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3 years ago

14

For the direct variation such that when y = 2 then x = 3 , find the constant of variation ( k) and then find the value of y when

x = - 0.5.

1 answer:

Sergeu [11.5K]3 years ago

8 0

Answer:

k is 2/3 and y is -1/3 when x is -0.5.

Step-by-step explanation:

The direct variation relationship is y = kx, where k is the const. of var.

Subbing 3 for x and 2 for y, 2 = 3k, or k = 2/3.

Now, if x = -0.5, y = (2/3)(-1/2) = -1/3

k is 2/3 and y is -1/3 when x is -0.5.

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

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

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

Can someone help me please

MrMuchimi

Answer:

is it from a textbook

Step-by-step explanation:

7 0

2 years ago

Based on the line plot, how many recipes call for more than 1/4 tsp of salt?

Studentka2010 [4]

It would be 6 haha I just took a test and got it right

5 0

3 years ago

Read 2 more answers

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50%50% of this population prefer

n200080 [17]

Answer:

0.1527

Step-by-step explanation:

Given that a researcher wishes to conduct a study of the color preferences of new car buyers.

Suppose that 50% of this population prefers the color red

15 buyers are randomly selected

Let X be the no of buyers who prefer red.

X has exactly two outcomes red or non red.

Also each buyer is independent of the other

Hence X is binomial with p = 0.5 and n = 15

Required prob =The probability that exactly three-fifths of the buyers would prefer red

= P(X=9)

= $15C9 (0.9)^9 (0.6)^6$

= $5005(0.0000305)=0.1527$

6 0

2 years ago

LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses five ounces of coffee. How many ounces o

ipn [44]

Answer:

40 ounces of coffee

Step-by-step explanation:

we know that

To make caffe mocha, LaVelle uses one ounce of chocolate syrup,and five ounces of coffee

so

To make 6 ounces of caffe mocha (one ounce of chocolate syrup plus 5 ounces of coffe), LaVelle uses one ounce of chocolate syrup,and five ounces of coffee

using proportion

Find out how many ounces of coffee does she need to make 48 ounces of caffe mocha

Let

x ---> ounces of coffee needed to make 48 ounces of caffe mocha

$\frac{6}{5}\ \frac{oz\ caffe\ mocha}{oz\ coffee} =\frac{48}{x}\ \frac{oz\ caffe\ mocha}{oz\ coffee}\\\\x=48(5)/6\\\\x=40\ oz\ coffee$

3 0

3 years ago