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3 years ago

show that if k is a positive constant, then the area between the x-axis and one arch of the curve y=sin kx is 2/k

1 answer:

8 0

Sin(kx)=0=>x=0,π,...
∫0πsin(kx)dx=−1/kcos(kx)|π0=−1/k(cos(kπ)−cos(k∗0))
if k is odd then,=−1/k(−1−1)=−1/k(−2)=2/k
if k is even then,=−1/k(1−1)=0

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Given the equation y = 2 x - 8, what is the slope and the y -intercept?

jeka94

Answer:

m=2 and b=-8

Step-by-step explanation:

This equation is organized in slope-intercept form, y=mx+b. In this form, m is the slope and b is the y-intercept.

When given the equation, y=2x-8, we can see that 2 is in the place of m and -8 is in the place of b. The reason the y-intercept isn't 8 is that y=2x-8 can be written as y=2x+(-8) since y=mx+b involves addition. Therefore, the slope is 2 and the y-intercept is -8.

m=2 and b=-8

I hope this helps!

4 0

2 years ago

ΔCAR has coordinates C (2, 4), A (1, 1), and R (3, 0). A translation maps point C to C' (3, 2). Find the coordinates of A' and R

shutvik [7]

Answer:

$A'= (2,-1)$ and $R'=(4,-2)$ under this translation.

Step-by-step explanation:

A translation in $R^{2}$ is a mapping T from $R^{2}$ to $R^{2}$ defined by $T(x,y) = (x + v_1,y+v_2)$ , where $v=(v_1,v_2)$ is a fixed vector in $R^{2}$ .

From the problem we know that $T(2,4)=(3,2)$ , so we need to find the values $v_1$ and $v_2$ such that $T(2,4) = (2 + v_1,4+v_2)=(3,2)$ , so $3=2 + v_1$ and $4+v_2=2$ , thus $v_1=1$ and $v_2=2$ .

Then $T(x,y) = (x + 1,y-2)$ and

$T(1,1)=(1+1,1-2)=(2,-1)=A'$

$T(3,0)=(3+1,0-2)=(4,-2)=R'$

Therefore $A'= (2,-1)$ and $R'=(4,-2)$ . The triangles CAR and C'Q'R' are shown in the figure below.

7 0

3 years ago

At a carnival game, you randomly throw two darts at the board and break two balloons. What is the probability that both the ball

Amanda [17]

4/15 of the balloons are purple. You have two darts. There are 105 combinations of hitting two balloons out of the 15. There are 6 combinations of purple balloons to be hit. This (Purple combinations over total combinations) is your probability. 6/105 simplified to 2/35 or 2:35
So your chance of picking the purple balloons, both purple, out is 2 in 35 or 2/35
Brainliest?

6 0

3 years ago

Write down a differential equation of the form dy/dt = ay + b whose solutions have the required behavior as t → ∞. all other sol

nordsb [41]

The ODE has an equilibrium point at

$\dfrac{\mathrm dy}{\mathrm dt}=ay+b=0\implies y=-\dfrac ba$

We want $y=2$ to be an unstable equilibrium solution - in other words, we want all solutions with initial condition $y(t_0)=c$ for $c$ near 2 to diverge from $y=2$ - so $-dfrac ba=2$ .

Divergence from $y=2$ would require that for $y>2$ , any solution is increasing, and for $y$ , and solution is decreasing. In order for that to happen, we need