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3 years ago

HELP!!!! What is the area of the shaded region?

Mathematics

2 answers:

Bezzdna [24]3 years ago

7 0

Answer:

15 cm

Step-by-step explanation:

multiply the two numbers

satela [25.4K]3 years ago

6 0

Area of shaded region = Area of bigger circle - Area of smaller circle

$= \pi( {5}^{2} - {3}^{2} ) \\ = 3.14 \times (25 - 9) \\ = 3.14 \times 16 \\ = 50.24 \: {cm}^{2} \\$

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Suppose the roots of the equation 2x^2−5x−6=0 are α and β.Find the quadratic equation with roots 1/α and 1/β.

pochemuha

Answer:

6x² + 5x - 2 = 0

Step-by-step explanation:

Given

2x² - 5x - 6 = 0 ← in standard form

with a = 2, b = - 5, c = - 6, then

sum of roots α + β = - $\frac{b}{a}$ = $\frac{5}{2}$

product of roots = $\frac{c}{a}$ = - 3, then

sum of new roots = $\frac{1}{\alpha }$ + $\frac{1}{\beta }$

= $\frac{\beta+\alpha }{\alpha \beta }$

= $\frac{\frac{5}{2} }{-3}$ = - $\frac{5}{6}$

product of new roots = $\frac{1}{\alpha }$ × $\frac{1}{\beta }$

= $\frac{1}{\alpha\beta }$ = - $\frac{1}{3}$

Hence the required equation is

x² + $\frac{5}{6}$ x - $\frac{1}{3}$ = 0 or

6x² + 5x - 2 = 0 ( multiplying through by 6 )

8 0

4 years ago

The length of a rectangle is 3 more than the width. If the perimeter of the rectangle is 16 units, find the

pentagon [3]

L = 3x width
2L + 2W = 16 units
2(3W) + 2W = 16 units
8W = 16 units
Width = 2 units

7 0

3 years ago

Convert 1 cal/(m^2 * sec * °C) into BTU/(ft^2 * hr * °F)

Crazy boy [7]

Answer:

$1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}$

Step-by-step explanation:

To find : Convert $1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}$ into $\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}$

Solution :

We convert units one by one,

$1\text{ m}^2=10.7639\text{ ft}^2$

$1\text{ sec}=\frac{1}{3600}\text{ hour}$

$1\text{ cal}=0.003968\text{ BTU}$

Converting temperature unit,

$^\circ C\times \frac{9}{5}+32=^\circ F$

$1^\circ C\times \frac{9}{5}+32=33.8^\circ F$

So, $1^\circ C=33.8^\circ F$

Substitute all the values in the unit conversion,

$1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{10.7639\times \frac{1}{3600}\times 33.8}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}$

$1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{0.101061}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}$

$1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}$

Therefore, The conversion of unit is $1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}$

3 0

3 years ago

Pls help me i need this to get a 100

rjkz [21]

Answer:

?- _ - _- -_ _- -

3 0

3 years ago

Read 2 more answers

What is the equation, in slope-intercept form, of the line

Sati [7]

Given:

Given that the graph of the equation of the line.

The line that is perpendicular to the given line and passes through the point (2,-1)

We need to determine the equation of the line perpendicular to the given line.

Slope of the given line:

The slope of the given line can be determined by substituting any two coordinates from the line in the slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the coordinates (-1,3) and (2,2), we get;

$m_1=\frac{2-3}{2+1}$

$m_1=-\frac{1}{3}$

Thus, the slope of the given line is $m_1=-\frac{1}{3}$

Slope of the perpendicular line:

The slope of the perpendicular line can be determined by

$m_2=-\frac{1}{m_1}$

Substituting $m_1=-\frac{1}{3}$ , we get;

$m_2=-\frac{1}{-\frac{1}{3}}$

simplifying, we get;

$m_2=3$

Thus, the slope of the perpendicular line is 3.

Equation of the perpendicular line:

The equation of the perpendicular line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting $m=3$ and the point (2,-1) in the above formula, we have;

$y+1=3(x-2)$

$y+1=3x-6$

$y=3x-7$

Thus, the equation of the perpendicular line is $y=3x-7$

Hence, Option d is the correct answer.

3 0

3 years ago