A fireboat salutes by shooting water into the air. The water height is described by
the equation, h = -16t² + 76t+ 20.
a. How high does the middle stream of water reach?
b. How long does it take for the drop to hit the river?

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Answer:

The area of the rectangle is 72 square feet

Step-by-step explanation:

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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Answer:

a. f(2) :

\(f(x) = 2x - 5 \\ f(2) = 2(2) - 5 \\ f(2) = 4 - 5 \\ f(2) = - 1\)

b. f(0) :

\(f(x) = 2x - 5 \\ f(0) = 2(0) - 5 \\ f(0) = - 5\)

c. f(-3) :

\(f(x) = 2x - 5 \\ f( - 3) = 2( - 3) - 5 \\ = - 6 - 5 \\ = - 11\)

Answer: Lenayah's presentation was 12 minutes long.

Step-by-step explanation:

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

---------------------------------

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Answer:

18% off

Step-by-step explanation:

i just took the test

In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.

Proportion shows the relative number of objects or people in the whole.

Proportions are ratios equated to each other.

They are expressed as fractional values, in decimals, percentages, and fractions.

The percentage of Boomers who want to shop in-store = 84%

The sample size of the Boomer Generation = 75

The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)

Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.

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Answer:

9

Step-by-step explanation:

Factor for 18 are:

1,2,3,6,9,18

Factors for 27 are:

1,3,9,27

Hope I helped <3

Answer:

A, B, E

Step-by-step explanation:

Edge21

Answer:

what your question tell me I will give you answer and also write down your name and question

The appropriate hypothesis test is a two-sample t-test for independent samples.

The appropriate hypothesis test in this scenario is a two-sample t-test for independent samples. Since the population standard deviations are known, we can use the Z-test instead.

The test statistic can be calculated using the formula:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

x1 and x2 are the sample means for Manufacturer A and Manufacturer B, respectively.

s1 and s2 are the population standard deviations for Manufacturer A and Manufacturer B, respectively.

n1 and n2 are the sample sizes for Manufacturer A and Manufacturer B, respectively.

Plugging in the given values:

x1 = 179, x2 = 178, s1 = 1, s2 = 5, n1 = n2 = 108

t = (179 - 178) / sqrt((1^2 / 108) + (5^2 / 108))

t = 1 / sqrt(0.00926 + 0.0463)

t ≈ 1 / sqrt(0.05556)

t ≈ 1 / 0.2357

t ≈ 4.241

To determine whether there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different, we compare the calculated t-value to the critical value from the t-distribution at the desired significance level (0.05).

The decision depends on the degrees of freedom for the test, which is calculated as (n1 + n2 - 2) = (108 + 108 - 2) = 214.

Using a t-table or statistical software, we find that the critical value for a two-tailed test with a significance level of 0.05 and 214 degrees of freedom is approximately ±1.972.

Since the calculated t-value of 4.241 exceeds the critical value of 1.972, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different at the 0.05 significance level.

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Answer:

Im trying to answer that one too but let me tel you the answer that i put

Step-by-step explanation:

melvin has to put it on opposite

Answer:

absolute value basically represents the distance a number is from zero on the number line. If you can imagine, nobody would say "My car went negative thirty miles today," so you wouldn't use negative "distances" on the number line either. That's why absolute values are always positive.

Step-by-step explanation:

a) The phasor form of E-field = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz) is 2√5 L(-63.43).

Polarization type is linearly polarised.

b) The phasor form of E-field = ?

E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz) is E(z,t) =2√5 L(-143.43). polarization type is elliptical.

We have given that

E⃗(z,t) =2xˆcos(wt - kz) - 4 yˆcos(wt - kz)

|r⃗ | = √((2cos(wt - kz))² + (- 4cos(wt - kz))²)

= √(4cos²(wt - kz) + 16cos²(wt - kz))

= √(20cos²(wt - kz))

= 2√5 cos(wt - kz)

φ = 4cos(wt - kz)/(2cos(wt - kz))

= tan⁻¹ 1(-2) = -63.43°

So, E(z,t) = 2√5 L(-63.43)

b) E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz)

= xˆ 2cos(wt + kz) - yˆ 4cos(wt + kz -π/2)

|r| = √((2cos(wt + kz))² + (- 4sin(wt -+kz))²)

= √20

phi = tan⁻¹(- 4cos(wt - kz)/(2cos(wt - kz)) - π/2

= tan⁻¹( -2) + π/2 = - 143.43

so, E(z,t) =2√5 L(-143.43)

