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3 years ago

8 cm 10 cm 3 cm 12 cm Work out the shaded area of the shape?

Mathematics

1 answer:

qwelly [4]3 years ago

6 0

Answer:

36 sq. cm

Step-by-step explanation:

triangle area= 0.5 * 12* 10

rectangle are= 8* 3

60 - 24 = 36

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po

sladkih [1.3K]

Answer:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

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

Point A has an x-coordinate of -1. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0$

Find the y-coordinate of Point A using the original equation:

$y(-1)=(-1)^3-3(-1)=2$

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

$y-2=0(x-(-1))$

Simplify:

$y=2$

Point B has an x-coordinate of 4. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45$

Find the y-coordinate of Point B:

$y(4)=(4)^3-3(4)=52$

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

$y-52=45(x-4)$

Simplify:

$y=45x-128$

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for x:

$2=45x-128$

We acquire:

$\displaystyle x=\frac{26}{9}$

Since one of our equations is y = 2, the y-coordinate is 2.

Hence, Point C is:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

5 0

3 years ago

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Which of the following could be an example of a function with a domain [a, infinity) and a range [b, infinity) where a >0 and

Semmy [17]

[a, infinity) and a range

6 0

3 years ago

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NEED HELP WHATS THE ANSWERS FOR THESE 2

Maurinko [17]

I believe the first on is -1 and the second one is NO SOLUTION

7 0

3 years ago

A cookie recipe calls for 1 2/3 cup of sugar. If you plan on changing the recipe to make 2 1/2 times as much. How much sugar wil

Morgarella [4.7K]

Answer:

= 4 1/6 ---------------> final answer

Step-by-step explanation:

1 2/3 cup of sugar

That is : 5/3 cups of sugar for 1 cookie recipe

So for 1 recipe ------------- 5/3 cups of sugar

hence for 2 1/2 recipe ---------------> (5/3) * (5/2)

= 25/6

= 4 1/6 ---------------> final answer

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3 years ago

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Find the center, vertices, and foci for the ellipse 25x^2+64y^2=1600

Ronch [10]

Answer:

Step-by-step explanation:

Answer:

Data

Equation 25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

3.- Find a, b and c

a² = 64 a = 8

b² = 25 b = 5

-Calculate c with the Pythagorean theorem

a² = b² + c²

-Solve for c

c² = a² - b²

-Substitution

c² = 8² - 5²

-Simplification

c² = 64 - 25

c² = 39

-Result

c = √13

4.- Find the center

C = (0, 0)

5.- Find the vertices

V1 = (-8, 0) V2 = (8, 0)

6.- Find the foci

F1 = (-√13, 0) F2 = (√13, 0)

4 0

3 years ago

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