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3 years ago

WHAT IS THE VALUE OF X?

Mathematics

1 answer:

Tanzania [10]3 years ago

7 0

It is a similar triangle so the side length of the smaller triangle (x and x-2) are in the same ratio as the bigger triangle (2x+5 and 2x-1). As the ratio is the same, you can equate them and solve for x.

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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

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

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

$y = 2x -4$

5 0

3 years ago

While on vacation at the beach, Eleanor drew the figure shown.In Eleanor’s drawing, the measure of ∠FMD is 15°, and the measure

bagirrra123 [75]

Answer:

oooooooooooooooophvih8gv

6 0

3 years ago

Read 2 more answers

Ms. Carr's Class Is Selling Magazines To Raise Money For A Field Trip. The Students In The Class Device They Wanted To Make 5.50

FinnZ [79.3K]

Here you are giving only the amount they want to raise (namely profit times number of magazines sold), and here you are also giving Money they want to raise... So clarifying, the money they want to raise, should include the money they will spend on buying the magazines (there is no statement saying they found them, or were given the magazines, so a cost should be involved)

Now if they are only making the count of "Field trip costs X amount of money, and given we have to make a profit of $5.5, How many must we sell?" then the equation should be n=X/5.5

Should the story be, how much money must they raise to have a profit of 5.5 on each magazine and still have enough for the field trip, then you have a different equation which varies only in adding the cost of each magazine, either case, M should be defined not as money they need to raise (cause here they will be short on their goal) but Money they must earn. And again, you should rewrite your equation to be:

M=Amount they must raise
C=Cost per magazine
n=Number of magazines
p=profit $5.5 per magazine

C+p=M/n

And rewriting the previous they should make:

n(C+p)=M -----> n(C+5.5)=M m/n = 5.50 
m/n x n = 5.50 x n //// multiply each side by n 

m = 5.5n

6 0

3 years ago

Read 2 more answers

Use distributive property to remove the parentheses -5(-2v+3y-1)

RoseWind [281]

Answer:

10v+-15y+5

Step-by-step explanation:

With distributive property, you multiply the number outside the parentheses to the numbers inside the parentheses separately then add them together and combine like terms.

4 0

3 years ago

Y=-1/4x-5 and 2x+8y=56 determine if paralllel ,nethier or perpendicular

Dominik [7]

Answer:

Parallel

Step-by-step explanation:

In the slope-intercept form (y=mx +c), the coefficient of x tells us the slope of the line.

2x +8y= 56

Let's rewrite this equation into the slope-intercept form.

8y= -2x +56

Dividing both sides by 8:

$y= - \frac{2}{8} x + \frac{56}{8}$

$y = - \frac{1}{4} x + 7$

Slope= -¼

y= -¼x -5

Slope= -¼

Since both lines have the same slope, they are parallel to each other.

3 0

2 years ago