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Sedaia [141]
3 years ago
11

Need help please and ​ match it

Mathematics
1 answer:
marshall27 [118]3 years ago
4 0

Answer:

1. C

2. B

3. A

Step-by-step explanation:

You reform the inequality as y, kind of like y= equations. For example x+y ≥ 2 means y ≥ 2 - x.

Anywhere it intersects for both lines it would be shaded red.

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The region bounded by y=x^2+1, y=x, x=-1, x=2 with square cross sections perpendicular to the x-axis.
VLD [36.1K]

Answer:

The bounded area is 5 + 5/6 square units. (or 35/6 square units)

Step-by-step explanation:

Suppose we want to find the area bounded by two functions f(x) and g(x) in a given interval (x1, x2)

Such that f(x) > g(x) in the given interval.

This area then can be calculated as the integral between x1 and x2 for f(x) - g(x).

We want to find the area bounded by:

f(x) = y = x^2 + 1

g(x) = y = x

x = -1

x = 2

To find this area, we need to f(x) - g(x) between x = -1 and x = 2

This is:

\int\limits^2_{-1} {(f(x) - g(x))} \, dx

\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx

We know that:

\int\limits^{}_{} {x} \, dx = \frac{x^2}{2}

\int\limits^{}_{} {1} \, dx = x

\int\limits^{}_{} {x^2} \, dx = \frac{x^3}{3}

Then our integral is:

\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx = (\frac{2^3}{2}  + 2 - \frac{2^2}{2}) - (\frac{(-1)^3}{3}  + (-1) - \frac{(-1)^2}{2}  )

The right side is equal to:

(4 + 2 - 2) - ( -1/3 - 1 - 1/2) = 4 + 1/3 + 1 + 1/2 = 5 + 2/6 + 3/6 = 5 + 5/6

The bounded area is 5 + 5/6 square units.

3 0
3 years ago
For any parallelogram what is not always true
tresset_1 [31]

Answer:

The diagonals are congruent.

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Space is a way of joining together points, lines, and
erastovalidia [21]
Space is a way of joining together points, lines and...

Shapes
4 0
3 years ago
1. Find the capacity in litres of a bucket 24cm in
Sav [38]

Answer:

6.36l

Step-by-step explanation:

We compute first the volume:

V=pi×h/3×(R²+r²+rR), where h=20cm is the height, R=24/2=12cm is the top radius, r=16/2=8cm is the bottom radius.

We get: V=pi×20/3(12²+8²+12×8)=

20×pi/3(144+64+96)cm³

V=20×pi/3×304=6363.73cm³

In dm³ we have (divide by 1000) V=6.36dm³

By definition, 1dm³=1l, so the capacity is 6.36l

8 0
3 years ago
the vertices of PQR are P(-5,1), Q(-4,6), and R(-2,3), graph P"Q"R" after a composition of the transformations in the order they
horsena [70]

SOLUTION

We are told to translate; (x, y) to (x -8, y). This means we have to add - 8 to each value of x in P(-5,1), Q(-4,6), and R(-2,3).

In P(-5,1), x = -5 and y = 1

In Q(-4,6), x = -4 and y = 6 and

In R(-2,3), x = -2 and y = 3

\begin{gathered} P(-5,\text{ 1) translates to (-5 -8, 1) }\rightarrow P^i(-13,\text{ 1)} \\ Q(-4,\text{ 6) translates to (-4 -8, 6) }\rightarrow Q^i(-12,\text{ 6)} \\ R(-2,\text{ 3) translates to (-2 -8, 3) }\rightarrow R^i(-10,\text{ 3)} \end{gathered}

For the dilation centered at the origin k =2, simply multiply the value of k, which is 2 into the translations.

\begin{gathered} At\text{ K = 2,  }P^i(-13,\text{ 1)  }\rightarrow\text{   }2(-13,\text{ 1)  }\rightarrow\text{  }P^{ii}(-26,\text{ 2)} \\ Q^i(-12,\text{ 6)  }\rightarrow\text{  }2(-12,\text{ 6)  }\rightarrow\text{   Q}^{ii}(-24,\text{ 12)} \\ R^i(-10,\text{ 3)   }\rightarrow\text{   }2(-10,\text{ 3)  }\rightarrow\text{   R}^{ii}(-20,\text{ 6)} \end{gathered}

5 0
1 year ago
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