Answer the question below please.

Number 15. Find the equation of the line that passes through (3,-1) and is perpendicular to the line that passes through (-5, 2)

MArishka [77]

For lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

So we first need to find the slope of the reference line.

m=(y2-y1)/(x2-x1)=(7-2)/(-1--5)=5/4

So the perpendicular line will have a slope of:

5m/4=-1

m=-4/5

So our perpendicular line so far is:

y=-4x/5+b, now we can use point (3,-1) to solve for the y-intercept, "b"

-1=-4(3)/5+b

-1=-12/5+b

-5/5+12/5=b

7/5=b

So the line is:

y=-4x/5+7/5 or more neatly

y=(-4x+7)/5

y=-0.8x+1.4

3 0

3 years ago

A baseball is thrown at an angle of 30° with respect to the ground and it reaches the ground in 2 seconds. What is its initial v

NeTakaya

Answer:

The answer to your question is vo = 19.62 m/s

Step-by-step explanation:

Data

angle = α = 30°

time = t = 2 s

vo = ?

g = 9.81 m/s²

Formula

$t = \frac{2vosin\alpha}{g}$

Solve for vo

$vo = \frac{tg}{2sin\alpha}$

Substitution

$vo = \frac{(2)((9.81)}{2sin 30}$

Simplification

$vo = \frac{19.62}{2(0.5)}$

$vo = \frac{19.62}{1}$

Result

vo = 19.62 m/s

3 0

2 years ago

Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩

fgiga [73]

A = {odd numbers between 0 and 100}
A = {1, 3, 5, 7,...., 95, 97, 99}

B = {numbers between 50 and 150 that are evenly divisible by 5}
B = {50, 55, 60, 65, ..., 140, 145, 150}

The notation A ∩ B means the set of items that are in set A and also in set B. In terms of venn diagrams, it's the overlapping region between circle A and circle B

In this case, the following values are found in both set A and set B
{55, 65, 75, 85, 95}

So that's why
A ∩ B = {55, 65, 75, 85, 95}
which is the final answer

6 0

3 years ago

There are 240 students going on a field trip each school bus can hold 48 students complete the equation to show which operation

NeTakaya

If you calculate 240/48, you will get 5 without any remainder, which means if you get 5 buses it can exactly take all students?

8 0

2 years ago

Describe how you would find the maximum and minimum values for tangent of the typical angles used on the unit circle. What are t

Ipatiy [6.2K]

3down votefavorite1Find minimum and maximum value of function f(x,y)=3x+4y+|x−y| on circle{(x,y):x2+y2=1}I used polar coordinate system. So I have x=cost and y=sint where t∈[0,2π).Then i exploited definition of absolute function and i got:h(t)={4cost+3sintt∈[0,π4]∪[54π,2π)2cost+5sintt∈(π4,54π)Hence i received following critical points (earlier i computed first derivative):cost=±45∨cost=±2√29Then i computed second derivative and after all i received that in (2√29,5√29) is maximum equal √29 and in (−45,−35) is minimum equal −235

6 0

2 years ago