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Mekhanik [1.2K]
3 years ago
8

Mark As Complete

Mathematics
1 answer:
Sveta_85 [38]3 years ago
8 0

Answer:

  • 22.5" < w < 23.25"

Step-by-step explanation:

<em>Refer to attached</em>

  • 82 model has a width of 22 1/2"
  • 92 model has a width of 23 1/4"

Calvin wants his surfboard be wider than 82 model and narrower than 92 model.

The measurement w of this surfboard could be greater than 22 1/2" and smaller than 23 1/4":

  • 22.5" < w < 23.25"
  • 23" would be an example

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Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2
Anastaziya [24]

Answer:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

Step-by-step explanation:

we would like to figure out the derivative of the following:

\displaystyle  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

to do so, let,

\displaystyle y =  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

By simplifying we acquire:

\displaystyle y =  3 -  \frac{2}{x}  -  \frac{1}{ {x}^{2} }

use law of exponent which yields:

\displaystyle y =  3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} }

take derivative in both sides:

\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  (3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} } )

use sum derivation rule which yields:

\rm\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  3 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

By constant derivation we acquire:

\rm\displaystyle  \frac{dy}{dx} =  0 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

use exponent rule of derivation which yields:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ - 1 -1} ) -     ( - 2 {x}^{  - 2 - 1} )

simplify exponent:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ -2} ) -     ( - 2 {x}^{  - 3} )

two negatives make positive so,

\displaystyle  \frac{dy}{dx} =   2 {x}^{ -2} +      2 {x}^{  - 3}

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

\displaystyle  \frac{dy}{dx} =   \frac{2 }{x^2}+       \frac{2}{x^3}

simplify addition:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

and we are done!

5 0
3 years ago
In ΔJKL, the measure of ∠L=90°, KL = 22 feet, and JK = 54 feet. Find the measure of ∠J to the nearest degree.
nydimaria [60]

We have been given that in ΔJKL, the measure of ∠L=90°, KL = 22 feet, and JK = 54 feet. We are asked to find the measure of angle J to nearest degree.

First of all, we will draw a triangle as shown in the attachment.

We can see from our attachment that side KL is opposite side to angle J and side JK is hypotenuse of right triangle.

We know that sine relates opposite side of right triangle to hypotenuse.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

\text{sin}(\angle J)=\frac{22}{54}

Using inverse sine or arcsin, we will get:

\angle J=\text{sin}^{-1}(\frac{22}{54})

\angle J=24.042075905756^{\circ}

Upon rounding to nearest degree, we will get:

\angle J\approx 24^{\circ}

Therefore, the measure of angle J is approximately 24 degrees.

8 0
4 years ago
Which quadrilateral below could have four different side lengths?
makvit [3.9K]

Answer:

c. trapezoid

Step-by-step explanation:

4 0
4 years ago
AB has endpoints at (-4,5) and (4,-3) using the midpoint formula what is the midpoint segment
Mamont248 [21]

Answer:

(0,1)

Step-by-step explanation:

5 0
3 years ago
Math help will mark brainliest
Natasha2012 [34]

Answer:

A

Step-by-step explanation:

all the other answers just dont make enough sense to be true, so that is why A is correct

also, just go through each answer and see if it makes any sense

4 0
3 years ago
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