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2 years ago

Is 14/4 and 3 1/2 equivalent

Mathematics

2 answers:

givi [52]2 years ago

7 0

Answer:

Yes.

Step-by-step explanation:

$3 \dfrac 12 = 3 + \dfrac 12 = \dfrac{7}2 = \dfrac{7 \times 2}{2 \times 2} = \dfrac{14}4$

grigory [225]2 years ago

3 0

Answer:

yes

Step-by-step explanation:

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

miss Akunina [59]

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid. When we rotate it about x = 1, we get a hollow cylinder shape. We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part. If we use shell method, we only need one integral. So let's use shell method.

Cut a thin, vertical slice of the region. The width of this slice is dx. The height of the slice is y₂ − y₁ = x − 0 = x. The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]

V = 2π (72⅔ − 12)

V = 121⅓ π

V ≈ 381.18

The volume is approximately 381.18 cubic units.

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Step-by-step explanation:

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The graph of the quadratic function y=-x^2-2x+3 is shown below

Karolina [17]

Answer:

The axis of symmetry is at $x=-1$

The graph has an x-intercept at $(1,0)$

The graph has a vertex at $(-1,4)$

Step-by-step explanation:

we have

$y=-x^{2}-2x+3$

Statements

case 1) The graph has root at $3$ and $1$

The statement is False

Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)

Observing the graph, the roots are at $-3$ and $1$

case 2) The axis of symmetry is at $x=-1$

The statement is True

Observing the graph, the vertex is the point $(-1,4)$

The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

the equation of the axis of symmetry is $x=-1$

case 3) The graph has an x-intercept at $(1,0)$

The statement is True

see procedure case 1)

case 4) The graph has an y-intercept at $(-3,0)$

The statement is False

Because, the y-intercept is the value of y when the value of x is equal to zero

Observing the graph, the y-intercept is the point $(0,3)$

case 5) The graph has a relative minimum at $(-1,4)$

The statement is False

Because, is a vertical parabola open downward, therefore the vertex is a maximum

The point $(-1,4)$ represent the vertex of the parabola, so is a maximum

case 6) The graph has a vertex at $(-1,4)$

The statement is True

see the procedure case 5)

see the attached figure to better understand the problem

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3 years ago

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Is 14/4 and 3 1/2 equivalent​

Is 14/4 and 3 1/2 equivalent