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3 years ago

Find the slope of the line from the points and the graph.

Mathematics

2 answers:

Marta_Voda [28]3 years ago

5 0

(2,4) and (5,13) is m=-1/3 and (4,5) and (9,-3) is m=-8/5

QveST [7]3 years ago

3 0

Answer:

15. m=3 16. m=-8/5 or -1.6

Step-by-step explanation:

The formula for slope is m= $\frac{y_2-y_1}{x_2-x_1}$

so for #15

$\frac{13-4}{5-2}$ = $\frac{9}{3}$ =3

and for #16

$\frac{-3-5}{9-4}$ = $\frac{-8}{5}$ =-1.6

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The regions bounded by the graphs of y=4x and y=x−x2+x3 are shaded in the figure above. What is the sum of the areas of the shad

lana66690 [7]

Find where the two curves intersect:

$4x = x - x^2 + x^3$

$\implies x^3 - x^2 - 3x = 0$

$\implies x (x^2 - x - 3) = 0$

$\implies x = 0 \text{ or } x^2 - x - 3 = 0$

Completing the square gives

$x^2 - x - 3 = \left(x - \dfrac12\right)^2 - \dfrac{13}4 = 0$

and solving for x,

$\implies x = \dfrac12 \pm \sqrt{\dfrac{13}4} = \dfrac{1 \pm \sqrt{13}}2$

The total unsigned area between the two curves is then

$\displaystyle \int_{(1-\sqrt{13})/2}^{(1+\sqrt{13})/2} \left|4x - \left(x - x^2 + x^3\right)\right| \, dx$

$= \displaystyle -\int_{(1-\sqrt{13})/2}^0 \left(4x - \left(x - x^2 + x^3\right)\right) \, dx + \int_0^{(1+\sqrt{13})/2} \left(4x - \left(x - x^2 + x^3\right)\right) \, dx$

$= \displaystyle -\int_{(1-\sqrt{13})/2}^0 \left(3x + x^2 - x^3\right) \, dx + \int_0^{(1+\sqrt{13})/2} \left(3x + x^2 - x^3\right) \, dx$

where we use the definition of the absolute value function to split up the integral at the point where one curve "overtakes" the other - in other words, y = 4x lies above the curve y = x - x² + x³ when x > 0, and vice versa otherwise.

We have the antiderivative

$\displaystyle \int (3x + x^2 - x^3) \, dx = \dfrac{3x^2}2 - \dfrac{x^3}x - \dfrac{x^4}4 + C$

so that by the fundamental theorem of calculus, the area we want is

$\displaystyle \int_{(1-\sqrt{13})/2}^{(1+\sqrt{13})/2} \left|4x - \left(x - x^2 + x^3\right)\right| \, dx = \boxed{\dfrac{73}{12}}$

5 0

3 years ago

The area of pizza is 264 square centimeters.<br> WILL MEDAL HELP PLEASE

Diano4ka-milaya [45]

Is is going to be 128

5 0

3 years ago

In the figure to the right, AB = 7 1/2 m, BC = 2 1/4 m, and DE = 1 1/4 m. Find the perimeter of the figure if all angles are rig

Andreas93 [3]

Answer:

Perimeter=22 m

Step-by-step explanation:

Perimeter Of A Figure

Perimeter is the distance measured around a shape. If the figure is line-shaped, the perimeter can be obtained by adding the individual lengths of each segment around the shape.

The figure shown is surrounded by line segments. We only have to add them all to find the perimeter. But we don't need each individual length to do so. We may notice the following (given all angles are right):

The sum of HG+FE+DC equals AB. So the upper and lower lengths are twice AB, or equivalently: 2*7 1/2 m =15 m

It can also be noted that AH+GF=BC+DE=2 1/4+1 1/4 = 3 1/2 m. It means that the two lateral lengths are twice this value: 2* 3 1/2 = 7 m

Thus, the total perimeter is 15 m + 7 m = 22 m

4 0

3 years ago

PLEASE HELP mE: Simplify the expression 5c - 4 + 2c +6

Olegator [25]

Answer:

7c+2

Step-by-step explanation:

Hope this helps!

Brain-List?

3 0

3 years ago

Santos went on a bike ride of 90 miles. He realized that if he had gone 24 mph faster, he would have

Gnoma [55]

<h3>Answer: 6 mph</h3>

========================================

Explanation:

distance = rate*time

90 = r*t

where r is the slower speed and t is the time it takes when going that slower speed.

If r is bumped up 24 mph faster, to r+24, then Santos takes t-12 hours to get there. The second equation is

90 = (r+24)(t-12)

-------------------------------------

We can solve the first equation for r to get r = 90/t

Then plug this into the second equation and do a bit of algebra

90 = (r+24)(t-12)

90 = (90/t+24)*(t-12)

90 = 90 - 1080/t + 24t - 288

90t = 90t - 1080 + 24t^2 - 288t

0 = 90t - 1080 + 24t^2 - 288t-90t

0 = 24t^2 - 288t - 1080

24t^2 - 288t - 1080 = 0

If you apply the quadratic formula, then you should get the two solutions t = -3 and t = 15. Due to time constraints, I'll skip these steps.

We'll ignore the negative t value. It makes no sense to have a negative time.

So we focus on t = 15 as the only solution.

-------------------------------------

If t = 15, then,

r = 90/t

r = 90/15

r = 6

Santos rode his bike at <u>6 mph</u> at first. Going this speed means he takes 15 hours.

If he rode 24 mph faster, at 6+24 = 30 mph, then he would ride for 15-12 = 3 hours instead. Note that 90/30 = 3.

5 0

3 years ago