Suppose a diver jumps from a ledge that is 115 feet above the ocean and the initial upward velocity is 8 feet per second. The vertical motion of the diver can be modeled by the function h = −t^2 + 8t + 115. How long will it take until the diver enters the water? How do you know?

given the expression

since

then

ten the correct answer is

Option C

82 meters

Explanation

Step 1

Draw:

as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion

so

therefore, the heigth of the tower is

82 meters

Step 1: We have two triangles with the following information:

• Upper Triangle has two known angles: 29 and 52 degrees

• Lower Triangle has one known angle: 33 degrees and two unknown: x and the third angle

Step 2: Let's find the third angle of the upper triangle, as folllows:

Third angle = 180 - 29 - 52

Third angle = 99

Step 3: Now we can see that the angle we just found on Step 2 is a congruent angle with the third angle from the lower triangle, which means they are equal.

Therefore, we know two angles of the lower triangle:

99 and 33

With these measurements, we can calculate x, as follows:

x = 180 - 99 - 33

x = 180 - 132

x = You can calculate the difference now

EXPLANATION

Given the exponential function:

45(1.085)^t

We have that 45=a is the initial value and 1.085 is the growth rate,

1.085 - 1 = 0.085* 100 = 8.5 % (This is the growth rate)

Let's compute the function with two values of t, as for instance, t=0 and t=1:

Now, the function in the form y = ae^kt will be as follows:

Substituting t by 1:

Dividing both sides by 45:

Applying ln to both sides:

Computing the argument:

The expression will be as follows:

As this is a growing function, the rates are positive.

The annual growth rate is 8.5% and It's was calculated above.

Now, we need to compute the continuous rate because It's given by the value of k:

k = 0.0816 --> Multiplying by 100 --> 0.0816 * 100 = 8.16%

The continuous growth rate is 8.16%

Factorial five. Factorial 16-5. And the response to this question is 4368. There are therefore 4000 368 options for these pizzas with five toppings.

The sum of all positive integers less than or equal to n, indicated by the symbol n!, is the factorial of a non-negative integer n. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1. The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1)

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Answer:

d

Step-by-step explanation:

Since the number of years must be non-negative, we can eliminate all the options except for d.

y = 7x+6

y = x + 20

Substituting the value of y of the second equation into the first equation, we get:

x + 20 = 7x + 6

20 - 6 = 7x - x

14 = 6x

14/6 = x

7/3 = x

Replacing this value into the first equation, we get:

The solution as an ordered pair is (7/3, 67/3)

The area of the flagpole is:

This represents a perfect square, because it can be represented as below:

Therefore we can use the notable product, square of the difference to factor the expression:

Since the area of the flagpole is the product between it's length and width, then we know that the length and width are equal and are equivalent to:

Answer:

No

Step-by-step explanation:

5:9 and 3:12 do not divide with the same number

For example:

3:6 and 9:18 would be equivalent as dividing 9:18 by 3 would give 3:6

Given the equation

you should have in mind that the expression x^2-9 and x^3-8 are "numbers" and that the product of two numbers is zero if and only if one of the numbers is zero. Then, by using this, you get the following auxiliary equations

which is equivalent to

so x=3 o x=-3.

Finally, for the other case

So

so the three possible solutions for the equation are x=3, x=-3 and x=2

If  the cost for using 35 HCF IS 61.83. . the cost for using 19 HCF of water is :$68.31.

Straight line: y=mx+b, m=slope, b=y-intercept

Let y=cost of using 19 HCF water

Let x =amount of water used

m=∆y/∆x =(61.83 - 32.13) / (35-19)

m=∆y/∆x =29.7 /16

m=∆y/∆x = 1.85625

m=∆y/∆x = 1.86  ($/HCF) (approximately)

equation: y=1.86x+b

Solving for b using point (19, 32.13)

32.13 =1.86×19+b

32.13=35.34+b

b=35.34 -32.13

b=3.21

equation:

f(x)=1.86x+3.21

f(25)=1.86×35+ 3.21

= 68.31

Cost of using 35 HCF water= $68.31

Therefore the cost price is $68.31.

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The exact value of indicated trigonometric function, sin θ is -0.92

The sine relation is the ratio of the height to the hypotenuse. Meanwhile, the cosine relation is the ratio of the base to the hypotenuse.

The relation of sine and cosine is given as follows:

[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}[/tex]

It is given that cos θ = (2/5)

So, the sine value can be obtained from the given value.

[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}\\=\pm\sqrt{1-(2/5)^2}\\=\pm\sqrt{21}/5\\ =-0.92[/tex]

So, the sine value for the given cosine value is - [tex]\sqrt{21}/5[/tex] or -0.92.

Note that we omitted the positive value because it is given that the tangent value is negative, so the angle lies in the fourth quadrant, where the sine value is also negative.

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Okay, here we have this:

Considering the provided amount in miles per hour, we are going to convert it to kilometers per hour, so we obtain the following:

Finally we obtain that 55 miles per hour are equivalent to 88 kilometers per hour.

Answer:

The maximum value is the same for both functions

Step-by-step explanation:

f(x) maximum is (0,5)

g(x) maximum is (2,5)

Answer:

The maximum value is the same for both functions.

Please give me brainlist!!!

Answer:

B

Step-by-step explanation:

Answer: B. Symbolic - the "Queen" represents suppression and deceit.

Prism surface is formed by

2 rectangles x and 2 rectangles y ,2 rectangles z

then

Area of rectangles for x= 2x13x6 = 156 m2

. For y = 2x5x6= 60 m2

. For z = 2x13x 5 = 130 m2

Then now add all these results

Prism area = 156 + 60 + 130 = 346

Then answer is

OPTION D) 346 m2

In the picture there is graph. The graph has a function is y=secx. The option c is correct.

