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3 years ago

Can you help me with this question.

Mathematics

1 answer:

Sauron [17]3 years ago

6 0

Answer:

27. (2x + 3)(x + 5)

Step-by-step explanation:

27.

Use the 'ac' method

a*c = 2 * 15 = 30

We need 2 numbers whose product is 30 and whose sum is 13.

3 and 10 look good so we write

2x^2 + 10x + 3x + 15

= 2x(x + 5) + 3(x + 5)

= (2x + 3)(x + 5) answer

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6.375 is greater than 6.333

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Step-by-step explanation:

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3 years ago

An ipad is worth R1200, excluding 15% VAT. What is the selling price of the ipad including VAT

alukav5142 [94]

Answer:

R1,380

Step-by-step explanation:

The price of the iPad without VAT is R1200

We calculate 15% to get;

$= \frac{15}{100} \times 1200$

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4 years ago

Find m<1 and find m<2

xenn [34]

Answer:

m∠1 = 50°

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Explanation:

m∠2 = 130° because of alternate exterior angles.

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8 0

3 years ago

A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u

OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

$\displaystyle\frac{8000\pi\sqrt{2}}{3}$

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

$x^2+y^2=15^2\to y=\sqrt{225-x^2}$

Then we set the integral for the volume by using shell method:

$\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx$

That can be solved by substitution:

$u=225-x^2\to du=-2xdx$

The limits of integration also change:

For x=5: $u=225-5^2=200$

For x=15: $u=225-15^2=0$

So the integral becomes:

$\displaystyle -\int_{200}^{0}\pi \sqrt{u}du$

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

$\displaystyle \int_{0}^{200}\pi u^{1/2}du$

Then applying the basic rule we get:

$\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}$

Since that is just half of the solid, we multiply by 2 to get the complete volume:

$\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}$

$=\displaystyle\frac{8000\pi\sqrt{2}}{3}$

5 0

4 years ago