One pound of candies costs $3.50. How many pounds of candies can be bought for $10.50?

Someone please help me with my homework please please help please help me with my homework

densk [106]

C=2x Pi x R so 2x3.14x17.5 = 109.9

5 0

4 years ago

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

3 years ago

After being exposed to an electromagnetic shrinking machine, Joe's height decreased by 120120120 cm over 1.51.51, point, 5 secon

LuckyWell [14K]

Answer:It is given that Joe was being exposed to an electromagnet shrinking machine. Because of this his height started decreasing .

Given,

The decrease was at a constant rate per second.

In 1.5sec, the height is decreased by 120cm.

So,

Variation per second =

Change in each second would be with negative sign indicate's decrease .

Hence, Answer is “-80” .

Step-by-step explanation:

5 0

3 years ago

The middle side of a triangle is half of 3 times the length of the shortest side. The longest side is 2 centimeters longer than

USPshnik [31]

Answer:

The difference between the longest and shortest sides of the triangle is 4 cm.

Explanation:

Step Number One:

Let the shortest side of the triangle have a length of x.

The middle side of the triangle has a length that is half of 3 times the length of the shortest side. This can be written as 1/2*3x, which equals 3/2x.

The longest side of the triangle has a length that is 2 centimeters longer than the length of the middle side. This can be written as 3/2x + 2.

Step Number Two:

The perimeter of the triangle, which can be found by adding the lengths of all of the sides of the triangle, is 18 centimeters. This can be shown by the following equations:

Shortest Side + Middle Side + Longest Side = Perimeter

x + 3/2x + 3/2x + 2 = 18

4x + 2 = 18

4x = 16

x = 16/4

x = 4

Step Number Three:

This means that the shortest side of the triangle has a length of 4 centimeters and the longest side of the triangle has a length of 8 centimeters.

8 cm - 4 cm = 4 cm

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Are you still confused? Not feeling confident in your ability to solve these types of problems? Some helpful topics to practice are listed below!

Still confused on ...

Step 1 - Practice equation solving!

Step 2 - Practice perimeter!

Step 3 - Practice addition and subtraction!

Remember: Certain problems may be tricky, but practice makes perfect!

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Answer by Math_Is_Me_123

7 0

3 years ago

What should be added to 3 to make the sum of 0?

garri49 [273]

Well if you have three and add negative 3 it equals 0

5 0

3 years ago

Read 2 more answers