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4 years ago

What is the slope of the line on the graph?

Mathematics

1 answer:

marshall27 [118]4 years ago

7 0

Answer:

y = 1/2x + 2

Step-by-step explanation:

Find your y-intercept (0,2) then a random point (-2,1). Then count the distance from the two points, 1 up & 2 right.

1/2 is now your slope!

y = 1/2x + 2

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

4 years ago

Incomes in a certain town are strongly right-skewed with mean $36,000 and standard deviation $7000. a random sample of 75 househ

Svet_ta [14]

Since the sample is greater than 10, we can approximate this binomial problem with a normal distribution.

First, calculate the z-score:

z = (x - μ) / σ = (37000 - 36000) / 7000 = 0.143

The probability P(x > 37000$) = 1 - P(x < 37000$),
therefore we need to look up at a normal distribution table in order to find
P(z < 0.143) = 0.55567
And
P(x > 37000$) = 1 - 0.55567 = 0.44433

Hence, there is a 44.4% probability that the sample mean is greater than $37,000.

4 0

4 years ago

Hi can anyone solve this for me please solve it on a piece of paper please

mojhsa [17]

Answer:

Awsten Knight

Step-by-step explanation: