Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:
[tex]a_1 = 101, q = 0.81[/tex]
Then, the height of the nth bounce is given by:
[tex]a_n = 101(0.81)^{n-1}[/tex]
And the height of the 5th bounce is:
[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]
The maximum height reached after the 5th bounce is of 43.48 feet.
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pls help! thank you!
Using the zero product property, we can set each factor equal to zero.
First Factor [tex]x^{4}+5x^{2}-36[/tex]
[tex]x^{4}+5x^{2}-36=0\\(x^{2}+9)(x^{2}-4)=0\\x^{2}+9=0, x^{2}-4=0\\x=\pm 3i, x=\pm 2[/tex]
Second Factor [tex]2x^{2}+9x+5[/tex]
Using the quadratic formula, we get [tex]x=\frac{-9 \pm \sqrt{41}}{4}[/tex].
A) all values at which h has a local maximum
B ) all local maximum values of h
For the given function h(x), we have:
a) at x = -2 and x = 2.
b) y = 0 and y = 3.
How to identify the maximums of function h(x)?
First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.
By looking at the horizontal axis, we can see that the maximums are at:
x = -2 and at x = 2.
Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.
The first maximum value is at y = 0 (the one for x = -2)The second maximum is at y = 3 (the one for x = 2).If you want to learn more about maximums:
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4, 5, 5, 6, 7, 8, 8,9
What is the range?
Helppp me pleaseeeee
I’LL GIVE BRAINLIST IF YOU ANSWER CORRECT:
Answer:
Step-by-step explanation:
Solution
The first step is to simplify the top of the fraction. Subtract 5.6 - 2.7
The numerator (top) and denominator(bottom) are decimal fractions. They are 2.9 for the top and 2.9 for the bottom.
The whole expression reduces down to 1, which is an integer.
Note
You have choices. If you want exact answers you will have to list those choices.
Answer: 1
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Solve the compound inequality. Write the solutions in interval notation.
x + 7 ≥ 4 and 11x - 8 ≥ 3
Answer: [1, infinity)
===========================================================
Explanation:
Let's isolate x in the first inequality mentioned.
x + 7 ≥ 4
x + 7-7 ≥ 4-7
x ≥ -3
I subtracted 7 from both sides to undo the +7.
Now isolate x in the second inequality. We first add 8 to both sides, then divide both sides by 11.
11x - 8 ≥ 3
11x - 8+8 ≥ 3+8
11x ≥ 11
11x/11 ≥ 11/11
x ≥ 1
------------------
The two solutions we found were
x ≥ -3 and x ≥ 1
Next, draw out a number line with closed circles at -3 and 1. Shade to the right of each closed circle endpoint as you see below.
Notice that the two inequalities overlap for x ≥ 1
In other words, if a number is -3 or larger AND 1 or larger, then the number is 1 or larger.
The two solutions intersect to form x ≥ 1
The inequality x ≥ 1 is the same as 1 ≤ x which is the same as 1 ≤ x < infinity
Then that turns into the interval notation of [1, infinity)
The square bracket includes the endpoint 1.
If needed, use the infinity symbol in place of the word "infinity".
Answer:
[1, ∞)
Step-by-step explanation:
To solve a compound inequality, first separate it into two inequalities and solve them separately:
Solution of Inequality 1:
x + 7 ≥ 4
⇒ x ≥ 4 - 7
⇒ x ≥ -3
Solution of Inequality 2:
11x - 8 ≥ 3
⇒ 11x ≥ 3 + 8
⇒ 11x ≥ 11
⇒ x ≥ 1
As both graphs overlap for x ≥ 1, this is the solution.
Therefore, in interval notation: [1, ∞)
If we changed the 3 to a 0 in the equation, what would happen to the graph?
A function assigns the values. The function will move down by 3 units.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.
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Julia is in charge of buying clothing in bulk for a sporting goods store. The table shows the unit prices of the items she intends to buy.
Unit Prices of Clothing Items for a Sporting Goods Store
Item
Unit Price
T-shirts
$7.50
Shorts
$9.00
Windbreakers
$12.25
If she will buy 35 T-shirts, 45 pairs of shorts, and 25 windbreakers, what will be her total cost?
$958.75
$973.75
$1,021.25
$1,038.75
The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers is $973.75.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Cost of 1 T-shirt = $7.50
Cost of 35 T-shirts = 7.50 x 35
= 262.5
Cost of 1 Shorts = $9.00
Cost of 45 T-shirt = 9.00 x 45
= 405
Cost of 1 windbreakers = $12.25
Cost of 25 windbreakers = 12.25 x 306.25
So, The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers
= 262.5+405+306.25
= $973.75
Hence Her total cost is $973.75.
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N(-2,-2) after a 90 degree counterclockwise rotation
Answer: (2,-2)
Step-by-step explanation:
Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)
Find the indefinite integral using the substitution provided.
