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3 years ago

Given that 27-1/3 3 = 94 + 3r 31 find the exact value of x.

Mathematics

1 answer:

borishaifa [10]3 years ago

5 0

Answer:

the exact value is x =1/2 or x=0.5

your welcome!

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

DanielleElmas [232]

Answer:

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

7 0

2 years ago

⅘ of a packet of sweets are fizzy. If there are 40 sweets in the packet, how many are fizzy sweets?

Colt1911 [192]

Answer:

32 fizzies

Step-by-step explanation:

4/5 = .8

.8 x 40 = 32

- I found that 80% of 40 is 32 therefore 32 fizzies are in the packet of sweets.

- Hope this helps! If you need a further explanation please let me know.

4 0

3 years ago

Which of these are coordinates for parts of the Ranger Station

anastassius [24]

ANSWER

F (2,3)

EXPLANATION

The coordinates are ordered pairs.

So the x-coordinate comes first and the y-coordinate second.

In other words the coordinate on the horizontal axis comes first and that of the vertical axis comes second.

The coordinates of the ranger station are:

(2,3),(2,4),(3,3),(3,4)

The correct choice is F.

6 0

2 years ago

Read 2 more answers

find the slope of the line passing through each pair of points or state that the slope is undefined. then indicate weather the l

Travka [436]

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..................

7 0

3 years ago

. Suppose that at UVA, 76% of all undergraduates are in the College, 10% are in Engineering, 7% are in Commerce, 3% are in Nursi

xxMikexx [17]

Answer: 34.2%

Step-by-step explanation:

76% of undergrads in The College

45% of those are male (since 55% female)

.76 x .45 = 34.2% of all undergrads are males in The College

4 0

3 years ago