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3 years ago

For what values of the variables are the following expressions defined? 5y+2

Mathematics

2 answers:

babymother [125]3 years ago

3 0

Answer:

all possible y values

Step-by-step explanation:

5y + 2 is defined for all values of y.

mina [271]3 years ago

3 0

Answer:

all real numbers

Step-by-step explanation:

There is no restriction on the value of y, so the expression is defined for all real numbers.

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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

6 0

3 years ago

in 2010, sarah spent $500 buying clothes. In 2013, she spent $350 buying clothes. What was the rate change from 2010 to 2013?

Yuki888 [10]

Answer:

150

Step-by-step explanation

because 500 minus 350 is 150

5 0

3 years ago

A rocking horse has a weight limit of 60pounds. What percentage of the weight limit is 33 pounds? What percentage of the weight

bixtya [17]

Answer:

The percentage is 55% when weight limit is 33 pounds.

The percentage is 190% when weight limit is 114 pounds.

The 95% of the limit weighs 57 pounds.

Step-by-step explanation:

Given:

Weight limit of rocking horse = 60 pounds.

We need to find:

a) What percentage of the weight limit is 33 pounds.

b)What percentage of the weight limit is 114 pounds.

c) What weight is 95% of the limit.

Now Solving for a we get;

Weight limit = 33 pounds

Now percentage of the weight limit can be calculated by dividing given weight limit with total weight limit and then multiplying by 100 we get;

framing in equation form we get;

percentage of the weight limit = $\frac{33}{60}\times100 = 55\%$

Hence The percentage is 55% when weight limit is 33 pounds.

Now Solving for b we get;

Weight limit = 114 pounds

Now percentage of the weight limit can be calculated by dividing given weight limit with total weight limit and then multiplying by 100 we get;

framing in equation form we get;

percentage of the weight limit = $\frac{114}{60}\times100 = 190\%$

Hence The percentage is 190% when weight limit is 114 pounds.

Now Solving for c we get;

Percentage Weight = 95%

Now Amount of weight limit can be calculated by multiplying Percentage weight limit with total weight limit and then Dividing by 100 we get;

framing in equation form we get;

percentage of the weight limit = $\frac{95}{100}\times60 = 57 \pounds$

Hence The 95% of the limit weighs 57 pounds.

4 0

3 years ago

Which special version of the Pythagorean Theorem can you use to find the length of any square's diagonal, d, using only the leng

kodGreya [7K]

The square's diagonal is the triangle's hypotenuse.

the original Pythagorean theorem is $a^{2} + b^{2} = c^{2}$ where a and b are the two sides and c is the hypotenuse.

that means the Pythagorean theorem for this question is:

$s^{2} + s^{2} = d^{2}$ or $2( s^{2} )= d^{2}$

8 0

3 years ago

Read 2 more answers

Would appreciate the help

raketka [301]

Answer:

x° = 37°

Step-by-step explanation:

* Lets revise some facts of a circle

- The secant is a line intersect the circle in two points

- If two secants intersect each other in a point outside the circle,

then the measure of the angle between them is half the difference

of the measures of their intercepted arcs

* Now lets solve the problem

- There is a circle

- Two secants of this circle intersect each other in a point outside

the circle

∴ The measure of the angle between them = 1/2 the difference of the

measures of their intercepted arcs

∵ The measure of the angle between them is x°

∵ The measures of their intercepted arcs are 26° and 100°

- Use the rule above to find x

∴ x° = 1/2 [ measure of the large arc - measure of small arc]

∵ The measure of the large arc is 100°

∵ The measure of the small arc is 26°

∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°

∴ x° = 37°

4 0

3 years ago