[tex]\int\limits({\frac{14e^2^x}{e^2^x+10}) } \, dx[/tex]
[tex]u=e^2^x+10[/tex]
Answer: [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]
This is the same as writing 7*Ln( e^(2x) + 10) + C
=======================================================
Explanation:
Start with the equation [tex]u = e^{2x}+10[/tex]
Apply the derivative and multiply both sides by 7 like so
[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]
The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)
This way we can do the following substitutions:
[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]
Integrating leads to
[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]
Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.
To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]
How can you make a sum of 12
There are several ways
Let's check all
1+112+103+94+85+76+60+12Solve 10x-4y=15 for y.
Answer:
y = 15/-4 + 2.5x
Step-by-step explanation:
10x - 4y = 15
-4y = 15 - 10x
y = 15/-4 + 2.5x
Apply the indicated operations to the matrix; then choose the correct answer.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is B.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
When the indicated operation 4R₁ → R₁ is applied then the matrix will be,
[tex]\left[\begin{array}{ccc}1&2&0\\-2&-1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}4&8&0\\-2&-1&3\end{array}\right][/tex]
Hence, the correct option is B.
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Math need help please
DEF, DF = 16 and m angle F = 45
Answer: [tex]8\sqrt{2}[/tex]
================================================
Work Shown:
x = length of each leg
Use the pythagorean theorem to get...
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = 16^2\\\\2x^2 = 256\\\\x^2 = 256/2\\\\x^2 = 128\\\\x = \sqrt{128}\\\\x = \sqrt{64*2}\\\\x = \sqrt{64}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
Or as an alternative path, you can divide the hypotenuse by [tex]\sqrt{2}[/tex] and then rationalize the denominator.
Both of these methods apply to 45-45-90 triangles only.
Answer:
[tex]8\sqrt{2}[/tex]
Step-by-step explanation:
We can sum the angles in a triangle to 180°:
m<D + m<E + m<F = 180°
m<D + 90° + 45° = 180°
m<D = 45°
Therefore, the triangle is an isosceles right triangle, since the base angles, <F and <D are the same measure. Because the triangle is isosceles, the legs are congruent, meaning that
DE = EF
We can use the Pythagorean Theorem([tex]a^{2} + b^{2} = c^{2}[/tex]) and plug in 16 as c, and DE and EF as a and b:
[tex]DE^{2} + EF^{2} = 16^{2}[/tex]
Since DE is the same as EF, we can substitute it in:
[tex]DE^{2} + DE^{2} = 256\\2DE^{2} = 256\\DE^{2} = 128\\DE = \sqrt{128}[/tex]
The square root of 128 is the same as [tex]8\sqrt{2}[/tex] since 128 can be factored into 64 x 2. So [tex]8\sqrt{2}[/tex] is the answer.
If you are looking for an easier way to do this, once you are able to recognize DEF is an isosceles triangle, you can say [tex]DE \times \sqrt{2} = 16[/tex] as this applies to all isosceles right triangles. This simplifies to:
[tex]DE = \frac{16}{\sqrt{2}} \\DE = \frac{16}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2} } \\DE = \frac{16\sqrt{2} }{2} \\DE = 8\sqrt{2}[/tex]
A triangle is placed in a semi circle with a radius of 9 mm find the area of the shaded region of the semi circle (not including the triangle)
The area of the shaded region will be 46.17 ft.²The number of unit squares that cover the surface of a closed-form is the figure's area.
What is the area?
The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
Given data;
Semicircle radius , r = 9 ft.
The height of the triangle, h=r=9 ft
The triangle is located where it is inscribed in the semicircle. The diameter of the semicircle is given as b, the base length of the triangle.
The diameter of the semicircle = 2 × The radius of the semicircle
D=2r
D= 2 × 9 ft
D= 18 ft.
Triangle base length,b = D= 18 ft.
The area of the triangle is found as;
[tex]\rm A= \frac{1}{2}bh \\\\ A = \frac{1}{2} \times 18 ft. \times 9 ft. \\\\ A = 81 \ ft^2[/tex]
[tex]A_{semi}={\rm \frac{A_{circle}}{2}} \\\\ A_{semi}= \frac{\pi \ r^2}{2}\\\\\ A_{semi}= \frac{3.14 \times 9^2}{2} \\\\ A_{semi} = 127.17 ft^2[/tex]
The area of the shaded region is;
a= 127.17 ft.² - 81 ft.²
a = 46.17 ft.²
Hence,the area of the shaded region will be 46.17 ft.²
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Which of the following statements are true?
The prime factorization of 21 is 3 x 7.
The LCM of 14 and 21 is 42.
The prime factorization of 14 is 2 x 7.
14 is a composite number.
21 is a prime number.
The GCF of 14 and 21 is 14.
Answer:
The prime factorization of 14 is 2 x 7.
Step-by-step explanation:
The prime factorization of 14 is 2 x 7.
Answer:
14 is a composite number
Step-by-step explanation:
HELP!!! PLEASE HURRY!!!!
Answer:
B, I solved then used interval notion to convert it.
Answer:
the answer is b
Answer:
the answer is b
Which of the following points is shown in the graph below?
