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3 years ago

Is it possible for an exponential equation to have no solutions? If so, give an example. If not, explain why.

1 answer:

4 0

A function f(x) has solutions if we can find a value to plug in that leads to 0. In other words, there are solutions to f(x) = 0. Another term for "solution" is "root" or "x intercept"

An exponential function may cross the x axis at one point only. Though there are plenty of cases when there are no solutions at all. For instance, in the case of f(x) = (2^x) + 10

The right hand side will never be equal to zero no matter what you plug in for x. The graph will never cross the axis.

To answer your question, yes it is possible to have an exponential equation to have no solutions.

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Find an overestimate for 22×68 by adjusting each factor up to the nearest ten. A) 1200. B) 2100. C) 1400 D)1800

Rina8888 [55]

Answer:

D. 1800

Step-by-step explanation:

An overestimate is pretty self-explanatory, an amount bigger than what it's supposed to be.

Multiplying 22 * 68

1496

Rounding it will give you 1500, but the overestimate would be 1800. Because its a respected amount that is close to the answer of 22 * 68.

3 0

2 years ago

AB is tangent to circle O at A. The diagram is not drawn to scale. if AO=21 and BC=14, what is AB?

barxatty [35]

Ab would equal to 7 using tringle steps

7 0

3 years ago

Read 2 more answers

Pythagorean Theorem POSSIBLE POINTS : 13:33 Two joggers run 12 miles north and then 8 miles west. What is the shortest distance

ivann1987 [24]

Answer:

14.4 miles

Step-by-step explanation:

Given that :

Distance moved North = 12 miles

Distance moved West = 8 miles

Shortest distance to reach starting point :

Let shortest distance to reach starting point = d miles

Using the relation :

Longest side of a right angled triangle:

d = sqrt(8^2 + 12^2)

d = sqrt(64 + 144)

d = sqrt(208)

d = 14.422205

d = 14.4 miles (nearest tenth of a mile)

4 0

3 years ago

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

3 years ago

(Geometry) Could anyone help me with this please and thanks

Ket [755]

Answer:

z = 32/3

Step-by-step explanation:

Presuming all the horizontal lines are parallel, the ratios of lengths will be identical.

3/8 = 4/z

3z = 8(4)

z = 32/3

8 0

3 years ago