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3 years ago

Over what interval will the immediate value theorem apply

Mathematics

1 answer:

koban [17]3 years ago

6 0

Answer:

Any [a,b] that does NOT include the x-value 3 in it.

Either an [a,b] entirely to the left of 3, or

an [a,b] entirely to the right of 3

Step-by-step explanation:

The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.

Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.

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Solve: y equals 6x - 8 y equals -3x + 10 solve for y and x

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2 years ago

Read 2 more answers

Vector v is shown in the graph.

Elis [28]

Question 4

<h3>Answer: Choice D</h3>

Explanation:

If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.

We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.

===========================================================

Question 5

<h3>Answer: Choice B</h3>

Explanation:

Vector v starts at (2,5) and ends at (-3,-2).

The x component of the vector is x2-x1 = -3-2 = -5 meaning we move 5 units to the left when going from the start point to the endpoint.

At the same time we move 7 units down because y2-y1 = -2-5 = -7 which is the y component of the vector.

The component form of vector v is

v = <-5, -7>

it says "move 5 units left, 7 units down".

Apply the pythagorean theorem to find the length of the vector.

a^2+b^2 = c^2

c = sqrt(a^2 + b^2)

||v|| = sqrt( (-5)^2 + (-7)^2 )

||v|| = 8.602 which is approximate.

Now let's use the arctangent function to find the angle

theta = arctan(b/a)

theta = arctan(-7/(-5))

theta = 54.462 which is also approximate.

There's a problem however. This angle is in Q1 but the vector <-5,-7> is in Q3. An easy fix is to add on 180 to rotate to the proper quadrant.

54.462+180 = 234.462

which is the proper approximate angle for theta.

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2 years ago

Morgan’s grandmother orders her groceries online and has them delivered to her house. Her bill is $120. She has a coupon for 20%

iragen [17]

Answer:

The total price of the groceries, including discount and tip is $110.4.

Step-by-step explanation:

Here, the bill amount of groceries = $120

Now, the coupon off = 20%

Calculating the discount, we get

20% of bill amount $120 = 20% of 120 = $\frac{20}{100} \times 120 = 24$

So, the 20% discount on the bill amount = $24

The actual payable amount = Bill Amount - Discount

= $120 - $24 = $96

Now, 15% tip is also applied on the actual payable amount $96.

15% of 96 = $\frac{15}{100} \times 96 = 14.4$

So, the total price t = Payable amount + Tip amount

= $96 + $14.4 = $110.4

or, t = $110.4

Hence, the total price of the groceries, including the discount and the tip is t = $110.4.

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3 years ago

How do you solve systems of equations using matrices? I need help with the steps please

seraphim [82]

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3 years ago

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serg [7]

Answer: 1.5..?

Step-by-step explanation:

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