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2 years ago

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Use the points (2, 45) and (8, 90) to find the slope and y-intercept of the trend line for the data comparing hours studied to t

est scores.
m =
b =

1 answer:

NARA [144]2 years ago

4 0

Answer:

m= 7.5

b= 30

Step-by-step explanation:

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The image shows a ray of light bending at the boundary of a glass block. According to a law of optics, = n, where n is a constan

UkoKoshka [18]

The formula for the light bend would be n1*sin i= n2 * sin r

If you use "sin (90-x)= cos x" principle, you can change the sin in the equation into
n1*sin i= n2 * sin r
n1 * cos a= n2 * cos b
n2/n1= cos a/ cos b

Assuming the n constant is the ratio of the glass compared to water then the answer would be: cos a/ cos b

3 0

2 years ago

Pleaseee help!!! If you can, answer both :))

kherson [118]

Okay the first one is what u did lol

6 0

2 years ago

The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section

LUCKY_DIMON [66]

Answer:

y2 = C1xe^(4x)

Step-by-step explanation:

Given that y1 = e^(4x) is a solution to the differential equation

y'' - 8y' + 16y = 0

We want to find the second solution y2 of the equation using the method of reduction of order.

Let

y2 = uy1

Because y2 is a solution to the differential equation, it satisfies

y2'' - 8y2' + 16y2 = 0

y2 = ue^(4x)

y2' = u'e^(4x) + 4ue^(4x)

y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)

= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)

Using these,

y2'' - 8y2' + 16y2 =

[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0

u''e^(4x) = 0

Let w = u', then w' = u''

w'e^(4x) = 0

w' = 0

Integrating this, we have

w = C1

But w = u'

u' = C1

Integrating again, we have

u = C1x

But y2 = ue^(4x)

y2 = C1xe^(4x)

And this is the second solution

5 0

2 years ago

Which rule describes the composition of transformations that maps rectangle PQRS to P''Q''R''S''? R0,270° ∘ T0,2(x, y) R0,180° ∘

Gekata [30.6K]

Answer: The correct option is

(C) T0,2(x, y)∘ R0, 270°.

Step-by-step explanation: We are given to select the rule that describes the composition of transformations that maps rectangle PQRS to P''Q''R''S''.

From the graph, we note that

the co-ordinates of the vertices of rectangle PQRS are P(-3, -5), Q(-2, -5), R(-2, -1) and S(-3, -1).

and the co-ordinates of the vertices of rectangle P''Q''R''S'' are P''(-5, 5), Q''(-5, 4), R''(-1, 4) and S(-1, 5).

Since the rectangle PQRS lies in the Quadrant III and P''Q''R''S'' lies in Quadrant II, so the rotation will be either 90° clockwise or 270° counterclockwise about the origin.

In the given options, we do not have rotation of 90°, so will consider the rotation through 270° counterclockwise about the origin.

Now, after this rotation, the vertices will transform according to the rule

(x, y) ⇒ (y, -x).

Therefore, the vertices of the image rectangle P'Q'R'S', after rotation through 270° counterclockwise about the origin, becomes

P(-3, -5) ⇒ P'(-5, 3),

Q(-2, -5) ⇒ Q'(-5, 2),

R(-2, -1) ⇒ R'(-1, 2),

S(-3, -1) ⇒ S'(-1, 3).

Now, to make the vertices of P'Q'R'S' coincide with the vertices of P''Q''R"S", we need to add 2 units to the y co-ordinate of each vertex , so that

P'(-5, 3) ⇒ P''(-5, 3+2) = P''(-5, 5),

Q'(-5, 2) ⇒ Q"(-5, 2+2) = Q''(-5, 4),

R'(-1, 2) ⇒ R''(-1, 2+2) = R"(-1, 4),

S'(-1, 3) ⇒ S''(-1, 3+2) = S''(-1, 5).

Thus, the required transformation rule is

rotation through 270° counterclockwise about the origin and a translation of (x, y) ⇒ (x, y+2).

Since the rigid transformations are written from right to left, so option (C) is correct.

3 0

2 years ago

Read 2 more answers

It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the

rjkz [21]

<h2>Answer:</h2>

The equation that will be used to find t is:

$3(2-t)+1.5t=5$

<h2>Step-by-step explanation:</h2>

Total distance that is traveled by Amir is: 5 miles.

and the total time taken by him is: 2 hours.

On the first part of the hike, Amir averaged 3 miles per hour.

Let t denote the time he spent hiking during the second i.e. difficult part of the hike.

Hence, the time he spent in first part of hike is: 2-t

( Since, the total time was 2 hours)

Also, we know that:

$Distance=Speed\times Time$

Hence, distance traveled in first part of hike is:

$Distance=3\times (2-t)$

Now, the distance he will travel in second part of hike will be: 5-3(2-t)

Since the total distance traveled by him is 5 miles.

It is given that his speed decreased to 1.5 miles per hour.

Now, we know that:

$Time=\dfrac{Distance}{Speed}$

Hence, time spent by him in second part of hike is:

$t=\dfrac{5-3(2-t)}{1.5}\\\\i.e.\\\\1.5t=5-3(2-t)\\\\i.e.\\\\3(2-t)+1.5t=5$

8 0

2 years ago

Read 2 more answers