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3 years ago

Which expression best represents all solutions of x for the equation cot x = –1.25, where k is any integer?

Mathematics

1 answer:

Alika [10]3 years ago

5 0

Answer:

The answer is " $-0.675+ k \ \pi$ "

Step-by-step explanation:

Given:

$\to \cot \ x = - 1.25\\\\\to \cot \ x = \cot (-0.675)\\\\\to x= k \pi + (-0.675)\\\\\boxed{\boxed{\boxed{x= -0.675 + k \pi}}}$

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Beverly made a deposit of $375 into her checking account. Then she withdrew $ 65. The next day, she wrote a check for $ 135. She

madreJ [45]

Start with 475
add 375(since made deposit)
475+375=850
850-65=785
785+135=$920

3 0

4 years ago

In a usually right-angled (x, y, z)-coordinate system, three planes are given by the following system of linear equations:

never [62]

Answer:

a) (x, y, z) = (1, -1, 0)

b) a = 0; L = {t, t, 0}

c) a = 1 . . or . . a = 3

d) No

Step-by-step explanation:

a) The solution using row-reduction techniques is shown in the first attachment, part (a). The generic solution is shown evaluated for a=2, the result being (1, -1, 0).

You will note that the solution gives indeterminate values for a=1 and a=3, which make the denominators zero.

b) For this, we use the point solution of part (a) together with the cross product of the normal vectors of planes 1 and 2. Said cross product will be in the direction of their line of intersection. We substitute the parametric equation for that line into the equation for plane 3 and solve for a. The result is a = 0.

The simplification of the resulting equation also gives a=1 and a=3, but we treat those as extraneous solutions because the corresponding common point of intersection of the planes does not exist.

c) The values a = 1 and a = 3 were found in part (a). These are values of a that make the common point indeterminate.

d) Substituting the given values for (x, y, z) gives three equations for a that have 3 different solutions. Hence there cannot be a value of a that makes this be a common point of intersection.

e) The second attachment illustrates part (a), with a=2. The third attachment illustrates part (b) with a=0.

The fourth attachment illustrates part (c). The first picture has the triangular tunnel between the planes in a vertical orientation (a=1). The second picture has the triangular tunnel extending from lower front to upper back (a=3).

7 0

3 years ago

Middle school problem attached :D

suter [353]

Answer: $638.40

Step-by-step explanation:

45% converted to a decimal is 0.45

0.45 of $1200 = 0.45* $1200 (of in this case means multiply)

0.45 * $1200= $440

Because they said 11% of remaining salary, we have to do:

$1200-$440=$760

Now 11% converted to a decimal is 0.11

5% converted to a decimal is 0.05

So 0.11+0.05

0.11+0.05= 0.16

Now 0.16 *$760=$121.60

Now we find the remaining amount so we subtract: $760-$121.60= $638.40

So our answer is $638.40 left

7 0

2 years ago

Read 2 more answers

The coordinates of points M,N, and P are ....

Rainbow [258]

Answer:

(-1, -1) Let me know if the explanation didn't make sense.

Step-by-step explanation:

If we graph the three points we can see what looks like a quadrilateral's upper right portion, so we need a point in the lower left. This means M is only connected to N here and P is only connected to N. So we want to find the slope of these two lines.

MN is easy since their y values are the same, the slope is 0.

NP we just use the slope formula so (y2-y1)/(x2-x1) = (-1-3)/(5-4) = -4.

So now we want a line from point M with a slope of -4 to intersect with a line from point P with a slope of 0. To find these lines weuse point slope form for those two points. The formula for point slope form is y - y1 = m(x-x1)

y-3 = -4(x+2) -> y = -4x-5

y+1 = 0(x-5) -> y = -1

So now we want these two to intersect. We just set them equal to each other.

-1 = -4x -5 -> -1 = x

So this gives us our x value. Now we can plug that into either function to find the y value. This is super easy of we use y = -1 because all y values in this are -1, so the point Q is (-1, -1)

8 0

3 years ago

20 POINTS!!! PLEASE HELP

pogonyaev

The logarithm of 10 to base 10 is 1

<h3>How to determine the logarithm?</h3>

The given parameters are: