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3 years ago

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Evaluate the expression below at x=5 (2x-5) (x-1) PLEASE HELP FASTT

1 answer:

GrogVix [38]3 years ago

5 0

Answer:

B. 20

Step-by-step explanation:

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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

which of the following is the missing reason? Statements Reasons three halves times x plus 5 equals negative 4 Given 3x + 10 = −

den301095 [7]

Answer:

The missing reason is Subtraction Property of Equality.

Step-by-step explanation:

$\frac{3}{2}x+5=-4$ ⇒ (Given)

On Solving we get;

Multiplying 2 on both side we get;

$2(\frac{3}{2}x+5)=-4\times2\\\\2\times \frac{3}{2}x+5\times 2=-4\times 2$

$3x+10=-8$ ⇒ (Multiplication Property of Equality)

Now Subtracting Both side by 10 we get;

$3x+10-10=-8-10$

$3x = -18$ ⇒ (Subtraction Property of Equality)

Now Dividing both side by 3 we get;

$\frac{3x}{3} = \frac{-18}{3}$

$x=-6$ ⇒ (Division Property of Equality)

Hence the missing reason is Subtraction Property of Equality.

8 0

3 years ago

Read 2 more answers

How do I do 3? Thanks a bunch

Nataly_w [17]

A does

Hope that helps!

5 0

3 years ago

NEED HELP ASAP WILL GIVE BRAINLY IF CORRECT 20 POINTS

Lunna [17]

The answer is the second one

7 0

3 years ago

Read 2 more answers

Joe is making a recipe that calls for 3/4 teaspoon of cinnamon. His only measuring spoon holds 1/8 teaspoon. How many times will

allochka39001 [22]

He will need to fill his measuring cup 8 times

6 0

3 years ago