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2 years ago

A flight of stairs is supported by two columns, as shown in the diagram.

Mathematics

1 answer:

dangina [55]2 years ago

4 0

Answer:

12 feet

Step-by-step explanation:

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The mass of a colony of bacteria, in grams, is modeled by the function P given by P(t)=2+5tan^−1.(t/2), where t is measured in d

ira [324]

Answer:

1.21 g/day

Step-by-step explanation:

We are given that

The mass of a colony of bacteria (in (grams) is given by

$P(t)=2+5tan^{-1}(\frac{t}{2})$

Where t=Time(in days)

Differentiate w.r.t t

$P'(t)=5(\frac{1}{1+\frac{t^2}{4}}\times \frac{1}{2})$

By using the formula $\frac{d(tan^{-1}(x)}{dx}=\frac{1}{1+x^2}$

$P'(t)=\frac{5}{2}(\frac{4}{4+t^2})$

$P'(t)=\frac{10}{4+t^2}$

We are given P(t)=6

Substitute the value

$6=2+5tan^{-1}(\frac{t}{2})$

$5tan^{-1}(\frac{t}{2})=6-2=4$

$tan^}{-1}(\frac{t}{2})=\frac{4}{5}$

$\frac{t}{2}=tan(\frac{4}{5})$

$t=2tan(\frac{4}{5})$

Substitute the value of t

$P'(2tan\frac{4}{5})=\frac{10}{4+4tan^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{10}{4}\times \frac{1}{1+tan^2(\frac{4}{5})}$

We know that $1+tan^2\theta=sec^2\theta$

Using the formula

$P'(2tan(\frac{4}{5})=\frac{5}{2}\times \frac{1}{sec^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times cos^2(\frac{4}{5})$

By using $cos^2x=\frac{1}{sec^2x}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times (0.696)^2=1.21$ g/day

Hence,the instantaneous rate of change of the mass of the colony=1.21g/day

7 0

2 years ago

Read 2 more answers

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

Elena-2011 [213]

Given:

The length of the segment of the chord DB is 8.2 units.

The length of the segment AB is 6.9 units.

The length of the radius AC be x units.

We need to determine the value of x.

Length of BC:

Since, we know the property that, "if a radius is perpendicular to the chord, then it bisects the chord".

Thus, applying the above property, we have;

DB ≅ BC

8.2 = BC

Thus, the length of BC is 8.2 units.

Value of x:

Since, ∠B makes 90°, let us apply the Pythagorean theorem to determine the value of x.

Thus, we have;

$AC^2=AB^2+BC^2$

Substituting the values, we have;

$x^2=6.9^2+8.2^2$

$x^2=47.61+67.24$

$x^{2} =114.85$

$x=10.7$

Thus, the value of x is 10.7 units.

Hence, Option A is the correct answer.

4 0

2 years ago

Adam has sticks of the following lengths: (3x+4) (2x+10) (x+12)cm

gladu [14]

Option I
(3x+4)cm =(2x+10)cm
3x-2x=6
x=6
Option II
(3x+4)= (x+12)
3x-x=12-4
2x=8
x=4
Option III
(2x+10)= (x+12)
2x-x=12-10
x=2

3 0

2 years ago

Read 2 more answers

What is 14.7 x 11.361

Y_Kistochka [10]

167.0067
I hope this helps!

4 0

2 years ago

Read 2 more answers

A bright blue parallelogram is painted on a playground. It has a height of 16 feet and a length of 23 feet. If one gallon of pai

vlada-n [284]

Answer:3 gallons of paint

Step-by-step explanation:multiply 23 times 16 and then divide by 175.

6 0

2 years ago