Which of the following is equivalent to the sum of

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equati

murzikaleks [220]

Answer:

$x-4y+4=0$

$f(x)=\sqrt x$ and x=4

Step-by-step explanation:

We are given that a curve

$y=\sqrt x$

We have to find the equation of tangent at point (4,2) on the given curve.

Let y=f(x)

Differentiate w.r.t x

$f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}$

By using the formula $\frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}$

Substitute x=4

Slope of tangent

$m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}$

In given question

$m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}$

$\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}$

By comparing we get a=4

Point-slope form

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

Using the formula

The equation of tangent at point (4,2)

$y-2=\frac{1}{4}(x-4)$

$4y-8=x-4$

$x-4y-4+8=0$

$x-4y+4=0$

8 0

3 years ago

Help me please I have no clue

Lynna [10]

Answer:

Step-by-step explanation:

You see that there’re angles with 30 and 90 degrees that means that -> 180-(90+30)=60 (measurement of the third angle)

Here you’ll need to use the 30,60,90 degree triangle rule:

The opposite side of 30 degree will be y

30->y

90->2y->12√3 => y=6√3

60->y√3->x => 6√3x√3=6x3=18

To understand the rule better you can check the picture below.Wish it will help you!Good luck!

8 0

2 years ago

(12y 2+17y-4)+(9y-13y+3)

IrinaVladis [17]

Answer:

4y+3

Step-by-step explanation:

8 0

2 years ago

Please help me find the area of shaded region and step by step

Bumek [7]

Answer:

Part 1) $A=60\ ft^2$

Part 2) $A=80\ cm^2$

Part 3) $A=96\ m^2$

Part 4) $A=144\ cm^2$

Part 5) $A=9\ m^2$

Part 6) $A=(49\pi -33)\ in^2$

Step-by-step explanation:

Part 1) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle

The area of rectangle is equal to

$A=bh$

where

b is the base of rectangle

h is the height of rectangle

so

$A=(12)(7)-(8)(3)$

$A=84-24$

$A=60\ ft^2$

Part 2) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior square

The area of square is equal to

$A=b^2$

where

b is the length side of the square

so

$A=(12)(8)-(4^2)$

$A=96-16$

$A=80\ cm^2$

Part 3) we know that

The area of the shaded region is equal to the area of four rectangles plus the area of one square

so

$A=4(4)(5)+(4^2)$

$A=80+16$

$A=96\ m^2$

Part 4) we know that

The shaded region is equal to the area of the complete square minus the area of the interior square

so

$A=(15^2)-(9^2)$

$A=225-81$

$A=144\ cm^2$

Part 5) we know that

The area of the shaded region is equal to the area of triangle minus the area of rectangle

The area of triangle is equal to

$A=\frac{1}{2}(b)(h)$

where

b is the base of triangle

h is the height of triangle

so

$A=\frac{1}{2}(6)(7)-(6)(2)$

$A=21-12$

$A=9\ m^2$

Part 6) we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

The area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

so

$A=\pi (7^2)-(3)(11)$

$A=(49\pi -33)\ in^2$

7 0

2 years ago

(3a ^2 + 1) - ( 4+2a^2)

xz_007 [3.2K]

Answer:

a^2 - 3

Step-by-step explanation:

(3a^2 + 1) - (4 + 2a^2)

3a^2 + 1 - 4 - 2a^2

a^2 - 3

8 0

2 years ago