1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mote1985 [20]
3 years ago
8

Use the given function to find the indicated value(s) of x. (Enter your answers as a comma-separated list.)

Mathematics
1 answer:
Nady [450]3 years ago
6 0

Answer:

For f(x) = √(2·x + 2) - √(x + 18), at f(x) = -1 the possible x-values includes;

-0.757, -17.5

Step-by-step explanation:

Given that the function is f(x) = √(2·x + 2) - √(x + 18)

The value of 'x' when f(x) = -1, is given as follows;

-1 = √(2·x + 2) - √(x + 18)

-1² = (√(2·x + 2) - √(x + 18))² = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)

1 = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)

2·√(2·x + 2)×√(x + 18) = 3·x + 20 - 1 = 3·x + 19

2·x² + 38·x + 36 = (3·x + 19)/2

2·x² + 38·x + 36 - (3·x + 19)/2 = 0

4·x² + 73·x + 53 = 0

From which we get;

x = (-73 ± √(73² - 4 × 4 × 53))/(2 × 4)

x ≈ -0.757, and x ≈ -17.5

You might be interested in
A swimming pool can be filled in 18 hours if water enters through a pipe​ alone, or in 25 hours if water enters through a hose a
pychu [463]
I am not sure, but this is what I got:
 <span>Pipe ALONE = 18 hours 

Pipe ALONE in 1 hour = 1/18 of the pool 

Hose ALONE in 1 hour = 1/25 of the pool 

TOGETHER in 1 HOUR = 1/18 +1/25 = 43/450 

TOGETHER they will fill the pool in 450/43 hours 

So 5/6 of the pool will take 5/6 X 450/43 = 2250/ 258 = 8.7209302 hours OR 

8 hours AND 43.26 minutes ANSWER
</span>
Hope this helps!


6 0
3 years ago
Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)
babunello [35]

\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k

We want to find f(x,y,z) such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=x^2+y

\dfrac{\partial f}{\partial y}=y^2+x

\dfrac{\partial f}{\partial z}=ze^z

Integrating both sides of the latter equation with respect to z tells us

f(x,y,z)=e^z(z-1)+g(x,y)

and differentiating with respect to x gives

x^2+y=\dfrac{\partial g}{\partial x}

Integrating both sides with respect to x gives

g(x,y)=\dfrac{x^3}3+xy+h(y)

Then

f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)

and differentiating both sides with respect to y gives

y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C

So the scalar potential function is

\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}

By the fundamental theorem of calculus, the work done by \vec F along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it L) in part (a) is

\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}

and \vec F does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them L_1 and L_2) of the given path. Using the fundamental theorem makes this trivial:

\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3

\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4

8 0
3 years ago
A tourist first walked 17km with a speed of v km/h. Then he hiked 12 km uphill with the speed that was 2 km/hour less than his o
ExtremeBDS [4]

Answer: t=\frac{17}{v}+\frac{12}{v-2}


Step-by-step explanation:

Given: A tourist first walked 17km with a speed of v km/h.

Since Speed=\frac{distance}{time}

therefore, Time=\frac{distance}{speed}

Let t_1 be the time he walked with speed v.

then t_1=\frac{17}{v}

Also he hiked 12 km uphill with the speed that was 2 km/hour less than his original speed.

Let t_2 be the time he hiked 12 km,

Then t_2=\frac{12}{v-2}

The total time for the whole trip is given by:-

t=t_1+t_2=

Substitute the values of t_1 and t_2 in the equation, we get

t=\frac{17}{v}+\frac{12}{v-2}

4 0
3 years ago
Mike has a collection of 140 canada stamps ,284 mexico stamps and 775 united states stamps about how many united states and cana
Doss [256]

Answer:

915 stamps

Step-by-step explanation:

140 + 775 = 915

4 0
3 years ago
1. $200 is deposited into an account that earns 6% simple interest
katen-ka-za [31]

Answer:

$260

Step-by-step explanation:

0.06 x 200 = 12

12 x 5 = 60

200 + 60 = 260

3 0
3 years ago
Other questions:
  • What is 9/27 simplified
    9·1 answer
  • What is X...……………………….
    15·1 answer
  • The Rivera family drove 267.9 miles from their home to Cape Cod, Massachusetts. They used 9.5 gallons of gas. How many miles per
    8·2 answers
  • Credit card balances follow a nearly normal distribution with a mean of $2,900 and a standard deviation of $860. A local credit
    13·1 answer
  • How do I tell my mom that really this good
    8·2 answers
  • Write the slope intercept form of the equation of the line through the given point with the given slope
    13·1 answer
  • Write in log base 10: log3 7
    15·1 answer
  • Help pls pls pls lol i know its a lot but thx
    14·1 answer
  • 5 - 3x &gt; -19 <br> Can someone please help me
    14·1 answer
  • A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 22 kilograms each, and the small box
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!