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1 year ago

What is the solution of |2x+3|< 19

Mathematics

1 answer:

Alex1 year ago

6 0

Answer:

- 11 < x < 8

Step-by-step explanation:

inequalities of the type | x | < a have solutions of the form

- a < x < a

then

| 2x + 3 | < 19

- 19 < 2x + 3 < 19 ( subtract 3 from each interval )

- 22 < 2x < 16 ( divide each interval by 2 )

- 11 < x < 8

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

vodomira [7]

Answer:

Step-by-step explanation:

Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.

Volume of a cone V = πr²h/3

<em>If the diameter and the height are equal, then r = h</em>

V = πh²h/3

V = πh³/3

If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min

Using chain rule to get the expression for dV/dt;

dV/dt = dV/dh * dh/dt

From the formula above, dV/dh = 3πh²/3

dV/dh = πh²

dV/dt = πh²dh/dt

20 = πh²dh/dt

To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.

20 = π(11)²dh/dt

20 = 121πdh/dt

dh/dt = 20/121π

dh/dt = 20/380.133

dh/dt = 0.0526ft/min

This means that the height of the pile is increasing at 0.0526ft/min

3 0

3 years ago

Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that

Deffense [45]

7 cups + 3 litres = 9.8 pints
$7c+3l=9.8p$ ⇒ Equation 1

5 litres - 9 cups = 6 pints
$5l-9c=6p$ ⇒ Equation 2

Relationship between cups and litres
Rearranging equation 1 to make pints the subject
$7c+3l=9.8p$
$p= \frac{7c+3l}{9.8}$ ⇒ substitute this into Equation 2

$5l-9c= \frac{7c+3l}{9.8}$
$49l-88.2c=7c+3l$
$49l-3l=7c+88.2c$
$46l=95.2c$
$l=2.1c$

Hence, 1 litre = 2.1 cups

Relationship between cups and pints
Rearrange equation 1 to make litres the subject
$7c+3l=9.8p$
$3l=9.8p-7c$
$l= \frac{9.8p-7c}{3}$ ⇒ Substituting this into Equation 2

$5( \frac{9.8p-7c}{3})-9c=6p$
$\frac{49p-35c}{3}-9c=6p$
$\frac{49}{3}p- \frac{35}{3}c-9c=6p$
$\frac{49p}{3}-6p= \frac{35}{3}+9c$
$\frac{31}{3}p= \frac{62}{3}c$
$p=2c$

Hence, 1 pint = 2 cups

Relationship between pints and litres
Rearranging equation 1 to make cup the subject

$7c=9.8p-3l$
$c= \frac{9.8p-3l}{7}$ ⇒ subsitute this into equation 2

$5l-9( \frac{9.8p-3l}{7})=6p$
$5l- \frac{63}{5}p+ \frac{27}{7}l=6p$
$5l+ \frac{27}{7}l=6p+ \frac{63}{5}p$
$\frac{62}{7}l= \frac{93}{5}p$
$l=2.1p$

Hence, 1 litre = 2.1 pints

7 0

3 years ago

Can someone help me plsHere are 2 right triangles.

prisoha [69]

Answer:

α = 44°

Step-by-step explanation:

For angle α, y is the opposite leg.

z is the hypotenuse.

sin α = opp/hyp

sin α = y/z

sin α = 0.7

α = sin-1 0.7

α = 44°

3 0

2 years ago

30 70 80 how many triangles cant you construct with these measurments

Alinara [238K]

Answer:

One triangle can be constructed.

Step-by-step explanation:

Recap that all the interior angles in a triangle add up to 180. With the given measurements of the angles, 70 plus 80 plus 30 equals 180. Each triangle has the sum of 180 degrees. Therefore, there can only be one triangle that can be constructed. I think you were suppose to put can, not can't. Hope this helps!

3 0

3 years ago

If Sarah travels at a rate of 45 miles per hour for 3 hours, how far does she travel?

Juliette [100K]

C)135 you have to multiply 45 by 3 for how many hours she traveled

6 0

2 years ago

Read 2 more answers