Answer:
Step-by-step explanation:
Comment
Only the x is minus. You know this because if you rotate the x axis 90 degrees clockwise, the plus axis will be on your right and the minus part of the axis on your left.The other 2 (y and z) are positive.All answers give - 4 in their choices. You are not helped much by -4y is on your left right now. That is the plus direction so y = 5z is 6 units up, so it is positive.Answer (-4,5,6)
B
Sally makes $3,000 each month. What is the most she can spend on housing?
Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent
Numbers and percentageGiven Data
Monthly Salary = $3000Percentage spent on rent = 30%Let us find 30% of $3000
= 30/100* $3000
= 0.3*$3000
= $900
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Solve f(-4) for f(x) = 7x - 4x
f(-4)= [?]
Enter
ternational Academy of Science. All Rights Reserved.
Answer:
-12
Step-by-step explanation:
What you have to do is plug -4 into the function as a puzzle. So, replace all x with -4.
f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12
f (-4) = 7x ( 1-4 ) - 4 (-4)
= -28 + 16
= -12
What is a equation example?
An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.
Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
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Adrian's annual salary is $111,000. He is not eligible for a Roth IRA because he makes
too much money. His company offers a matching program that is 1:1 up to 3% of annual
salary. (do not include commas or dollar signs in your answers)
How much should he contribute to Roth IRAS?
If he is not eligible for Roth IRAs, then he cannot contribute to Roth IRAs. However, he can contribute $3,330 monthly under his company's Matching Program.
What is a Roth IRA?The Individual Retirement Account to which employees in the United States can contribute after-tax earnings is called the Roth IRA.
Under its governing principles, certain individuals whose annual income exceeds stipulated amounts are INELIGIBLE to contribute.
How do we arrive at $3,330?Recall that the question indicates that his company offers a matching program with a ratio 1:1 up to 3% of his annual salary.
Since his annual salary is $111, 000,
3% x 111,000 = 3,330.
This means that annually, the total matching contribution due to Adrian would be:
3,330 x 2 = 6, 660.
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Rewrite the expression as a product of four linear factors:
(x² – 3x)² – 14(x² – 3x) + 40
-
Answer:
Submit Answer
[tex]~~(x^2 -3x)^2 -14(x^2 -3x) +40\\\\=u^2-14u+40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Let}~ u = x^2 -3x]\\\\=u^2 - 10u-4u +40\\\\=u(u-10)-4(u-10)\\\\=(u-4)(u-10)\\\\=(x^2 -3x -4)(x^2 -3x -10)~~~~~~~~~~~~~;[\text{Substitute back}~ u = x^2 -3x]\\\\=(x^2 -4x+x-4)(x^2 -5x+2x-10)\\\\=\textbf{[}x(x-4) +(x-4) \textbf{]} \textbf{[}x(x-5) +2(x-5) \textbf{]} \\\\=(x+1)(x-4)(x+2)(x-5)[/tex]
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The table shows the value of a townhome for 3 years after it is purchased. The values
form a geometric sequence. If the pattern continues, how much will the townhome be
worth after 7 years?
The amount that the home will be worth after 7 years is $457763.67
The geometric sequence is sometimes called the exponential sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:
Tn = ar^n-1
where
a is the first term = 120,000
r is the common ratio = 150000/120000 = 1.25
Required
7th term
Substitute
T7 = 120,000(1.25)^7-1
T7 = 120,000(1.25)^6
T7 = 120,000(3.8147)
T7 = $457763.67
Hence the amount that the home will be worth after 7 years is $457763.67
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Answer:
(c) $457,763.67
Step-by-step explanation:
hope this helps:)
Evaluate the limit. lim x → 0 4ex/2 − 4 − 2x − 1 2 x2 x3
The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
Limit of the function
The limit of the given expression is calculated as follows;
lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³]
= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)
= (4)/2 - 4
= 2 - 4
= - 2
Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
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If x = 2y = 3
find xy-y+ x × x
Answer:
here ....x = 2 and y = 3
[tex] = xy - y + x \times x[/tex]
[tex] = 2 \times 3 - 3 + 2 + 2 \times 2[/tex]
[tex] = 6 - 3 + 2 + 4[/tex]
[tex] = 12 - 3[/tex]
[tex] = 9[/tex]
A music club has $187 to buy ice cream for a party. Each carton of ice cream costs $4. If the club buys as many cartons as possible, how much money will the club have left?
Answer:
They would have $3 dollars left over.
Step-by-step explanation:
If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.
Two large trees, 5.5m and 6.8m tall, stand 12m apart. A bird flies directly from the top of one tree to the top of the other. How far has the bird flown?
Evaluate 15÷3·(-2) + |-10|
[tex]15 \div 3( - 2) + | - 10| \\ 5( - 2) + 10 \\ - 10 + 10 \\ 0[/tex]
Hope it helps
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Select the expressions whose value is 4.
0(-2)²
02(-2)
0-4÷2
0-41
Answer: The correct answer is A, [tex](-2)^{2}[/tex].
Step-by-step explanation:
A negative multiplied with another negative is a positive. Squaring is multiplying an integer by itself. Thus, it would look like -2×-2, which is equal to 4. I hope this helps!! :)