What is the measure of <1

All values of t for which the rocket's height is 92 feet are;

t= 0.55 or 10.89 seconds  

Given that model rocket is launched with an initial upward velocity of 164 ft/s.

The rocket's height h (in feet) after t seconds :

To Find:  

Find all values of t for which the rocket's height is 92 feet.

h=164t – 16t²

92 = 164t – 16t²

-164t + 16t² + 92 = 0

Solve with the quadratic formula:

t = [ -(-164) ± √((-164)² − 4(16)(92)) ] / 2(16)

t = (164± √27409) / 32

t = (164± √27409) / 32

t ≈ 0.55 or 10.89

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I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

Answer:

Fractions that are above 1/2 or 0.5

Step-by-step explanation:

Answer:

-5 is the answer

Hope it will be helpfull....

Answer:

no it is really easy question to answered so do it your self

Answer:

Answer would be B.

Step-by-step explanation:

there are two dors located at x= -4 and x=9

Answer:

Compound amount = $2,000e^(.0353 × 3)

= $2,223.42

Interest = $2,223.42 - $2,000 = $223.42

The exact value of the expression cos(arcsin(15/17)) is 1.

The inverse sine function, denoted as arcsin, gives the angle whose sine is a given value. Since the range of the sine function is -1 to 1, the range of the arcsin function is -90 degrees to 90 degrees.

In this case, the value of the expression is given by cos(arcsin(15/17)). To find the exact value of this expression, we can first use the definition of the inverse sine function to find the value of arcsin(15/17). Since the sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle, we can set up the following equation:

Since the sine function has a period of 180 degrees, we can add or subtract multiples of 180 degrees to the angle x to find the value of the expression for all possible angles. For example,

Using this information, we can find the values of the expression for all possible angles:

x = arcsin(15/17) => cos(arcsin(15/17)) = cos(x)

                                                           = √(1 - sin^2(x))

                                                           = √(1 - (15/17)^2)

                                                           = √(289/289)

                                                           = 1

x + 180 = arcsin(15/17) + 180 => cos(arcsin(15/17) + 180) = cos(x + 180)

                                                                                         = -cos(x)

                                                                                         = -1

x - 180 = arcsin(15/17) - 180 => cos(arcsin(15/17) - 180) = cos(x - 180)

                                                                                       = -cos(x)

                                                                                       = -1

Since the cosine function has a period of 360 degrees, the values of the expression for all possible angles can be expressed as:

cos(arcsin(15/17) + 360k) = 1 for all integers k

cos(arcsin(15/17) + 180 + 360k) = -1 for all integers k

Therefore, the exact value of the expression cos(arcsin(15/17)) is 1.

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Answer:

B)  divide a binomial by a trinomial

Step-by-step explanation:

We know that the polynomials are very nearest to the addition, subtraction and the multiplication part but the same cannot happen under the division part since the division of two polynomials could not become a polynomial it is not necessary  condition that it could become a polynomial

So if we divide the binomial by a trinomial therefore it would provides a rational expression and have a negative exponent and a negative exponent is not permitted under the polynomial

Therefore the option B is correct

Answer:

Step 4

Step-by-step explanation:

because 100/20=5

so 60/5=12

Virtue based ethics holds that character is more important than actions.

Virtue based ethics is the aspect of ethics that holds that the moral character of a person if of more paramount importance than the person's actions and its consequences.

Hence, the true statement about virtue based ethics from the options is that; "according to the principles of virtue-based ethics, character is more important than actions."

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Answer:

The cost of two folder is $ 1.94

Solution:

Given that 3 folders cost $ 2.91

We have to determine the cost of 2 folder

From given,

Cost of 3 folder = $ 2.91

To find the cost of 1 folder, divide 2.91 by 3

Thus cost of 1 folder is $ 0.97

We are asked to find cost of two folders.

Therefore, multiply cost of 1 folder by 2

Thus cost of two folder is $ 1.94

Answer:

Suppose that we have two line segments, AB and CD. We know that they have the same length.

