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kari74 [83]
3 years ago
10

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 8y = sin(x)

.

Mathematics
1 answer:
zavuch27 [327]3 years ago
5 0
Consider, please, the suggested full solution. Modify the design according to local requirements.

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Find an equation of the vertical line through (3 comma negative 1 )in the form axplusbyequals​c, where​ a, b, and c are integers
Sati [7]

The equation of the vertical line is 1x+0y=3

Explanation:

It is given that the vertical line passes through the points (3,-1)

For vertical line, the slope is undefined.

Hence, b=0

Let us substitute the coordinate (3,-1) in the equation ax+by=c, we have,

3a+0y=c

Simplifying, we have,

3a=c

3=\frac{c}{a}

where a=1 and c=3

Substituting the values of a, b and c in the equation ax+by=c, we have,

1x+0y=3

Thus, the equation of the vertical line is 1x+0y=3

8 0
3 years ago
The marked price of a television set is #480. What is the sale price if a discount of 15% is given?
aivan3 [116]

Answer:

408

  • Step-by-step explanation:15% * 480=72
  • 480-72=408
  • hence answer is 408

6 0
3 years ago
A merry go around has a radius of 18 ft. If a passenger gets on a horse located at the edge of the wheel and travels 38ft, find
kipiarov [429]

Answer:

121 degrees

Step-by-step explanation:

Given

Radius r = 18ft

Length of the arc = 38ft

Required

angle of rotation

Using the formula

Length of an arc = theta/360 * 2πr

Substitute the given data

38 = theta/360 * 2π(18)

38 = theta/360 * 113.04

theta/360 = 38/113.04

theta/360 = 0.33616

theta = 0.33616 * 360

theta = 121.02

Hence the angle of rotation to the nearest degree is 121 degrees

4 0
3 years ago
3. Find the GCF of 120x2y5 and 80x3y2
Morgarella [4.7K]
So we have
120x2y5 and 80x3y2
120 doesnt divide into 80 evenly, but we know 40 goes into both.
so the first part is 80x
2y and 3y dont have a common factor other than y so the second part is
y
2 and 5 dont share any common factors so we simply leave that alone
so we have 40xy
3 0
4 years ago
The distance around a lake is 6 7/12 kilometers. Evan rode his bike 5/6 of the distance around the lake. What is the distance in
Firdavs [7]

Answer:

5 35/72 kilometers

Step-by-step explanation:

The distance around a lake is 6 7/12 kilometers. Evan rode his bike 5/6 of the distance around the lake. What is the distance in kilometers that Evan rode

This is calculated as:

Total distance = 6 7/12 km

Evan rode = 5/6 of the distance

Hence:

The distance Evans rode is

5/6 of 6 7/12

= 5/6 × 79/12

= 395/72

= 5 35/72 km(kilometers)

6 0
3 years ago
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