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3 years ago

If the diameter of the sphere is increased by 20% . By what % does its curved surface area increase?

Mathematics

1 answer:

mihalych1998 [28]3 years ago

8 0

Answer:

Curved surface area of sphere = 2πr × 2r=4πr^2;

The new diameter is 120/100 from the old diameter;

2R = (120/100)x(2r);

So, R = 1.2 x r;

Curved surface area of new sphere = 4πR^2 = 4π(1.2xr)^2= 4πr^2x1.44= curved surface of old sphere x (144%);

Finnaly, the increase is 44%.

Step-by-step explanation:

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What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y

Ostrovityanka [42]

Answer:y=-10

Step-by-step explanation:

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

+2y 6(2) +2y

3y=-1/2 4(12+3)

multiplie 4 times 12 and 4 times 3

3y=-1/2 48+12

add 48 and 12

3y=-1/2 60

divide -1/2 and 60

3y/3=-30/3

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3 0

3 years ago

Write the equation of a line parallel to the line 2x + y = 3 that passes through the point (2,6)

Lady bird [3.3K]

Answer <u>(assuming it can be in slope-intercept form)</u>:

$y = -2x +10$

Step-by-step explanation:

1) First, we need to find the slope of the given equation. To do that easily, convert it to slope-intercept form, represented by the formula $y = mx + b$ . Isolate y:

$2x + y = 3\\y = -2x + 3$

The number in place of $m$ , or the coefficient of the x-term, represents the slope of the equation. So, the slope of the given equation is -2.

Lines that are parallel share the same slope. So, the slope of the new equation will be -2 as well.

2) Now, remember that the slope-intercept form is represented by the formula $y = mx + b$ . In order to write an equation of a line using that formula, we need to substitute values for $m$ and $b$ . We know $m$ is the slope, so we already know what that equals. Now, we just need to find $b$ .

To do that, substitute -2 for $m$ in the slope-intercept formula. Additionally, substitute the x and y values of the point (2,6) for the x and y in the formula as well. This sets up the equation so that we can isolate $b$ and find its values:

$y = mx +b\\6 = (-2)(2)+b\\6 = -4 + b\\10 = b$

So, $b$ = 10.

3) Substitute values for $b$ and $m$ into the slope-intercept formula to write the slope-intercept form of the line:

$y = -2x +10$

6 0

3 years ago

Simplify by rationalizing the denominator.<br> 15√2 / √270

ladessa [460]

$\frac{ \sqrt{15} }{3}$ ✅

Step-by-step explanation:

$\frac{15 \sqrt{2} }{ \sqrt{270} } \\ \\ = \frac{15 \sqrt{2} }{ \sqrt{270} } \times \frac{ \sqrt{270} }{ \sqrt{270} } \\ \\= \frac{15 \sqrt{2} \times \sqrt{270} }{270} \\\\ (∵ \sqrt{a} \times \sqrt{a} = a) \\\\ = \frac{15 \sqrt{540} }{270} \\ \\= \frac{ \sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 5} }{18} \\ \\ = \frac{ \sqrt{ {2}^{2} \times {3}^{2} \times 15 } }{18} \\ = \frac{2 \times 3 \sqrt{15} }{18} \\ \\ = \frac{6 \sqrt{15} }{18} \\ \\ = \frac{ \sqrt{15} }{3}$