All categories

1 year ago

Which equation represents a line that passes through (5, 1) and has a slope of StartFraction one-half EndFraction?

Mathematics

2 answers:

saul85 [17]1 year ago

5 0

Answer:

y – 1 = y minus 1 equals StartFraction one-half EndFraction left-parenthesis x minus 5 right-parenthesis.(x –5)

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=\frac{1}{2}$

$(5,1)$

substitute

$y-1=\frac{1}{2}(x-5)$

stealth61 [152]1 year ago

4 0

Answer:

THIRD OPTION

Step-by-step explanation:

You might be interested in

Which angles form a linear pair? AnglePRL and AngleLRM AngleORP and AngleMRN AngleMRN and AngleNRO AngleLRP and AngleORP

Andrew [12]

Answer: C (AngleMRN and AngleNRO)

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect. Two angles are linear if they are adjacent angles (angles next to each other) formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

AngleMRN and AngleNRO together is 180 degrees

I'm not very good at explaining but hope this helps ! :)

4 0

1 year ago

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

1 year ago

Mr. Jones waffle recipe uses 3/4 cups of milk to make 8 waffles how many cups of milk should be used to make 24 waffles?

ella [17]

Answer:

9/4

Step-by-step explanation:

If you need 3/4 cups of milk to make 8 waffles, you would need 9/4 cups to make 24 waffles because you are making 3 times the amount of waffles, so you need 3 times the amount of milk.

5 0

1 year ago

Ana wrote four statements to describe circle S. Statements: AB is a diameter. ST , SP and SQ are radii. SQ = 12 cm PQ = 12 cm Ar

wel

Two of the four statements that Ana wrote are correct. Number 1, "AB is a diameter" is incorrect, and so is number 3, "SQ = 12 cm". AB is not a diameter because it is instead a chord. "ST , SP and SQ are radii" is correct because they are straight lines from the center of the circle to the circumference of the circle, which is the exact definition of radius. The third statemet is incorrect because since ST is a radius and it equals 6, that means all radii are equal to 6. SQ is a radius of circle S, so it should also equal 6, not 12. The last statement is correct because PQ is a diameter of circle S. By rule, the diameter is always equal to double of the radius. The radius is 6, so 6 x 2= 12.

8 0

1 year ago

A certain club has $50$ people, and $4$ members are running for president. Each club member votes for one of the $4$ candidates.

erastova [34]

Answer:

The number of different possible vote totals is 184.

Step-by-step explanation:

It is provided that there are N = 50 people in a club.

The position of President is open. And there are x = 4 members running for he post of President.

So, there are n = N - x = 50 - 4 = 46 people voting for these 4 members.

Each member of the club has x = 4 possible choices.

So, the number of different possible vote totals are:

Number of different possible votes = n × x

= 46 × 4

= 184

Thus, the number of different possible vote totals is 184.

8 0

1 year ago