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4 years ago

What are the multiples of 37?

Mathematics

2 answers:

ladessa [460]4 years ago

7 0

37: 37, 74, 111 and so on....just add 37 to the number before.

makvit [3.9K]4 years ago

3 0

1 = 37 2 = 74 3 = 111 4 = 148 5 = 185 6 = 222 7 = 259 8 = 296 9 = 333 10 = 370 And so on...

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A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate

LenaWriter [7]

Answer:

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Step-by-step explanation:

A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.

Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.

According to the Pythagorean Theorem:

$\displaystyle x^2+y^2=1521$

Let's take the derivative of both sides with respect to time t. Hence:

$\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right]$

Implicitly differentiate:

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

Simplify:

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

The area of the triangle formed will be given by:

$\displaystyle A = \frac{1}{2} xy$

Again, let's take the derivative of both sides with respect to time t:

$\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right]$

From the Product Rule:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)$

At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.

$\displaystyle y = \sqrt{1521-(15)^2}=36$

The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:

$\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}$

Evaluate for dy/dt:

$\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}$

Finally, using dA/dt, substitute in appropriate values:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)$

Evaluate. Hence:

$\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}$

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

8 0

3 years ago

True or false? these numbers can be used to calculate the standard deviation of this distribution

lakkis [162]

The answer would be False

4 0

4 years ago

Read 2 more answers

(2 tens 1 one)x10 in unit form and standard form

omeli [17]

When the number expression given as (2tens 1 one) x 10 is written in standard form, the standard form is 210 and the unit form is 2 hundred, and 1 ten

<h3>How to write the number in standard form?</h3>

The number expression is given as:

(2tens 1 one) x 10

2 tens is represented as:

2 * 10

1 one is represented as:

1 * 1

So, the number expression can be rewritten as:

(2tens 1 one) x 10 = (2 * 10 + 1 * 1) x 10

Evaluate the product

(2tens 1 one) x 10 = (20 + 1) x 10

Evaluate the sum

(2tens 1 one) x 10 = (21) x 10

Evaluate the product

(2tens 1 one) x 10 = 210

When the number expression given as (2tens 1 one) x 10 is written in standard form, the standard form is 210 and the unit form is 2 hundred, and 1 ten

Using the above steps as a guide, we have:

(5 hundreds 5 tens) * 10 ⇒ 5 thousands and 5 hundreds ⇒ 5500
(2 thousands 7 tens) / 10 ⇒ 2 hundreds and 7 units ⇒ 207
(4 ten thousands 8 hundred) / 10 ⇒ 4 thousands and 8 tens ⇒ 4080