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3 years ago

Karen makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working hours.

Mathematics

1 answer:

Makovka662 [10]3 years ago

5 0

Let the number of hours she work be n
So the equation will be
P = 9n

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A math workbook has 100 pages. Each chapter of the book is 10 pages long. What percent of the book does each chapter make up?

kobusy [5.1K]

To find the percentage divide 10 by 100.. each chapter would make up 10% of the book.

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3 years ago

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Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without e

svet-max [94.6K]

ANSWER

$y = 2x -4$

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

$x = 5 + ln(t)$

$y = {t}^{2} + 5$

From the first equation we make t the subject to get;

$x - 5 = ln(t)$

$t = {e}^{x - 5}$

We put it into the second equation.

$y = { ({e}^{x - 5}) }^{2} + 5$

$y = { ({e}^{2(x - 5)}) } + 5$

We differentiate to get;

$\frac{dy}{dx} = 2 {e}^{2(x - 5)}$

At x=5,

$\frac{dy}{dx} = 2 {e}^{2(5 - 5)}$

$\frac{dy}{dx} = 2 {e}^{0} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

$y-y_1=m(x-x_1)$

$y - 6 = 2(x - 5)$

$y = 2x - 10 + 6$

$y = 2x -4$

Without eliminating the parameter,

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

$\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} }$

$\frac{dy}{dx} = 2 {t}^{2}$

At x=5,

$5 = 5 + ln(t)$

$ln(t) = 0$

$t = {e}^{0} = 1$

This implies that,

$\frac{dy}{dx} = 2 {(1)}^{2} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

$y-y_1=m(x-x_1)$

$y - 6 = 2(x - 5) =$

$y = 2x -4$

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3 years ago

For each point on the unit circle, select the angle that corresponds to it.

IgorC [24]

Answer:

A) 3π/4

B) 9π/7

C) 11π/6

Step-by-step explanation:

In the picture attached, the points are shown

Point A is between π/2 radians (90°) and π radians (180°). The only possible option is 3π/4

Point B is between π radians (180°) and 3π/2 radians (270°). The only possible option is 9π/7

Point C is between 3π/2 radians (270°) and 2π radians (360°). The only possible option is 11π/6

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3 years ago

Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma

Dmitry [639]

If she ran one mile in an hour wouldn't that mean her unit rate is one mile per hour? I think that's right but ask your teacher for reinsurance.

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3 years ago

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What is -x divided by 4?

exis [7]

The answer is just -x/4 because you can divide a variable

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2 years ago

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