Given that,

In the picture there is graph.

We have to find the graph has a function.

The graph is of y=secx.

Secant will not present at

x = - 5∏/2 , - 3∏/2 , -∏/2 , ∏/2, 3∏/2 , 5∏/2

At certain places, the graph will also include asymptotes. The graph of the secant on the range of - 5∏/2 is shown below.  - 5 ∏/2

The graph also always has a value greater than 1 and less than -1. It shouldn't come as a huge surprise. Keep in mind that -1≤ cos (x)≤ 1. One will be more than one when divided by a number that is less than one. Additionally, 1 / ±1 = ±1, therefore we obtain the following secant ranges.

We can write as sec(x)≥1 and sec(x)≤-1

Therefore, the graph has a function is y=secx. The option c is correct.

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The smallest whole numbers that makes the statement true are:

(a) 41 - 9 ≡ 2 (mod 5)

(b) 17 + 8 ≡ 4 (mod 7)

Let a, b and m be integers. Then a is said to be congruent to b modulo m if m divided a-b. That is,

a ≡ b(mod m) if and only if m divided a-b.

Also here, if b is the smallest integer satisfying this relation, then b is the remainder when a is divided by m.

(a) So for  41 - 9 ≡   (mod 5)

⇒ 32 ≡    (mod 5)

The smallest whole number satisfying this congruence is the remainder when 32 is divided by 5 which is 2.

That is,  41 - 9 ≡ 2 (mod 5)

(b) Similarly for 17 + 8 ≡   (mod 7)

⇒ 25 ≡   (mod 7)

The smallest whole number which makes this statement true is the remainder when 25 is divided by 7, which is 4.

Hence, 17 + 8 ≡ 4 (mod 7)

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If the Hypothesis p is false and conclusion q is false then the disjunction ∼q⟶p is false.

In classic propositional logic, a conjunction is a binary operator, that is, used to connect two propositions. A conjunction between two propositions is always true if and only if each of the two propositions are also true, otherwise the compound proposition is false.

Logic Disjunction; consider p and q are propositions.

The dis-junction of p and q, is denoted by p ∨ q, is the proposition called "p or q".

The rule for the 'or' operation would be; If any of the propositions are true, then the result is true.

Thus, If the Hypothesis p is false and conclusion q is false then the disjunction ∼q⟶p is false.

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2(l+b)=338 2(l+77)=338

154×l=338 l=338÷154=2ans

Answer:

The length is 92 yards.

Step-by-step explanation:

Just use the rectangle perimeter formula and substitute the given values.

P=2l+2w    Rectangle formula

We know the perimeter and the width already.

So, 338=2L+2(77)

Now solve:

338=2L+154

338-154=2L

184=2L

184/2=L

92=L  Answer

Given that the weight of goat increased by 12 pounds to be 38 pounds.

It means that the weight became 38 pounds after attaining an extra 12 pounds to its initial weight.

Suppose that 'x' is the initial weight of the goat, then adding 12 to is will become 8,

Therefore, the third option is the correct choice.

One needs to sell $6750 worth of goods to make the straight commission be at least good to the secondary offer

Straight offer = 6% commission on the sales

Second offer = $270 + 2% of the sales

For the straight offer to be competitive with the second offer it should be able to cover the fixed income of $270

Let x be the sales made in the week

Formulating the equation we get the following:

6% of x = 270 + 2% of x

6/100x = 270 + 2/100x

4/100x = 270

x = 6750

So, for sales up to $6750, the second job offer is good, while for sales more than $6750 the first job offer is good

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Answer:

D. Negative

Step-by-step explanation:

The slope is negative because the line goes down from left to right. In other words, as x increases, y decreases.

A slope would be positive when the line goes up from left to right. In other words, as x increases, y increases.

A slope would be zero if the line is horizontal, so as x increases, y remains constant.

A slope would be undefined if the line is vertical. It is undefined because x remains constant while y changes. Lines are functions, which mean for every input there is exactly 1 output. If there are multiple y values for 1 x value, then this is not a function and therefore has an undefined slope.

The correct option A. (d- e)², is the expression is missing from step 7.

For the given question.

The missing value of the 7th term is -

(√1 + d²)² + (√e² + 1)²  = (d- e)²

Such that the 8th terms becomes after squaring the both sides are;

(1 + d²) + (e² + 1)  = d² + e² - 2de.

Thus, the missing term in the step 7 is (d- e)².

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Answer:

212°

Step-by-step explanation:

Keep subtracting 360 from 1652 until you get a number under 360

First, let's solve for x in the inequality to find an interval, the options that are not included in the interval are not part of the solution set, we can do it by following these steps:

1. 3x-18> 12 , add 18 on both sides:

3x - 18 + 18 > 12 + 18

3x > 30

2. Divide both sides by 3:

3x/3 > 30/3

x > 10

So, to be a part of the solution, x must be greater than 10, then the interval that represents the solution is (10, ∞). From the given options, the only one that is not included in this interval is 8, because it is less than 10, then the answer is 8.

Given

Find

Plot the graph

Explanation

To plot the graph we need points ,

let

The rate of return of the 12 shares purchased by A is 72.72%.

Here, we are given that A purchases 12 shares at $22 per share.

So the cost price of 12 shares will be = 12 × 22

= 264

A sold these shares at $465.

The commission on sale = $9.

Thus, the total cost of the shares will be = 264 + 9

= $273

Hence, the total profit of A will be-

465 - 273

= 192

The rate of return is calculated as-

Rate of return = profit/cost price × 100

Thus, here-

Rate of return = 192/264 × 100

= 0.7272 × 100

= 72.72%

Thus, the rate of return on these 12 shares purchased by A is 72.72%.

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