delta f(x,y,z)=\lambda \Delta g(x,y,z)$

Therefore,

$10=\lambda 10x\implies x=\frac{1}{\lambda}$

$10=10y\lambda\implies y=\frac{1}{\lambda}$

$3=6z\lambda$

$z=\frac{1}{2\lambda}$

Substitute the values in g(x)

Then, we get

$\frac{5}{\lambda^2}+\frac{5}{\lambda^2}+\frac{3}{4\lambda^2}=43$

$\frac{20+20+3}{4\lambda^2}=43$

$\frac{43}{4\lambda^2}=43$

$\lambda^2=\frac{43}{4\times 43}$

$\lambda=\pm\frac{1}{2}$

When $\lambda=\frac{1}{2}$ then,

$x=2,y=2,z=1$

When $\lambda=-\frac{1}{2}$

Then, $x=-2,y=-2,z=-1$

$f(2,2,1)=10+10+3=23$

$f(-2,-2,-1)=-10-10-3=-23$

Hence, maximum value of f(x,y,z) is 23 at (2,2,1) and minimum value of f(x,y,z) is -23 at (-2,-2 ,-1).

8 0

3 years ago

A waitress sold ribeye steak dinners and grilled salmon dinners, totaling $ on a particular day. Another day she sold ribeye s

Paul [167]

Answer:

ribeye steak: $24.37
grilled salmon: $9.30

Step-by-step explanation:

If we let r and g represent the costs of a ribeye steak dinner and grilled salmon dinner, respectively, the sales figures give rise to two equations.

17r +15g = 553.74

22r +5g = 582.65

If we multiply the second equation by 3 and subtract the first, we have ...

3(22r +5g) -(17r +15g) = 3(582.65) -(553.74)

49r = 1194.21

r = 1194.21/49 ≈ 24.37

g = (553.74 -17r)/15 ≈ 9.30

The steak dinner costs $24.37; the salmon dinner costs $9.30.

_____

<em>Check</em>

17(24.37) +15(9.30) = 553.79 . . . not 553.74

22(24.37) +5(9.30) = 582.64 . . . not 582.65

There is no exact solution to this problem.

4 0

3 years ago

Read 2 more answers

68 ounces equals in pounds in fraction form?

Vlada [557]

<span>1 ounce = 0.0625 pounds

0.0625 * 65 = 4.25
68 ounces = 4.25 pounds

.25 is the same as 25/100..

4 25/100

25 / 25 = 1
100 / 25 = 4

4 1/4.

So, 68 ounces = 4.25 lb = 4 1/4.

Hope I helped ya!! </span>

7 0

3 years ago

Read 2 more answers