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VMariaS [17]
2 years ago
13

A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes throug

h the points (1, 0) and (0, negative 6).
What value of b will cause the system to have an infinite number of solutions?

y = 6x – b

–3x + StartFraction one-half EndFractiony = –3

b =

2
4
6
8
Mathematics
2 answers:
natali 33 [55]2 years ago
5 0

Answer:

its option C,   6

Step-by-step explanation:

tensa zangetsu [6.8K]2 years ago
3 0

Answer: C

Step-by-step explanation:

Given that the line -3x + y/2 = -3 passes through the points (1, 0) and (0, -6).

First rearrange the equation

-3x + y/2 = -3

Y = 2( 3x - 3 )

Y = 6x - 6 ..... (1)

Also, the slope of points (1, 0) and (0, -6). Will be

M = ( -6 - 0 )/( 0 - 1 )

M = -6/-1

M = 6

Using general linear equation

Y = MX + C

Let Y = 0 and X = 1

0 = 6(1) + C

C = -6

Substitutes C back into the equation

Y = 6x - 6 ...... (2)

The value of b that will cause the system to have infinitely many number of solutions is 6

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The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas
iren [92.7K]

For the last part, you have to find where f'(t) attains its maximum over 0\le t\le8. We have

f'(t)=-6\sin3t+6\cos2t

so that

f''(t)=-18\cos3t-12\sin2t

with critical points at t such that

-18\cos3t-12\sin2t=0

3\cos3t+2\sin2t=0

3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0

\cos t(3\cos^2t-9\sin^2t+4\sin t)=0

\cos t(12\sin^2t-4\sin t-3)=0

So either

\cos t=0\implies t=\dfrac{(2n+1)\pi}2

or

12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi

where n is any integer. We get 8 solutions over the given interval with n=0,1,2 from the first set of solutions, n=0,1 from the set of solutions where \sin t=\dfrac{1+\sqrt{10}}6, and n=1 from the set of solutions where \sin t=\dfrac{1-\sqrt{10}}6. They are approximately

\dfrac\pi2\approx2

\dfrac{3\pi}2\approx5

\dfrac{5\pi}2\approx8

\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1

2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7

2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6

4 0
2 years ago
A clock is showing the time as exactly 3:00 p.m. and 25 s. Because a full minute has not passed since 3:00, the hour hand is poi
Grace [21]
I had to read this a couple of times to see this was not about time, but is a right triangle problem. If the hour hand is at three, let us consider that a leg of a right triangle, we will consider the hypotenuse as the second hand.
Sketch the picture. 

The hypotenuse is 9 cm. the angle is found by: 

the (hour hand) is pointing directly at the 12. I expect you mean the minute hand. The angle between the minute hand and the second hand is 25/60*360 = 150 which make the angle between the hour hand and the second hand. 150 -90 =60 

so the second hand and the hour hand gives us a right triangle, with a 60 degree angle and a hyp. of 9 cm. 

cos 60 = x/9 

9 cos 60 =x 
<span>
x = 4.5 cm

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
3 0
2 years ago
which of the sets shown includes the elements of set Z that both negative numbers and multiples of ?. Z={-34,-28,-16,-2,4,8,12,2
Ronch [10]

Answer:

multiples of 2

Step-by-step explanation:

6 0
2 years ago
There were 324 adults surveyed. Among the participants, the mean number of hours of sleep each night was 7.5 and the standard de
kirill [66]
0.17 sense you have to round it to the nearest hundreth


5 0
2 years ago
Read 2 more answers
What is the value of x in the figure below? In this diagram, ABD~CAD
olga55 [171]

Answer:

x = 25/4

Step-by-step explanation:

Because of the known similarity of the triangles, we know that

10       x

----- = ----

16      10

Cross-multiplying, we get 16x = 100, and thus x = 100/16 = 50/8 = 25/4

x = 25/4

4 0
2 years ago
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