I know that AB¯¯¯¯¯¯¯¯=CD¯¯¯¯¯¯¯¯ means AB is identical to CD (aka. They are the same lines), and also that AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ means that AB and CD have the same size, but what does AB=CD mean?

Step-by-step explanation:

Answer:

\(d = \dfrac{9t^{2} }{2} - \dfrac{2}{9} t + \dfrac{t^3}{3}\)

Step-by-step explanation:

Given the equation of velocity w.r.to time 't':

\(v=9t-\dfrac{2}{9}+t^2 ...... (1)\)

Formula for Displacement:

\(Displacement = \text{velocity} \times \text{time}\)

So, if we find integral of velocity w.r.to time, we will get displacement.

\(\Rightarrow \text{Displacement}=\int {v} \, dt\)

\(\Rightarrow \int {v} \, dt = \int ({9t-\dfrac{2}{9}+t^2}) \, dt \\\Rightarrow \int{9t} \, dt - \int{\dfrac{2}{9}} \, dt + \int{t^2} \, dt\\\Rightarrow s=\dfrac{9t^{2} }{2} - \dfrac{2}{9} t + \dfrac{t^3}{3} + C ....... (1)\)

Here, C is constant (because it is indefinite integral)

Formula for integration used:

\(1.\ \int({A+B}) \, dx = \int {A} \, dx + \int{B} \, dx \\2.\ \int({A-B}) \, dx = \int {A} \, dx - \int{B} \, dx \\3.\ \int{x^{n} } \, dx = \dfrac{x^{n+1}}{n+1}\\4.\ \int{C } \, dx = Cx\ \{\text{C is a constant}\}\)

Now, it is given that s = 0, when t = 0.

Putting the values in equation (1):

\(0=\dfrac{9\times 0^{2} }{2} - \dfrac{2}{9}\times 0 + \dfrac{0^3}{3} + C\\\Rightarrow C = 0\)

So, the equation for displacement becomes:

\(s=\dfrac{9t^{2} }{2} - \dfrac{2}{9} t + \dfrac{t^3}{3}\)

\(\bold\purple{Hopeithelps}\)

\(\bold{Study}\)\(\bold{Well}\)~

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer: 2 hours

Step-by-step explanation:

if you split it by 2 people each it would take two hours and 6 divided by 3 = 2

The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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Answer:

29/10 or 2 9/10

4 4/5 - 1 9/10

make them into improper fractions

4 4/5 = 24/5

1 9/10 = 19/10

24/5 - 19/10 we need to get common denominators

24/5 × 2 = 48/10

48/10-19/10 = 29/10 = 2 9/10

Answer:

$ 30,000

Step-by-step explanation:

0.15(50,000 - x) - 0.1x = 2,500

7,500 - 0.15x - 0.1x = 2,500

7,500 - 2,500 = 0.15x + 0.1x

5,000 = 0.25x

5,000/0.25 = x

x =20,000

50,000 - 20,000 = 30,000

0.15 * 30,000 = $4,500

0.1 * 20,000 = $2,000

$4,500 - $2,000 = $2,500

Answer:

Average: 26.223529411764706 (Please round to the place value necessary since it does not say in the question.)

Step-by-step explanation:

We first find the number of items sold: 170

Then we find the total cost: 4458

We then divide 4458 by 170

We end up with the answer 26.223529411764706. (Please round to the place value necessary since it does not say in the question.)

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

3840

Step-by-step explanation:

Using the fundamental counting principle

The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages.

There are 5 independent events happening (5 prixe dinners)

(1) soup or salad (not both)

We have five kinds of soup, three kinds of salad

soup or salad (not both), = 5 + 3

= 8

(2) appetizer = 4

(3) entrees = 6

(4) dessert = 5

(5) Beverage = 4

Hence,

8 × 4 × 6 × 5 × 4

= 3840

The number of different prix fixe dinners are possible is 3840

Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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