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3 years ago

The graph below shows two functions f(x) and g(x)

Mathematics

2 answers:

Yuki888 [10]3 years ago

8 0

Answer:

The value of k is 7

Step-by-step explanation:

The image shows the graph of g(x) and f(x). g(x) is shifted up f(x) by a number k such that:

g(x) = f(x) +k

To know the value of k, we select a value for x and calculate the value of k.

For example, for x=0, f(0)=-6, g(0)=1, and:

g(0) = f(0) +k

1 = -6 +k

k = 7

We can select any other value for x which g and f values can be clearly seen. For example, for x=-5, f(-5)=0, g(-5)=7, thus:

g(-5) = f(-5) +k

7 = 0 +k

k = 7

The value of k is 7

iris [78.8K]3 years ago

7 0

the answer above is correct

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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

Question is in the picture pls help.

Usimov [2.4K]

Answer:

c. is the answer

5 0

3 years ago

Read 2 more answers

FIRST ACTUAL ANSWER WILL GET BRAINLY 25 POINTS

krok68 [10]

You forgot the image , here if you want some free points to repost it just go to a point put a bogus answer in one of my questions . That mistake happens to me all the time

7 0

3 years ago

What is the simplified form of (3.25x10^3)(7.8x10^6) written in scientific notation?

BabaBlast [244]

Answer: $2.535*10^{10}$

Step-by-step explanation:

1. By definition, scientific notation has the following form:

$a*10^{b}$

Where:

a is a number between 1 and 10 but does not include 10.

b an integer.

2. When you multiply 3.25 by 7.8 the result is 25.35 and when you multiply $10^{3}$ by $10^{6}$ , you obtain $10^{9}$ , but to write ree thsult in scientific notation, the decimal point must be after the first digit. Therefore, you must move the decimal point one place to the left. So, the exponent changes from 9 to 10:

$(3.25*10^{3})(7.8*10^{6})=2.535*10^{10}$

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3 years ago

Which of the following inequities are true?

yanalaym [24]

Answer:

c and e ................

7 0

3 years ago