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3 years ago

Find the range of the function

Mathematics

1 answer:

Zina [86]3 years ago

6 0

Answer:

Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).

Find the domain of g(y), and this will be the range of f(x).

If you can't seem to solve for x, then try graphing the function to find the range.

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Calculate s26 for the arithmetic sequence in which a14=4.1 and the common difference is d=1.7

sweet-ann [11.9K]

Answer:

The value of $s_{26}=84.5$

Step-by-step explanation:

We have given $a_{14}=4.1$

d=1.7

We have to find $s_{26}$

So, $a_{14}=a+13d$ from the formula

$a_n=a+(n-1)d$

When n=14

$a_{14}=a+(14-1)(1.7)=a+13(1.7)$

$4.1=a+22.1$

$-18=a$

$a=-18$

Using the formula:

$s_n=\frac{n}{2}[2a+(n-1)d$

When n=26

$s_{26}=\frac{26}{2}[2(-18)+(26-1)(1.7)]$

On simplification we get:

$s_{26}=84.5$

8 0

2 years ago

Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220

Doss [256]

Answer:

1,000 km

Step-by-step explanation:

Assume that when two train pass each other, Lian has traveled x (km)

=> The time Lian has traveled when two trains pass each other is:

Time = Distance/ Rate = x/ 250 (hour)

As Lian and Yuto travelled from the two opposite train stations and the train stations are 1,880 km apart

=> When two train pass each other, Yuto has traveled 1,880 - x (km)

=> The time Yuto has traveled when two trains pass each other is:

Time = Distance/ Rate = (1,880 - x)/220 (hour)

As Lian and Yuto board at the same time, so that when two trains pass each other, the time both of them have traveled is equal

=> x/ 250 = (1,880 - x)/220

=> 220x = 250 x (1,880 -x)

=> 220x = 470,000 - 250x

=> 470x = 470,000

=> x = 1,000

So that, when two train pass each other, Lian has traveled x = 1,000 km

6 0

3 years ago

Read 2 more answers

Tell which equation you would use to isolate a variable in order to solve the system using substitution. Explain your reasoning.

vampirchik [111]

2x+y=-10
Multiply both side by 3
2x*3+y*3=-10*3
6x+3y=-30

3x-y=0
Multiply both side by 2
3x*2-y*2=0*2
6x-2y=0
Next, use substitute property
6x+3y=-30
-
6x-2y=0
=
y=-30
3x-y=0
Substitute y with -30
3x-30=0
Add 30 to each side
3x-30+30=0+30
3x=30
Divided both side by 3
3x/3=30/3
x=10, so the solution pair is (10,-30). In this case, there is the first way to solve these two equation.
Then, I would use equation 3x+1.5y=-15 in this question by multiply 2x+y=-10 by multiplying both side by 3/2 to eliminate x and to solve variables for y. Hope it help!

3 0

3 years ago

The graph of the equation y=12x−3 Determine the value of y for the point (4, y).

Novosadov [1.4K]

Answer:

$y=45$

Step-by-step explanation:

$y=12x-3$

$y=12(4)-3$

$y=45$

4 0

2 years ago

Read 2 more answers

Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

son4ous [18]

The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}$

and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\tan t$

4 0

2 years ago