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3 years ago

Solve the inequality help me sos

Mathematics

1 answer:

Anna007 [38]3 years ago

8 0

-7a + 5a < -(7-a) -(2a +1) Turns to -7a +5a < -7 +a -2a -1 Which turns to -2a < -1a -8 Which turns to -1a < -8 Which turns to 1a > 8 :)

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What is the volume of the plastic rocket???

Snezhnost [94]

Answer:

A) 151 in³ or 151 cubic inches

Step-by-step explanation:

Volume of rocket = Volume of Cylinder + Volume of Cone

Step 1

Find the volume of the cylinder

Volume of a cylinder = πr²h

r = Diameter/2

= 5/2 = 2.5 inches

h = 6 inches

Hence,

π × 2.5² × 6

= 117.81 cubic inches

Step 2

Find the volume of the cone

Volume of a cone =1/3 πr²h

h = 11 inches - 6 inches

= 5 inches

r = 2.5 inches

Hence,

1/3 × π × 2.5² × 5

= 32.72 cubic inches

Therefore:

Volume of rocket = Volume of Cylinder + Volume of Cone

= 117.81 cubic inches + 32.72 cubic inches

= 150.53 cubic inches

Approximately to the nearest inch = 151 in³ or 151 cubic inches

Option A is correct

7 0

3 years ago

find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

6 0

3 years ago

A granite monument has a volume of 25,365.4 cm3. The density of granite is 2.7 g/cm3. Use this information to calculate the mass

Vaselesa [24]

Answer:

<h3>The answer is 68,486.58 g</h3>

Step-by-step explanation:

The mass of a substance when given the density and volume can be found by using the formula

<h3>mass = Density × volume</h3>

From the question

volume of granite monument =

25,365.4 cm³

density = 2.7 g/cm³

The mass of the granite monument is

mass = 25,365.4 × 2.7

We have the final answer as

Hope this helps you

6 0

3 years ago

A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs ` 45 per l

tekilochka [14]

Answer:

4500

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Gradient of a straight line that is perpendicular to y = 4x + 2

lana66690 [7]

If a line's slope is $\frac{a}{b}$ , the slope of the perpendicular line is $-\frac{b}{a}$
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5 0

4 years ago