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2 years ago

14

At their school's craft fair, Diego and Rachel are both selling homemade bars of soap. So far,

2 answers:

Andrei [34K]2 years ago

7 0

182829 $$3 siahahanJsnaa

Karolina [17]2 years ago

7 0

Answer: it’s Rachel

Step-by-step explanation:

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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

The total price for a computer and a

8_murik_8 [283]

Answer:

$289

Step-by-step explanation:

If you know the cost of one of the two items, you can subtract that item from the total in order to find the price of the second item

So: total price - computer price = printer cost

So: $1039- $750 = $289

The printer is $289

3 0

2 years ago

By visual inspections, determine the best fitting regression model for the scatterplot

Marrrta [24]

For this case, we observe that the dispersion diagram has a behavior similar to a straight line.
we observe that as the values of x increase, the values of y decrease.
Therefore, the line is of negative slope.
Answer:
Linear
option C

4 0

3 years ago

Read 2 more answers

What is the range for the graph shown?

maxonik [38]

Answer:

D)

Step-by-step explanation:

Answer is D)

Range lies in between -2 and 3

=> -2 <= y <= 3

(-2 less than or equal to y, less than or equal to 3)

8 0

2 years ago

URGENT I HAVE ALMOST 0 TIME LEFT I NEED LAST MINUTE HELP

jonny [76]

Answer:

The zeros are the points where the parabola intercepts the x-axis.

$\sf x = 7 \implies x - 7 = 0$

$\sf x = 1 \implies x - 1 = 0$

$\sf \implies y = a(x - 7)(x - 1)$ where a is some constant

If the parabola passes through point (3, 4) then:

$\sf \implies a(3 - 7)(3 - 1) = 4$

$\sf \implies a(-4)(2) = 4$

$\sf \implies -8a = 4$

$\sf \implies a = -\dfrac12$

So the equation of the parabola is:

$\sf y = -\dfrac12(x - 7)(x - 1)$

Or in standard form:

$\sf y = -\dfrac12x^2+4x-\dfrac72$

7 0

1 year ago