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3 years ago

Find f'(x) for f(x) = cos^2(3x^3).

1 answer:

6 0

$f(x) = \cos^2(3x^3)\\f'(x) = \frac{d}{dx}[\cos^2(3x^3)]\\= 2\cos(3x^3) \cdot \frac{d}{dx}[cos(3x^3)]\\= 2\cos(3x^3) \cdot (-\sin(3x^3)) \cdot \frac{d}{dx}[3x^3]\\= 2\cos(3x^3) \cdot (-\sin(3x^3)) \cdot 9x^2\\= -18x^2\cos(3x^3)\sin(3x^3)$

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3 years ago

What fraction is between 3/4 and 1?

oksano4ka [1.4K]

Answer:

7/8, 15/16, 99/100, 23/25

Step-by-step explanation:

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5 0

3 years ago

Read 2 more answers

(0.3d-1.5)/3 1/3=0.84:7/15

Anika [276]

Answer:

d = 25

Step-by-step explanation:

Perhaps you want to solve for d:

(0.3d -1.5)/(3 1/3) = 0.84/(7/15)

Change the division by a fraction to multiplication by its inverse.

(0.3d -1.5)·(3/10) = (0.84)·(15/7)

0.09d -0.45 = 1.8 . . . . . . . . . . . . simplify

d - 5 = 20 . . . . . . . . . . . . . . . . . . divide by 0.09

d = 25 . . . . . . . . . . . . . . . . . . . . . add 5

_____

Grouping symbols help show what is being divided by what. Especially where mixed numbers are involved, parentheses help show that the number 3 1/3 is not supposed to be interpreted as the product of 3 and 1/3.

4 0

3 years ago

The surface area of the cone is 43.75pie cm^2. What is the slant height of the cone and the diameter is 5

Masteriza [31]

If the diameter of the cone is 5, then the radius of it will be half that, or 2.5, thus

$\bf \textit{total surface area of a cone}\\\\
SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~
\begin{cases}
r=radius\\
h=height\\
------\\
SA=43.75\pi \\
r=2.5
\end{cases}
\\\\\\
43.75\pi =\pi (2.5)\sqrt{r^2+h^2}+\pi (2.5)^2
\\\\\\
43.75\pi -\pi (2.5)^2=2.5\pi \sqrt{r^2+h^2}
\\\\\\
43.75\pi -6.25\pi =2.5\pi \sqrt{r^2+h^2}\implies 37.5\pi =2.5\pi \sqrt{r^2+h^2}
\\\\\\
\cfrac{37.5\pi }{2.5\pi }=\sqrt{r^2+h^2}\implies 15=\sqrt{r^2+h^2}$

3 0

3 years ago

A sample of blood pressure measurements is taken for a group ofadults, and those values (mm Hg) are listed below. The values a

scoundrel [369]

Answer:

1. coefficient of variation(systolic) = 13.88%

2. coefficient of variation(diastolic) = 16.2%

3. The coefficients of variation for each data set are within 5 percentage points of each other Therefore the systolic measurements vary signifcantly less than the diastolic

Step-by-step explanation:

1. Mean of systolic = ( 117+126+158+96+157+122+116+134+127+122)÷10

= 127.5

Standard Deviation of systolic = (((117-127.5)^2 +(126-127.5)^2+(158-127.5)^2+ (96-127.5)^2 + (157-127.5)^2 + (122-127.5)^2 + (116-127.5)^2 +(134-127.5)^2 +(127-127.5)^2 +( 122-127.5)^2) ÷ 10)^(0.5)

SD = 17.7

coefficient of variation(systolic)

= Standard Deviation of systolic /mean of systolic

= $\frac{17.7}{127.5} * 100$

coefficient of variation(systolic) = 13.88%

2. Mean of diastolic = ( 80+77+76+51+90+89+60+64+72+83) ÷ 10

= 74.2

Standard Deviation of diastolic = (((80-74.2)^2 +(77-74.2)^2+(76-74.2)^2+ (51-74.2)^2 + (90-74.2)^2 + (89-74.2)^2 + (60-74.2)^2 +(64-74.2)^2 +(72-74.2)^2 +(83-74.2)^2) ÷ 10)^(0.5)

SD = 12

coefficient of variation(diastolic)

= Standard Deviation of diastolic /mean of diastolic

= $\frac{12}{74.2} *100$

coefficient of variation(diastolic) = 16.2%

3. The coefficients of variation for each data set are within 5 percentage points of each other Therefore the systolic measurements vary signifcantly less than the diastolic

8 0

3 years ago