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3 years ago

Jude types 1,162 characters in 7 minutes. What is her typing rate in characters per minute?

Mathematics

2 answers:

amm18123 years ago

7 0

166 characters per minute. 1,162 divided by 7 = 166 : )

tia_tia [17]3 years ago

4 0

166 characters per minute

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A wooden log 10 meters long is leaning against a vertical wall with its other end on the ground. The top end of the log is slidi

Andre45 [30]

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is $\frac{dx}{dt}$ when y = 6 and $\frac{dy}{dt}=-2$ .

The equation for Pythagorean's Theorem is

$x^2+y^2=c^2$ where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ and divide everything by 2 to simplify:

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ . Looking at that equation, it looks like we need a value for x, y, $\frac{dx}{dt}$ and $\frac{dy}{dt}$ .

Since we are looking for $\frac{dx}{dt}$ , that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

$x^2+6^2=10^2$ and

$x^2+36=100$ and

$x^2=64$ so

x = 8.

NOW we can fill in the derivative and solve for $\frac{dx}{dt}$ .

Remember the derivative is

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

$8\frac{dx}{dt}+6(-2)=0$ and

$8\frac{dx}{dt}-12=0$ and

$8\frac{dx}{dt}=12$ so

$\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec$

7 0

3 years ago

Iam stuck on this quiz and I need help!!

olya-2409 [2.1K]

Answer:

I think it is 3?

Step-by-step explanation:

3, -2 ≤ 0

-5, 0 < -2 ≤ 5

3, -2 > 5

The second two lines do not hold true, as -2 is less than 0 and 5, not greater. The only that is true is the first one, but I am not sure that is how you do it.1

3 0

3 years ago

The population of a city is expected to increase by 3 percent next year. If p represents the population, write an expression to

fomenos

Answer:

The equation would be A = .03p

Step-by-step explanation:

To create this model, we know that we need to multiply the percentage by the current population. So we would multiply 3% or .03 by the variable given. You can set that equal to anything. I picked A for amount.

8 0

4 years ago

14. Solve the following equations.<br> (a), 7x + 8 = 10 + 3x

3241004551 [841]

answer: x = 1/2

<u>explanation</u>

subtract 3x from both sides

4x+8=10

subtract 8 from both sides

4x=2

divide both sides by 4

x=2/4

simplify

x=1/2 OR x=.5

hope i helped!

4 0

3 years ago

Read 2 more answers

Is $12 for 3 books; $28 for 7 books proportion

anastassius [24]

Yes, it is proportional. Every book is $4. 3 x 4 is 12, 7 x 4 is 28.

3 0

3 years ago

Read 2 more answers