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oksano4ka [1.4K]
3 years ago
6

Consider the line which passes through the point P(3, 1, 5), and which is parallel to the line x=1+5t,y=2+5t,z=3+1t Find the poi

nt of intersection of this new line with each of the coordinate planes:
xy-plane: ( , , )
xz-plane: ( , , )
yz-plane: ( , , )

Mathematics
1 answer:
padilas [110]3 years ago
7 0

Answer:

The point of intersection

(0,-14,22/5), (2,0,24/5), (-22,-24,0).

Step-by-step explanation:

Check attachment for solution

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The vector has components +5 and +7 along the x- and y-axes respectively. along a set of axes rotated 90 degrees counterclockwis
lisabon 2012 [21]
Refer to the diagram shown below.

Let the coordinates of the rotated vector be (a,b).
From the Pythagorean theorem,
d = √(5² + 7²) = 8.6023

The angle θ is given by
tan θ = 7/5 = 1.4
θ = tan⁻¹ 1.4 = 54.46°
φ = 180 - (90 + 54.46) = 35.54°

The coordinates of the rotated vector are
a = - d cos φ = - 8.6023*cos(35.54) = 7
b = d sin φ = 8.6023*sin(35.54) = 5

Answer:  (-7, 5)

6 0
3 years ago
Read 2 more answers
Sara has $1.30 less than double what Billy does. Sara has $53.72. How much money does Billy have?​
lilavasa [31]

Answer:

Billy has $27.51

Step-by-step explanation:

First let's set up an equation to solve this problem.

Assign a variable to Billy's amount. Let's make it x.

Then we just interpret the problem and solve:

2x - 1.30 = 53.72

     +1.30    +1.30

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

2x = 55.02

(Divide by 2 on both sides)

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

x = $27.51

2x = Billy's amount doubled

2x - 1.30 = Taking away 1.30 from double Billy's amount

53.72 = Sara's amount

6 0
3 years ago
A store manager ordered 28 crates of mangoes.There were 36 mangoes in each crate.WHEN the mangoes were delivered, he sold the ri
Kisachek [45]

Answer:

Number of ripe mangoes were sold as 132

Step-by-step explanation:

Let's assume number of rip mangoes were sold as 'x'

A store manager ordered 28 crates of mangoes

Number of crates =28

There were 36 mangoes in each crate

Number of mangoes in each crate=36

Total number of mangoes=( Number of crates)*(Number of mangoes in each crate)

Total number of mangoes is

=28\times 36

=1008

WHEN the mangoes were delivered

he sold the ripe mangoes and repacked the rest equally into 73 boxes

There were 12 mangoes in each box

Total number of mangoes is

=73\times 12+x

=876+x

now, we can set them equal

1008=876+x

x=132

5 0
3 years ago
Find the area of the figure. Round your answer to the nearest tenth
expeople1 [14]

Answer:

4 in

Step-by-step explanation:

5 0
3 years ago
Please help!! x = 2 - 3 cos t, y = 1 + 4 sin t in rectangular form?<br><br> thank you! :)
sukhopar [10]

Answer:

\frac{(x-2)^2}{9}+\frac{(y-1)^2}{16}=1

Step-by-step explanation:

x=2-3\cos(t)

y=1+4\sin(t)

Let's solve for \cos(t) in the first equation and then solve for \sin(t) in the second equation.

I will then use the following identity to get right of the parameter, t:

\cos^2(t)+\sin^2(t)=1 (Pythagorean Identity).

Let's begin with x=2-3\cos(t).

Subtract 2 on both sides:

x-2=-3\cos(t)

Divide both sides by -3:

\frac{x-2}{-3}=\cos(t)

Now time for the second equation, y=1+4\sin(t).

Subtract 1 on both sides:

y-1=4\sin(t)

Divide both sides by 4:

\frac{y-1}{4}=\sin(t)

Now let's plug it into our Pythagorean Identity:

\cos^2(t)+\sin^2(t)=1

\frac{x-2}{-3})^2+(\frac{y-1}{4})^2=1

\frac{(x-2)^2}{(-3)^2}+\frac{(y-1)^2}{4^2}=1

\frac{(x-2)^2}{9}+\frac{(y-1)^2}{16}=1

5 0
2 years ago
Read 2 more answers
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