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2 years ago

What is the value of b and the missing symbol in Jamilla’s inequality?

Mathematics

2 answers:

Vikentia [17]2 years ago

5 0

Answer:

The answer for my question was also C..

Step-by-step explanation:

Sindrei [870]2 years ago

4 0

Answer:

$b=1, \geq$

Step-by-step explanation:

we know that

The absolute value function has two solutions

Observing the graph

the solutions are

$x\geq 1$ and $x\leq -3$

First solution (case positive)

assume the symbol of the first solution and then compare the results

$\left|x+b\right|\ge2$

$(x+b)\ge2$

$x\ge2-b$

$2-b=1\\b=2-1\\ b=1$

Second solution (case negative)

$-(x+b)\ge2$

Multiply by -1 both sides

$(x+b)\leq-2$

substitute the value of b and compare the results

$(x+1)\leq-2$

$x\leq-2-1$

$x\leq-3$ -------> is correct

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Nathan is out rafting. He rafts 16 miles with the river current. At the end of 16 miles, he turns around and rafts the same dist

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S = d/t

st = d

t = d/s

The time going is t1.
The time returning is t2.
The total time is 4 hours, so we have t1 + t2 = 4

The speed of the current is c.
The speed going is 9 + c.
The speed returning is 9 - c.

t1 = 16/(9 + c)

t2 = 16/(9 - c)

t1 + t2 = 16/(9 + c) + 16/(9 - c)

4 = 16/(9 - c) + 16/(9 + c)

1 = 4/(9 - c) + 4/(9 + c)

(9 + c)(9 - c) = 4(9 - c) + 4(9 + c)

81 - c^2 = 36 - 4c + 36 + 4c

81 - c^2 = 72

c^2 = 9

c^2 - 9 = 0

(c + 3)(c - 3) = 0

c + 3 = 0 or c - 3 = 0

c = -3 or c = 3

We discard the negative answer, and we get c = 3.

The speed of the current is 3 mph.

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2 years ago

Read 2 more answers

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Anon25 [30]

Use the quadratic formula, the second, the 6th answers are correct.

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2 years ago

A weight lifter can deadlift 275 pounds. She can increase the weight that she can lift according to the function W(x)=275(1.05)^

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Answer:

$350.98\ pounds$

Step-by-step explanation:

we have

$W(x)=275(1.05^{x})$

where

W is the weight in pounds

x is the number of training cycles completed

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2 years ago

Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a

Artyom0805 [142]

Answer:

$\frac{dh}{dt} = \frac{216}{1875\pi}$

Step-by-step explanation:

Given

Represent radius with r and height with h

$h = 12ft$

$r = 10ft$

$Rate = \frac{8ft^3}{min}$ when $h = 10ft$

Express radius in terms of height

$\frac{r}{h} = \frac{10}{12}$

$\frac{r}{h} = \frac{5}{6}$

$r = \frac{5}{6}h$

First, we need to determine the volume of the cone in terms of height.

$Volume = \frac{1}{3}\pi r^2h$

Substitute $r = \frac{5}{6}h$

$V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h$

$V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h$

$V = \frac{1}{3} * \pi * \frac{25}{36}h^3$

$V = \frac{25}{108} \pi h^3$

Differentiate both sides w.r.t time (t)

$\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}$

$\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}$

Solve for $\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}$

At this point, $h = 10$ and $\frac{dv}{dt} = \frac{8ft^3}{min}$

So, we have:

$\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}$

$\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}$

$\frac{dh}{dt} = \frac{864}{7500\pi}$

$\frac{dh}{dt} = \frac{216}{1875\pi}$

Hence:

The rate is $\frac{216}{1875\pi} ft/min$

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