Ask question

Ask question

All categories

3 years ago

13

19 Kayla's car can hold 15 gallons of gas. She gets 20.5 miles per gallon The tank is full. About how far can Kayla drive if she

uses all the gas in her tank? A 80 miles 6 160 miles c 230 miles D 310 miles

1 answer:

Nata [24]3 years ago

6 0

Answer:

D

Step-by-step explanation:

You might be interested in

-8x+32=4(-2-4x)<br>What does X equal

marshall27 [118]

Answer:

x = - 5

Step-by-step explanation:

Given

- 8x + 32 = 4(- 2 - 4x) ← distribute parenthesis on right side

- 8x + 32 = - 8 - 16x ( add 16x to both sides )

8x + 32 = - 8 ( subtract 32 from both sides )

8x = - 40 ( divide both sides by 8 )

x = - 5

7 0

2 years ago

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

I need help figuring out when to use law of sine or law of cosine?

irina [24]

When you have angle and its corresponding (opposite) side then you need to use law of sin. Problems 3,4,5(in 5 you need at first find angle X=180-92-62)

when you have two sides and angle between them, this is law of cos, problem 6,8

problem 7 you can use both, but if you can use both better to use law of sin, it is just easier

4 0

3 years ago

Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Rus_ich [418]

Answer:

b must equal 7 and a second solution to the system must be located at (2, 5).

Step-by-step explanation:

Rearranging the first equation:

y = (x - 3)^2 + 4

From this we see that the vertex is at the point (3,4).

So one solution of equation 2 is (3 ,4).

Substituting in equation 2:

4 = -3 + b

b = 7.

So equation 2 is y = - x + 7.

Now we check if (2, 5) is on this line:

5 = -2 + 7 = 5 , therefore (2, 5) is on this line.

Verifying if (2, 5) is also on y = (x - 3)^2 + 4:

5 = (2 - 3)^2 + 4 = 1 + 4 = 5

- so it is. and a second solution to the system is (2, 5).

5 0

2 years ago

Simplify.<br> (w5)<br> I need this ASAP please

Ilya [14]

I’m pretty sure it’s w^25

5 0

3 years ago