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1 year ago

Simplify the following expression

Mathematics

1 answer:

inysia [295]1 year ago

8 0

The simplified form of given expression is $\frac{z^{3}}{x y^{2}}$

Answer: Option B

<u>Step-by-step explanation:</u>

Given expression:

$\frac{4 x^{0} y^{-2} z^{3}}{4 x}$

To find the simplified form of the given expression

We know, x to the power 0 is equal to 1. i.e. $x^{0}=1$ . Therefore, it gets removed in the given expression.

$\frac{4 y^{-2} z^{3}}{4 x}$

As common ‘4’ in numerator and denominator also gets cancelled in the given expression

$\frac{y^{-2} z^{3}}{x}$

Bring negative exponents (in numerator) down (to denominator) to form positive exponents, we get the simplified form of given expression as below,

$\frac{z^{3}}{x y^{2}}$

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The angle measures associated with which set of ordered pairs share the same reference angle

Trava [24]

Answer:

Option 3 is right.

Step-by-step explanation:

Reference angle of x is obtained by either 180-x, 180+x. or 360-x depending on the posiiton of terminal whether II quadrant or iv quadrant, or iii quadrant, etc.

In whatever way we find reference angles,

cos will remain cos only and sin will remain sin only there may be only changes in sign.

Of all the ordered pairs given, we find that I, II, and Iv there is a switch over form cos to sine and sin to cos. Hence these options cannot be for reference angles.

III option is $(-\frac{1}{2} ,\frac{-\sqrt{3} }{2} )(\frac{1}{2} ,\frac{\sqrt{3} }{2} )$

show that both sign and cos changed sign. This is possible only in III quadrant.

ie reference angle of orignal angle t = 180+t

SO this option is right.

7 0

1 year ago

Read 2 more answers

You have two circles, one with radius r and the other with radius R. You wish for the difference in the areas of these two circl

gtnhenbr [62]

Answer:

maximum difference of radii = $(r-R)=\frac{1}{2\pi ^{2}}$

Step-by-step explanation:

We know that area of circle is given by

$A=\pi \times (radius)^{2}$

For circle with radius 'r' we have

$A_{1}=\pi \times (r)^{2}$

For circle with radius 'R' we have

$A_{2}=\pi \times (R)^{2}$

Now according to given condition we have

$A_{1}-A_{2}\leq \frac{5}{\pi }$

$\Rightarrow \pi r^{2}-\pi R^{2}\leq \frac{5}{\pi }\\\\\Rightarrow (r^{2}-R^{2})\leq \frac{5}{\pi ^{2}}\\\\(r+R)(r-R)\leq \frac{5}{\pi ^{2}}\\\\\because (a^{2}-b^{2})=(a+b)(a-b)\\\\(r+R)=10(Given)\\\\\Rightarrow(r-R)\leq \frac{5}{10\pi ^{2}}\\\\\therefore (r-R)\leq\frac{1}{2\pi ^{2}}$

Thus maximum difference of radii = $(r-R)=\frac{1}{2\pi ^{2}}$

6 0

2 years ago

"On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wi

Vika [28.1K]

0.25 inches represents 1 mile

----------------------------------------------
Find 1 inch:
----------------------------------------------
1 inch represents 1 ÷ 0.25 miles
1 inch represents 4 miles

----------------------------------------------
Find 3.75 inches:
----------------------------------------------
1 inch represents 4 miles
3.75 inches represent 4 x 3.75 miles
3.75 inches represent 15 miles

----------------------------------------------
Find 2.25 inches:
----------------------------------------------
1 inch represents 4 miles
2.25 inches represent 4 x 2.25 miles
2.25 inches represent 9 miles

----------------------------------------------
Find Area:
----------------------------------------------
Area = Length x Width
Area = 15 x 9
Area = 135 miles²

----------------------------------------------
Answer: 135 miles²
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6 0

2 years ago

Read 2 more answers

Three friends went running. The table below shows their last 3 lap times.

Goryan [66]

Answer: 1 min 50 sec

Step-by-step explanation:

The range is max value - min value

min value = 14 mins 40 sec

max value = 16 mins 30 sec

so now subtract these 16 mins 30 sec - 14 mins 40 sec

= 1 min 50 sec

5 0

2 years ago

Luke has 1/5 of a package of dried apricots. He divides the dried apricots equally into 4 small bags. Luke gives one of the bags

Ivahew [28]

Answer:

3/80

Step-by-step explanation:

If one fifth of apricots are split into 4 parts, each bag has 1/5 * 1/4 of the original apricots

1/5 * 1/4 = 1/20

Luke keeps 3/4 of those so that's

3/4 * 1/20 = 3/80

7 0

1 year ago