. In Exercise 16, the height of the rocket was given by h=256t-167². Use the
discriminant to answer the following questions.
a. Will the rocket reach an altitude of 1000 ft?
b. Will the rocket reach an altitude of 1024 ft?
c. Will the rocket reach an altitude of 1048 ft?

Answer:

x = 5

y = 37.5

We can graph the two equations to find our solution.

-> See attached

-> They intersect at point (5, 37.5) so this is our answer.

-> Coordinate points are in terms of (x, y)

We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

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Answer:

Step-by-step explanation:

Answer:

What events or steps are described?

Do these things need to occur in a particular order?

Step-by-step explanation:

Answer:

Part A : 1/62   Part  b : 1/60

Step-by-step explanation:

Well lets start with part A

(62)x=1

anything in parenthesis means multiply

62x= 1

divide everything by 62 to get x by itself

x= 1/62

Part A : 1/62

Part B : 60x = 1

x = 1/60

because same  reasoning

Answer:

A

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Dilatation is acutally for medicine and dilation is actually for phycology.

Answer:

its B

Step-by-step explanation:

Using simple interest, it is found that the monthly payments are of $854.875.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem, the parameters are A(0) = 49000, r = 0.0665, t = 7, hence the total amount is of:

\(A(t) = A(0)(1 + rt)\)

\(A(t) = 49000[1 + 0.0665(7)]\)

\(A(t) = 71809.5\)

Payments over a period of 12 x 7 = 84 months, hence the monthly payments are of:

71809.5/84 = $854.875.

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Answer:

mean=57

range=19

Step-by-step explanation: there you go

Answer:

1.07 x 10^8

Step-by-step explanation:

Chad will purchase 0.432 gallons of red and white paint.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.

Given

Dimension of the door = 18 feet by 6 feet

Area of the door = 108 square feet

1 gallon of paint covers 250 square feet

Let x gallon paint covers 108 square feet

Proportion of paint to area covered

1/250 = x/108

x = 108/250

x = 0.432

Hence, 0.432 gallons of red and white paint, Chad will purchase.

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Answer:

F(x)= 4x

y=4x

now, switch the variables

x= 4y

simplify the equation so that y is by itself. Divide each side by 4

x/4= y

or f(x)= x/4 is the answer

Step-by-step explanation:

Answer:

x/4 = f(x)

Step-by-step explanation:

First you put Y in for f(x)

1. y=4x

Then you flip x and y so you are solving for x

2.x=4y

Now, you divide by 4 to solve

3. x/4=y

Each day's weight can then be plotted as a point on the graph, and a line can be drawn connecting the points to show the trend in the squirrel's weight over time.

What is Graph ?

Graph can be defined as visual representation of data using given ordered pairs.

For tracking the weight of a baby squirrel over a month, a line graph would be the best option.

A line graph is used to display data that changes continuously over time, making it ideal for showing the daily weight of the squirrel over the course of a month.

The horizontal axis can represent the time (in days), and the vertical axis can represent the weight of the squirrel.

Therefore, Each day's weight can then be plotted as a point on the graph, and a line can be drawn connecting the points to show the trend in the squirrel's weight over time.

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Answer:

The transformation was a 90° rotation about the origin.

Step-by-step explanation:

Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4) A' (–1, –1) B' (–1, 1) C' (–4, 1) Which best describes the transformation? The transformation was a 90° rotation about the origin. The transformation was a 180° rotation about the origin. The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.

Answer: Transformation is the process of moving a point in a graph to another point. The new point formed is the image of the old point. When an object is transformed each point of the object is moved to another point. There are three types of transformation: Reflection, Rotation, Translation and dilation.

If a point O(x, y) is rotated 90° rotation about the origin., the new point is at O'(-y, x). That is the x coordinates becomes negative of the y coordinate and the y coordinate becomes the x coordinate.

The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4), If a transformation of 90° rotation about the origin is done, the new points are A' (–1, –1) B' (–1, 1) C' (–4, 1)

Answer:

The answer is a

Step-by-step explanation:

Answer: D Mario owes the bank a little less than $50

Applying the alternate interior angles postulate, the measure of angle HLI in the diagram is: 56°.

An example of interior angles that lie alternate to each other along a transversal are the angles shown in the image as angle HIL and angle MLI.

According to the alternate interior angles postulate, angle HIL is congruent to angle MLI.

Given that, the measure of angle MLI = 56°, since angles HIL and MLI are congruent angles based on the alternate interior angles postulate, therefore:

Measure of angle MLI = measure of angle HLI

Thus:

The measure of angle HLI = 56°

In conclusion, applying the alternate interior angles postulate, the measure of angle HLI in the diagram is: 56°.

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The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

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The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Answer:

270

Step-by-step explanation:

the arc length is the same as the angle. the right triangle shows 90... so subtract 360 by 90 and you get 270.

pretty sure that how you get it or it might be the angle but yeah, hope this helps

Answer:

C

Step-by-step explanation:

8 : 10 = 18

12 : 15 = 27

36 : 45 = 81

Answer:

The united nations flag the translation can be any of the blue triangles and the reflection if the flag itself as it is symmetrical

Step-by-step explanation:

The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.

If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

If you're reflecting a point (x,y) along x axis, then its abscissa will stay same but ordinates will negate. Thus (x,y) turns to (x, -y)

Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)

Therefore, The united nations flag the translation can be any of blue triangles and the reflection if the flag itself as it is symmetrical.

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Answer:

yes she is correct

Step-by-step explanation:

(4^3)^3=262144 and 2^18=262144

(4^3)^3=2^18

hope this helps! :)

(4^3)^3 can be rewritten as 2^18 .

The result of multiplying an integer (not a fraction) by itself is called square of a number. Example: 4 × 4 = 16, so 16 is a square number.

Now the given number is,

(4^3)^3

Since we know tha 4 is the square of 2

i.e 2x2 = 4

or, 2^2 = 2x2 =  4

Therefore we can write,

{(2^2)^3}^3

Using the exponential property,

(a^b)^c = a^bc

So,

(2^2)^3 = 2^6

and,

{(2^2)^3}^3 = (2^6)^3 = 2^18

Hence,(4^3)^3 can be rewritten as 2^18

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Answer:

204 in²

Given:

Base: 17 inch

Height: 24 inch

Area of Triangle:

1/2 * Base * Height

1/2 * 17 * 24

1/2 * 408

204 in²

The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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Without additional information about the test's validity, reliability, and normative data, it is difficult to draw definitive conclusions about its overall effectiveness as an assessment tool.

Based on the results provided, it appears that the new mechanical aptitude test has a wide range of scores and can produce different results when administered multiple times. The maximum possible score of 100 points suggests that the test measures a broad range of mechanical abilities. The fact that the test is administered twice within a 2-week period also indicates that it may be designed to assess changes or improvements in mechanical skills over time. Based on the given results, it appears that the new mechanical aptitude test, which has a maximum possible score of 100 points and is administered twice within a 2-week period, may have inconsistent results or low test-retest reliability. The significant score differences between Time 1 and Time 2 for Basheer, Ben, Flodina, and Miguel suggest that the test may not be a reliable measure of mechanical aptitude.

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Answer:

Step-by-step explanation:

Answer:

10x +8y ≥ 160

Step-by-step explanation: