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3 years ago

Find an equation for the tangent to the curve at the given point y=x^3 , (2,8)

1 answer:

5 0

$\bf y=x^3\implies \left. \cfrac{dy}{dx}=3x^2 \right|_{x=2}\implies \stackrel{\stackrel{m}{\downarrow }}{12} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{8})~\hspace{10em} slope = m\implies 12 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-8=12(x-2) \\\\\\ y-8=12x-24\implies y=12x-16$

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A machine in an office can shred 65 sheets of paper every 5 seconds. How many sheets of paper can the machine shred in 60 second

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Answer:

780 sheets

Step-by-step explanation:

we know that

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Find out how many sheets of paper can the machine shred in 60 seconds

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Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the ste

olga_2 [115]

1. "the graph has the same zeros" : so let a be the "triple" root of the cubic polynomial function.

2. So f(x)= $(x-a)^{3}$

3. Don't forget that the expression might have a coefficient b as well, and still maintain the conditions:

$f(x)=b(x-a)^{3}$

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$-5=-ba ^{3}$

$5=ba ^{3}$

$b= \frac{5}{ a^{3} }$

5. the function is $f(x)=\frac{5}{ a^{3} }(x-a)^{3}$ where a can be any real number except 0

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3 years ago

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Cameron is trying to find the equation of a line that

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Yes it does I went on Desmos graphing Calculator and put in the equation and got those answers

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3 years ago

What is the value of the expression x^2y–y+xy^2–x for x=4 and y=0.25?

stepan [7]

Answer:

0 (zero)

Step-by-step explanation:

${x}^{2} y - y + x {y}^{2} - x \\ = {4}^{2} \times 0.25 - 0.25 + 4 \times {0.25}^{2} - 4 \\ = 16 \times 0.25 - 0.25 + 4 \times 0.0625- 4 \\ = 4 - 0.25 + 0.25 - 4 \\ = 0 \\ \\ \purple {\boxed{ \bold{ \therefore \: {x}^{2} y - y + x {y}^{2} - x = 0}}}$

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3 years ago

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

Slav-nsk [51]

Answer:

Systolic on right

$\hat{CV} =\frac{18.68}{127.5}=0.147$

Systolic on left

$\hat{CV} =\frac{12.65}{74.2}=0.170$

So for this case we have more variation for the data of systolic on left compared to the data systolic on right but the difference is not big since 0.170-0.147 = 0.023.

Step-by-step explanation:

Assuming the following data:

Systolic (#'s on right) Diastolic (#'s on left)

117; 80

126; 77

158; 76

96; 51

157; 90

122; 89

116; 60

134; 64

127; 72

122; 83

The coefficient of variation is defined as " a statistical measure of the dispersion of data points in a data series around the mean" and is defined as:

$CV= \frac{\sigma}{\mu}$

And the best estimator is $\hat {CV} =\frac{s}{\bar x}$

Systolic on right

We can calculate the mean and deviation with the following formulas:

[te]\bar x = \frac{\sum_{i=1}^n X_i}{n}[/tex]

$s= \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}$

For this case we have the following values:

$\bar x = 127.5, s= 18.68$

So then the coeffcient of variation is given by:

$\hat{CV} =\frac{18.68}{127.5}=0.147$

Systolic on left

For this case we have the following values:

$\bar x = 74.2 s= 12.65$

So then the coeffcient of variation is given by:

$\hat{CV} =\frac{12.65}{74.2}=0.170$

So for this case we have more variation for the data of systolic on left compared to the data systolic on right but the difference is not big since 0.170-0.147 = 0.023.

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2 years ago