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2 years ago

Which two whole numbers lies between the square root of 445?

Mathematics

1 answer:

vaieri [72.5K]2 years ago

8 0

The square root of 445 is 21.095 so the two whole numbers could be 20 and 21

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. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ft/sec, and the bottom of the l

Vlada [557]

Answer:

0.75 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.

So we can set a Pythagoras theorem as:

$x^2+y^2=25^2$

$x^2+y^2=625$

Now, we need to find the derivative of above equation with respect to time.

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: $20-1(5)=20-5=15$

Let us solve for y using Pythagoras theorem.

$y^2+15^2=25^2$

$y^2+225=625$

$y^2=625-225$

$y^2=400$

Take positive square root:

$\sqrt{y^2}=\sqrt{400}$

$y=20$

Upon substituting our given values in derivative equation, we will get:

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

$2(15)\cdot(-1)+2(20)\cdot \frac{dy}{dt}=0$

$-30+40\cdot \frac{dy}{dt}=0$

$40\cdot \frac{dy}{dt}=30$

$\frac{dy}{dt}=\frac{30}{40}$

$\frac{dy}{dt}=0.75$

Therefore, the ladder is moving up at a rate of 0.75 feet per second.

3 0

2 years ago

Question 45 A length of pipe that weighs 45 pounds is cut into two pieces. One of the pieces is 3 feet long and weighs 18 pounds

dmitriy555 [2]

Answer: 4.5 pounds.

Step-by-step explanation:

Given : Weight of original pipe =45 pounds

Weight of first piece = 18 pounds

Then, Weight of other piece = 45- 18 = 27 pounds

Length of first piece = 3 feet

Let x be the length of other piece.

As length is directly proportional to weight.

Then, $\dfrac{x}{27}=\dfrac{3}{18}$

$\Rightarrow\ \dfrac{x}{27}=\dfrac{1}{6}\\\\\Rightarrow\ x=\dfrac{1}{6}\times27 =4.5$

Hence, the he length of the other piece = 4.5 pounds.

7 0

2 years ago

For Problems 21 and 22, use Figure 4.5a.

Leno4ka [110]

Answer:

omg college math is so hard omg i feel baddddddd

Step-by-step explanation:

5 0

2 years ago

a total of 17100 seats are still available for the next hockey game.if 62% of the tickets are sold how many seats are in the are

BartSMP [9]

If 62% of the seats are sold;

100-62= 38% seats still available.

17100=38% seats available

17100/38= seats in 1%
450 seats

In 100%,
450×100=450000 seats total.

Hope I helped :)

3 0

2 years ago

Suppose that you bet $5 on each of a sequence of 50 independent fair games. Use the central limit theorem to approximate the pro

amm1812

Answer:

chances chances of happening = 0.0119

Step-by-step explanation:

given data

bet = $5

independent fair games = 50

solution

we will think game as the normal distribution

so here mean is will be

mean = $\frac{50}{2}$

mean = 25

and standard deviation will be

standard deviation = $\sqrt{50*0.5*0.5}$

standard deviation = 3.536

we have to lose 33 out of 50 time for lose more than $75

so as chance of doing things z score is

z score = $\frac{33-25}{3.536}$

z score = 2.26

so from z table

chances chances of this happening = 0.0119

8 0

2 years ago