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3 years ago

Determine the range of the following graph

Mathematics

1 answer:

Ierofanga [76]3 years ago

7 0

Given:

The graph of a function is given.

To find:

The range of the graph.

Solution:

We know that, the domain is the set of input values and range is the set of output values.

In a graph, domain is represented by the x-axis and range is represented by the y-axis.

From the given graph it is clear that there is an open circle at (-8,-8) and a closed circle at (3,4). It means the function is not defined at (-8,-8) but defined for (3,4).

The graph of the function is defined over the interval $-8$ . So, the domain is (-8,3].

The values of the function lie in the interval $-8$ . So, the range is (-8,4].

Therefore, the range of the function are all real values over the interval (-8,4].

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Which pair of angles are vertical angles?

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2 years ago

Express in simplest radical form. \frac{\sqrt{96}}{2}

Gelneren [198K]

Answer:

$\frac{ \sqrt{96} }{2} = \frac{ \sqrt{16 \times 6} }{2} = \frac{4\sqrt{6} }{2} = \boxed{2 \sqrt{6}}\\$

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8 0

3 years ago

Evaluate the function. f(x) = 3x² – x Find f(10)

kirill [66]

Answer:

f(10)=290

Step-by-step explanation:

Function Evaluation

Given a function f(x) as an explicit expression, finding f(x=a) implies substituting the value of x by a in every instance it occurs.

We are given the function:

$f(x)=3x^2-x$

It's required to find f(10). We replace the x for 10:

$f(10)=3*10^2-10$

Operating:

$f(10)=3*100-10$

$f(10)=300-10$

$f(10)=290$

Thus, f(10)=290

4 0

3 years ago

Find the value of x such that the area of a triangle whose vertices have coordinates (6, 5), (8, 2) and (x, 11) is 15 square uni

Serjik [45]

Answer:

$x =12\ or\ -8$

Step-by-step explanation:

Given

$(x_1,y_1) = (6,5)$

$(x_2,y_2) = (8,2)$

$(x_3,y_3) = (x,11)$

$Area = 15$

Required

Find x

The area is calculated as thus:

$Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Substitute values

$15 = \frac{1}{2}|6*(2 - 11) + 8*(11 - 5) + x(5 - 2)|$

$15 = \frac{1}{2}|6*(-9) + 8*(6) + x(3)|$

$15 = \frac{1}{2}|-54 + 48 + 3x|$

$15 = \frac{1}{2}|-6 + 3x|$

Multiply through by 2

$2 * 15 = \frac{1}{2}|-6 + 3x| * 2$

$30 = |-6 + 3x|$

Remove absolute sign

$30 = -6 + 3x\ or\ -30 = -6 + 3x$

Add 6 to both sides

$36 = 3x\ or\ -24 = 3x$

Divide by 3

$12 = x\ or\ -8 = x$

$x =12\ or\ -8$

So, the coordinates are (-8, 11) or (12,11)

3 0

2 years ago

The radius of a cylinder is 7 c m and its height is 10 c m. Find curved surface area and volume.

erma4kov [3.2K]

Answer:

CSA of the cylinder = 440 sq. cm

Volume of the cylinder = 1540 cu. cm

$\\$

Step-by-step explanation:

Given:

Radius of the cylinder = 7 cm
Height of the cylinder = 10 cm

$\\$

To Find:

Curved surface area
Volume

$\\$

Solution:

$\\$

Using formula:

$\dashrightarrow \: \: { \underline{ \boxed{ \pmb{ \sf{ \purple{CSA \: of \: cylinder = 2\pi rh}}}}}} \: \star \\ \\$

Substituting the required values: 

$\\$

$\dashrightarrow \: \: \sf CSA {(cylinder)} = 2 \times \dfrac{22}{7} \times 7 \times 10 \\ \\ \\ \dashrightarrow \: \: \sf CSA {(cylinder)} = 2 \times 22 \times 10 \\ \\ \\ \dashrightarrow \: \: \sf CSA {(cylinder)} = 44 \times 10 \\ \\ \\ \dashrightarrow \: \: \sf CSA {(cylinder)} = 440 \: {cm}^{2} \\ \\ \\$

Now,

$\dashrightarrow \: \: { \underline{ \boxed{ \pmb{ \sf{ \purple{Volume {(cylinder)}= \pi {r}^{2} h}}}}}} \: \star \\ \\ \\$

Substituting the required values, 

$\\$

$\dashrightarrow \: \: \sf Volume {(cylinder)}= \dfrac{22}{7} \times {(7)}^{2} \times 10 \\ \\ \\ \dashrightarrow \: \: \sf Volume {(cylinder)}= \frac{22}{7} \times 49 \times 10 \\ \\ \\ \dashrightarrow \: \: \sf Volume {(cylinder)}= 22 \times 7 \times 10 \\ \\ \\ \dashrightarrow \: \: \sf Volume {(cylinder)}= 1540 {cm}^{3} \\ \\ \\$

Hence,

CSA of the cylinder = 440 sq. cm

Volume of the cylinder = 1540 cu. cm

8 0

2 years ago

Read 2 more answers