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4 years ago

Log(100) = log(400) - log(4) "

1 answer:

5 0

When working with logarithms, remember that a subtraction sign means you can divide.
log(400) - log(4) can be turned into log(400/4), which is further simplified to log(100).

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Finding an Equation of a Tangent Line In Exercise, use implicit differentiation to find an equation of the tangent line to the g

Karo-lina-s [1.5K]

Answer:

$y=\frac{4}{3}-\frac{x}{3e}$

Step-by-step explanation:

Equation of tangent line of given function at (e,1) is found by implicitly differentiating the given function w.r.to x

$y^{2}+ln(xy)=2\\\\y^{2}+ln(x)+ln(y)=2\\\\\frac{d}{dx}(y^{2}+ln(x)+ln(y))=\frac{d}{dx}(2)\\\\2y\frac{dy}{dx}+\frac{1}{x}+\frac{1}{y}\frac{dy}{dx}=0\\\\\frac{dy}{dx}(2y+\frac{1}{y})=-\frac{1}{x}\\\\\frac{dy}{dx}=-\frac{y}{x(2y^{2}+1)}\\\\at (e,1)\\\\\frac{dy}{dx}=-\frac{1}{e(2+1)}\\\\\frac{dy}{dx}=\frac{1}{3e}$

Equation of tangent line is

y-y₁=m(x-x₁)

at (e,1)

$y-1=-\frac{1}{3e}(x-e)\\\\y=1-\frac{1}{3e}(x-e)\\\\y=1+\frac{1}{3}-\frac{x}{3e}\\\\y=\frac{4}{3}-\frac{x}{3e}\\$

6 0

4 years ago

When Carson runs the 400 meter dash, his finishing times are normally distributed with a mean of 65 seconds and a standard devia

just olya [345]

Given Information:

Mean time to finish 400 meter dash = μ = 65 seconds

Standard deviation to finish 400 meter dash = σ = 2.5 seconds

Confidence level = 95%

Required Information:

95% confidence interval = ?

Answer:

$CI = 60 \: to \: 70 \: seconds$

Step-by-step explanation:

In the normal distribution, the empirical rule states approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.

The confidence interval for 95% confidence limit is given by

$CI = \mu \pm 2\sigma$

Since approximately 95% of all the data lie within 2 standard deviations from the mean. μ is the mean time Carson takes to finish 400 meter dash and σ is the standard deviation.

$CI = 65 \pm 2(2.5)$

$CI = 65 \pm 5$

$CI = 65 - 5 \: to \: 65 + 5$

$CI = 60 \: to \: 70 \: seconds$

Therefore, the 95% confidence interval is between 60 to 70 seconds

What does it mean?

It means that we are 95% confident that the Carson's mean to finish 400 meter dash is within the interval of (60, 70).

4 0

3 years ago

Which point lies on the line with point-slope equation y - 3 = 4(x + 7)?

mixas84 [53]

Answer:

Step-by-step explanation:

The standard form of a point slope equation of a line is expressed as shown;

y-y₀ = m(x-x₀) where;

m is the slope of the line

(x₀, y₀) is the coordinate of the point that lies in the line.

Comparing the standard equation given with the equation in question

y - 3 = 4(x + 7) to get the point on the line we will have;

y₀ = 3 and -x₀ = 7

for -x₀ = 7;

multiply both sides with a minus sign

-(-x₀) = -7

x₀ = -7

<em>Hence the coordinate of the point required (x₀, y₀) is (-7, 3).</em>

7 0

3 years ago

Math Help Help Fast Alot of points

MrMuchimi

Here mark the angles

m<FHG=75
m<FGH=55
m<GHI=59°
m<GIH=63°

By using angle sum property

m<IGH=180-122=58

m<FGH < m<IGH <m<GHI <m<GIH <m <FHG

FH<IH<GI<GH<FG

8 0

3 years ago

Read 2 more answers

Enter the value of P so that the expression 3 (4 + n) is equivalent to 3 (n+p).

Gala2k [10]

Answer:

3 (4+n)=0

3×4+3×n=0

12+3n=0.... equation 1

3 (n+p)

3×n+3×p=0

3n+3p=0........... equation 2

eq 1 multiply 3 eq 2 multiply 3

36+9n=0

9n+9p=0

_ _ =0

_9n is +9n Crush

36+9p=0

p=36÷9

p=4

p is 4 ans

4 0

3 years ago