E(z,t) = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz)

if wt = 0°

E(z,t) = xˆ 2cos(0 - kz) - yˆ 4cos(0- kz)

= 2xˆ - 4yˆ

wt = 30° , E(z,t) = xˆ 2cos( - kz) - yˆ 4cos(0- kz)

E(z,t) = √3/2(2) xˆ - √3/2(4) yˆ

= √3xˆ - 2√3yˆ

for wt = 45°

E(z,t) = √2 xˆ - 2√2 yˆ

for wt = 90° =>E(z,t) = 0

for wt = 60° , E(z,t) = xˆ - 2 yˆ as seen in above graph that is linear polarised

For part (b) ,

E(z,t) = 2 xˆcos(wt - kz) - 4yˆ sin(wt + kz)

From graph elliptical polarised,

for wt = 0 , E(0,t) = 2 xˆ

for wt = 90° , E(0,t) = -4yˆ

for wt =180° , E(0,t) = -2 xˆ

for wt = 270° , E(0,t) = -4yˆ

Hence, we get the answer of both parts.

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Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

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

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

\(x = 2\) corresponds to a horizontal line tangent to \(f(x) = -3\cdot x^{2}+12\cdot x -11\).

Step-by-step explanation:

Let \(f(x) = -3\cdot x^{2}+12\cdot x -11\), its first derivative represents a formula to determine the slope of lines tangent to a given point of the curve and slopes of horizontal tangent line corresponds to those values of \(x\) such that \(f'(x) = 0\).

We obtain the first derivative and equalize it to zero:

\(-6\cdot x +12 = 0\)

And solve it for \(x\):

\(x = 2\)

\(x = 2\) corresponds to a horizontal line tangent to \(f(x) = -3\cdot x^{2}+12\cdot x -11\).

Answer:

407,102 meters

Step-by-step explanation:

Convert the kilometers to meters.

394 km x 1000 = 394000 meters

13 km x 1000 = 13000 meters

Add the results together.

407,000

Now add the remaining values to 407,000

407,000 + 34 = 407,034

407,034 + 68 = 407,102

The answer is 407,102 meters.

Hope I helped :)

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The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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Step-by-step explanation:

\(56 + 51 + y = 180 \\ y = 180 - 107 \\ y = 73\)

\(y + x + 72 = 180 \\ 73 + 72 + x = 180 \\ x = 180 - 145 \\ x = 35\)

Hope it helps

A straight angle is an angle equal to 180 degrees

Solve for y

y + 51° + 56° = 180°

y = 180° - 56° - 51°

y = 73°

Total interior angle of a triangle sum ups to 180°

Solve for x

y + x + 72° = 180°

73° + x+ 72° = 180°

x = 180° - 72° - 73°

x = 35°

Okay, here we have this:

Considering the provided circle and information, we are going to calculate the requested area of the shaded sector, so we obtain the following:

Then we will substitute in the following formula:

Sector Area = r² × θ × π / 360

Replacinig:

Sector Area = (4 units)² × 80° × π / 360

Sector Area = 16 units² × 80° × π / 360

Sector Area = 11.17 units²

Finally we obtain that the sector area is approximately 11.17 units^2.

Answer:

his salary after three months would be 1300

Step-by-step explanation:

10 percent of 1000 is a hundred and multiply that by 3, it would equal 300 and add that to the 1000.

Answer:

Step-by-step explanation:

This is a combination problem. Combination has to do with selection

Total people competing in the event = 21people

Prizes to be won = 3(Gold, silver and bronze)

Using the formula

nCr = n!/(n-r)!r!

21C3 = 21!/(21-3)!3!

21C3 = 21!/18!3!

21C3 = 21×20×19×18!/18!3!

21C3 = 21×20×19/3!

21C3 = 21×20×19/6

21C3 = 1330

Hence 1330 possible outcome are there for the event.

Answer:c, the answer is c

Step-by-step explanation:

Answer:

2.25km

Step-by-step explanation:

a scale of 1 : 25000 means:

1 cm on map ------> equals 25000 cm on ground  

hence,

9 cm on map ------> equals 25000 x 9 cm = 225,000 cm = 2.25km on ground

Answer:

x =-1 y=4

Step-by-step explanation:

-1 ×4 is -4. 2×4 is 8

8 +-4 =4

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

the answer is 36

Step-by-step explanation: