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3 years ago

Solve the problem below and show your work

Mathematics

1 answer:

ehidna [41]3 years ago

6 0

The derivative of the function is 2x/(3+x²).

<h3>What is Derivative?</h3>

The derivative is the instantaneous rate of change of a function with respect to one of its variables.

Given function:

y= ln(3+x²)

Differentiating and applying chain rule

=1/(3+x²) d/dx(3+x²)

=1/(3+x²) (2x)

= 2x/(3+x²)

Hence, the derivative of the function is 2x/(3+x²).

Learn more about derivative here:

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Tomas and Tasha were hiking at a speed of 3.5 mph. On their way back, they were tired and their speed was 2 mph. How long was th

Anna35 [415]

To get the length of the route use the expression for speed,

Distance = Speed × Time

Length of the route is 7 miles.

It's given in the question,

Speed of Tomas and Tasha initially = 3.5 mph

Therefore, distance travelled by both with the speed of 2 mph one way will be,

Distance = 3.5t [Here, t = time ]

Speed of both while coming back = 2 mph

And the time taken = t + (1 hour 30 minutes)

= (t + 1.5) hours

Therefore, distance travelled while coming back = Speed × Time

= 2(t + 1.5)

Since, length of the route is same both ways,

3.5t = 2(t + 1.5)

3.5t = 2t + 3

3.5t - 2t = 3

1.5t = 3

t = 2 hours

Now substitute the value of t in the expression to get the distance of the route,

Distance = 3.5t

= 3.5 × 2

= 7 miles

Therefore, route was 7 miles long.

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7 0

3 years ago

Read 2 more answers

Can someone provide some assistance.

Ugo [173]

Answer:

m<E=120°

m<T=60°

Step-by-step explanation:

10m+4m+12=180

14m=168

m=12

m<E=10m=10(12)=120

m<T=4m+12=4(12)+12=48+12=60

8 0

3 years ago

Read 2 more answers

66 to 40 as a simple fraction

shepuryov [24]

The reduced form of

4 0

4 years ago

Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?

Nady [450]

One half life 1000 mg to 1000/2 =500 mg
One half life 500 mg to 500/2 = 250 mg
One half life 250 mg to 250/2 = 125 mg
Etc .......

7 0

3 years ago

Find the value of x of this question

mel-nik [20]

<h3><u>Let's</u><u> </u><u>understand</u><u> </u><u>the concept</u><u>:</u><u>-</u></h3>

Here angle B is 90°
So $\triangle ABC$ and $\triangle ABD$ Are right angled triangle
So we use Pythagoras thereon for solution

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>

First in triangle ABC

perpendicular=p=8cm

Hypontenuse =h =10cm

We need to find base=b

According to Pythagoras thereon

${\boxed{\sf b^2=h^2-p^2}}$

Substitutethe values

$\longrightarrow$ $\sf b^2=10^2-p^2$

$\longrightarrow$ $\sf b={\sqrt {10^2-8^2}}$

$\longrightarrow$ $\sf b={\sqrt{100-64}}$

$\longrightarrow$ $\bf b={\sqrt {36}}$

$\longrightarrow$ $\sf b=6$

$\therefore$ $\overline{BC}=6cm$

BD=BC+CD

$\longrightarrow$ $BD=9+6$

$\longrightarrow$ $BD=15cm$

Now in $\triangle ABD$

Perpendicular=p=8cm

Base =b=15cm

We need to find Hypontenuse =AD(x)

According to Pythagoras thereon

${\boxed {\sf h^2=p^2+b^2}}$

Substitute the values

$\longrightarrow$ $\sf h^2=8^2+15^2$

$\longrightarrow$ $\sf h={\sqrt {8^2+15^2}}$

$\longrightarrow$ $\sf h={\sqrt {64+225}}$

$\longrightarrow$ $\sf h={\sqrt {289}}$

$\longrightarrow$ $\sf h=17cm$

$\therefore$ ${\underline{\boxed{\bf x=17cm}}}$

8 0

3 years ago