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3 years ago

Use familiar figures to find the area of the figure shown. Show all work

Mathematics

2 answers:

Mumz [18]3 years ago

8 0

So, are of a trapezoid is add the bases, divide the hieght by two, and multiply them together.
the bases were 3 and 5, so add them together, you get 8.
the height was 2, so divide 2 by 2, you get 1
Multiply them, you get 8
8 is the area of your trapezoid.

The area of a rectangle or a square is to multiply the base times the height.
the base was 3 and the height was 10, so multiply and you get 30.
30 is the area of your rectangle.

The area of a triangle is to multiply the base by times the height and then divide by 2.
3 is the base, height is 4, multiply and you get 12.
divide 12 by 2, and you get 6.
6 is the area of the triangle.

To find the area of the entire shape, you add all the areas together.

8 is the area of the trapezoid.
30 is the area of the rectangle.
6 is the area of the triangle.
30+8+6=44

Your area is 44in^2

Hunter-Best [27]3 years ago

7 0

Area of the triangle-
(4*3)/2= 6

Area of the rectangle-
10*3= 30

Area of the trapizoid
(3+5)/2*2= 8

add them all together:
30+8+6= 44

your answer is 44 inches (:

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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

6 0

3 years ago

Which system of equations can be used to solve for the point of intersection of the lines on the graph? A) y = x - 7; y = 2x + 2

ratelena [41]

Answer:

C) y = 2x + 7; y = 2x + 2

Step-by-step explanation:

The two lines are parallel and so will have the same slope.

From the graph, the slope of both lines are two.

Using slope intercept formula, y=mx+c, with m=2, we have y=2x+c

The blue line has a y-intercept of 2 so the equation is

$y = 2x + 2$

The red line has a y-intercept of -7 so the equation is

$y = 2x - 7$

Hence the system is

y=2x+2

y=2x-7

The correct answer is C

4 0

3 years ago

Which pair of measurements is not equivalent?

mamaluj [8]

D is not equivalent
hope this helps :)

5 0

3 years ago

Read 2 more answers

Find the area of the shape

Gwar [14]

Answer:

3pi

Step-by-step explanation:

First find the area of the entire circle

A = pi r^2

A = pi * 2^2

A = 4 pi

We know that this is 3/4 of a circle so multiply the area by the fraction of the circle

3/4 * 4 pi

3 pi

4 0

3 years ago

Read 2 more answers

5 1/8+5/6+5/12=6.375 what is 6.375 as a fraction? A 6 3/4. B.6 3/8. C6 3/12. D 6 3/24 please help

vovikov84 [41]

B. 6 3/8
How do we get this? Simple:
6.375--->We already know that 6 will be the whole number in the mixed fraction.

We then move on to represent the decimal part as the fraction. 375 will be the numerator. The denominator depends on how many decimal places we have (3 in this case, since there are 3 numbers after the period--375). Each decimal place represents a 10 (or a 0 after the 1). So we get that our denominator will be a 1000.

We get the following fraction
6 375/1000

We simplify. Let's start by dividing numerator and denominator by 5:
6 75/200

Let's divide by 5 again:
6 15/40

Let's divide by 5 again:
6 3/8

Or we could have divide by 125 from the get go and get the same results.

3 0

3 years ago