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klasskru [66]
3 years ago
15

If x = 4cosa and y = 5tana, find (x^2/16) - (y^2/25)​

Mathematics
1 answer:
Cloud [144]3 years ago
3 0

x = 4 \cos(a)

\frac{x}{4}  =  \cos(a)  \\

( { \frac{x}{4} })^{2}  =  ({ \cos(a) })^{2}  \\

\frac{ {x}^{2} }{16}  =  {cos}^{2} (a) \\

_____________________________________________

y = 5 \tan(a)

\frac{y}{5}  =  \tan(a)  \\

( { \frac{y}{5} })^{2}  = ( { \tan(a) })^{2}  \\

\frac{ {y}^{2} }{25}  =  {tan}^{2} (a) \\

_____________________________________________

Thus ;

\frac{ {x}^{2} }{16}  -  \frac{ {y}^{2} }{25}  =  \\

{cos}^{2} (a) -  {tan}^{2} (a)

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Answer:

D. 8pi>24 cause this is the right answer

7 0
3 years ago
Two rectangles are similar. The first rectangle has a length of 15 cm and a width of 10 cm. The width of the second rectangle is
Margarita [4]

Answer:

Its length is 37.5 cm.

Step-by-step explanation:

If two rectangles are similar, their sides are proportional, that is, they have equal ratios. So

The first rectangle has a length of 15 cm and a width of 10 cm. The width of the second rectangle is 25 cm.

So

\frac{15}{10} = \frac{l}{25}

10l = 25*15

Simplifying by 10.

l = 2.5*15 = 37.5

Its length is 37.5 cm.

7 0
3 years ago
The Martinez family visit the aquarium and saw 483 salt water fish and 358 freshwater fish later that month workers moved 139 fi
VARVARA [1.3K]

Answer:

702

Step-by-step explanation:

The total number of Fish in the aquarium is got by adding up the

Number of Salt Water Fish, and

Number of Fresh water Fish

Number of Salt water Fish = 483

Number of Fres hwater Fish = 358

Total Fish in Aquarium = 483 + 358 = 841

Later, 139 were moved to a new aquarium, the number of fish remaining is 841 MINUS 139. That is:

841 - 139 = 702 fish remaining now

6 0
3 years ago
A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindr
Kobotan [32]
For the wooden box, if you do 7560 ÷ 180 you get 42. that's how many boxes you would need. multiply 42 by the cost of the wooden boxes: 42 × 0.70 you get 29.40 dollars

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to save money, the company should use the plastic containers because it costs less than the wooden ones.
8 0
3 years ago
Read 2 more answers
Which exponential functions have been simplified correctly check all that apply
Fittoniya [83]
Principle: Law of Exponents - Combination of product to a power & power to a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In equation it is,

(xy)^a = (x^a)(y^a)

The latter is when raising the base with a power to a power, the base will remain the same and the powers will be multiplied. In equation it is, 
(x^a)(x^b) = x^ab

Check:


f(x) = 5*(16)^.33x = 5*(8*2)^0.33x = 5*(8^0.33x)(2^0.33x) = 5*(2^x)*(2^0.33x) = 5*(2^1.33x)

f(x) = 2.3*(8^0.5x) = 2.3*(4*2)^0.5x = 2.3*(2^x)(2^0.5x) = 2.3*(2^1.5x)

f(x) = 81^0.25x = 3^x

f(x) = 0.75*(9*3)^0.5x = 0.75*(3^x)*(3^0.5x) = 0.75*3^1.5x

f(x) = 24^0.33x = (8*3)^0.33x = (2^x)*(3^0.33x)


Therefore, the answer is third equation.

<em>ANSWER: f(x) = 81^0.25x = 3^x</em>
5 0
3 years ago
Read 2 more answers
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