Gloria, an experienced bungee jumper, leaps from a tall bridge and falls toward the river below. The bridge is 200 feet above the water and Gloria's bungee cord is 130 feet long unstretched. When will Gloria's cord begin to stretch? Round your answer to two decimal places.
Answers
We are given that Gloria jumps from a bridge using a bungee cord. The quadratic expression that models an object falling freely is the following:
[tex]h=h_0+v_0t-\frac{1}{2}gt^2[/tex]Where:
[tex]\begin{gathered} h_0=\text{initial height} \\ v_0=\text{initial velocity} \\ g=\text{acceleration of gravity} \\ t\text{ = time} \end{gathered}[/tex]A representation of the problem is the following:
If we assume that the initial velocity is zero, we get the following values:
[tex]\begin{gathered} h_0=200 \\ h=200-130 \\ g=32 \\ \end{gathered}[/tex]The height is equivalent to the total height of the bridge minus the longitude of the cord. The value for "g" is a constant equivalent to 32 feet per second.
Replacing we get:
[tex]200-130=200-\frac{1}{2}(32)t^2[/tex]Now we solve for "t", first by subtracting 200 to both sides:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Solving the operation:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Multiplying both sides by -2:
[tex]260=32t^2[/tex]Dividing both sides by 32:
[tex]\frac{260}{32}=t^2[/tex]Taking square root on both sides of the equation:
[tex]\sqrt[]{\frac{260}{32}}=\sqrt{t^2}[/tex]Solving the operations:
[tex]2.85=t[/tex]Therefore, the cord starts stretching at 2.85 seconds.
Related Questions
Harry wants to buy a motorbike that costs £600.He saves 30% of his wages each month.Each month Harry earns £400.Calculate how many months it will take Harry to save enough money?
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First, let's calculate how much money he saves each month, by calculating 30% of £400:
[tex]\frac{30}{100}\cdot400=30\cdot4=120[/tex]He saves £120 each month.
So, to reach the value of £600, the number of months needed is:
[tex]\frac{600}{120}=5[/tex]Therefore it will take 5 months to save enough money.
The water level of a tank every minute since it began filling is indicated by segments A,B,and C on the graph
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SOLUTION
From the graph
The slope of line A is
[tex]m=\frac{60-20}{2-0}=20[/tex]The slope of line B is
[tex]n=\frac{80-60}{6-2}=5[/tex]The slope of line C is
[tex]p=\frac{110-80}{9-6}=10[/tex]The least segment is the segment with the least slope.
The required arrangement is
[tex]B,C,A[/tex]The quadratic equation y = - 16t² +40t+2 represents the height of aprojectile, y, in feet, at a particular time, t, in seconds.For what interval or intervals of time will the projectile be above 18 feet?
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The given equation is:
[tex]y=-16t^2+40t+2[/tex]It is required to find which interval or intervals of time will the projectile be above 18 feet.
To do this, solve the inequality:
[tex]\begin{gathered} y>18 \\ \Rightarrow-16t^2+40t+2>18 \end{gathered}[/tex]First, find the critical points of the inequality by solving the equation:
[tex]\begin{gathered} −16t^2+40t+2=18 \\ \text{ Subtract 18 from both sides:} \\ \Rightarrow-16t^2+40t+2-18=18-18 \\ \Rightarrow−16t^2+40t-16=0 \\ \text{ Factor the left-hand side of the equation:} \\ \Rightarrow−8\left(2t−1\right)\left(t−2\right)=0 \\ \text{ Equate the factors to 0 to find the t-values:} \\ \Rightarrow(2t-1)=0\text{ or }(t-2)=0 \\ \Rightarrow2t=1\text{ or }t=2 \\ \Rightarrow t=\frac{1}{2}=0.5\text{ or }t=2 \end{gathered}[/tex]The possible interval of solutions are:
[tex]t<0.5,\;0.52[/tex]Use test values in the intervals to check which interval whose set of values satisfies the given inequality.
The only interval that satisfies it is 0.5.
Hence, the answer is between 0.5 second and 2 seconds.
The answer is option (c).Hello there! can you help me on questions 3, 4, and 5 please? Thank you!
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(3) A rate that is increasing means as the y variable increases, so does the x variable. This graph has its line rising up from left to right
(4) A graph with a rate that is decreasing would have the line sloping downwards from left to right (like the one provided in your question)
(5) A graph with a rate of zero means that, the y variable does not change, whereas the x variable keeps changing. This graph is a horizontal line (its parallel to the x-axis)
The rate is increasing
The rate is decreasing
The rate of change is zero
12. To prepare an aquarium for use, you can clean it with a saltwater solution. The amount of salt varies directly with the volume of the water. The solution has 2 teaspoons of aquarium salt for every gallon of water. a. How many teaspoons of aquarium salt are needed for 5 gallons of water? b. Write an equation that relates x gallons of water to y teaspoons of salt. c. Use the equation to find the number of gallons of water to use for 12 teaspoons of salt.
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Given:
The solution has 2 teaspoons of aquarium salt for every gallon of water.
a.) How many teaspoons of aquarium salt are needed for 5 gallons of water?
- To be able to determine how many teaspoons of aquarium salt are needed, we will be using ratios and proportions.
[tex]\text{ 2 teaspoon of salt : 1 gallon of water = x : 5 gallons of water}[/tex]Where,
x = teaspoons of aquarium salt
We get,
[tex]\text{ 2 teaspoon of salt : 1 gallon of water = x : 5 gallons of water}[/tex][tex]\frac{2}{1}\text{ = }\frac{x}{5}[/tex][tex]\text{ (2)(5) = (x)(1)}[/tex][tex]\text{ 10 = x}[/tex]Therefore, you will be needing 10 teaspoons of aquarium salt for 5 gallons of water.
b.) Write an equation that relates x gallons of water to y teaspoons of salt.
Let,
x = gallons of water
y = teaspoons of salt
[tex]\text{ }\frac{2\text{ teaspoons of salt}}{1\text{ gallon}}\text{ = }\frac{y}{x}\text{ }\rightarrow\text{ }\frac{2}{1}\text{ = }\frac{y}{x}\text{ }\rightarrow\text{ 2 = }\frac{y}{x}[/tex][tex]\text{ 2x = y}[/tex]Therefore, the equation of the mixture will be 2x = y.
c.) Use the equation to find the number of gallons of water to use for 12 teaspoons of salt. Substitute, y = 12.
[tex]\text{ 2x = y}[/tex][tex]\text{ 2x = 12}[/tex][tex]\text{ }\frac{2x}{2}\text{ = }\frac{12}{2}[/tex][tex]\text{ x = 6}[/tex]Therefore, you will be needing 6 gallons of water for 12 teaspoons of salt.
At what point will the lines x= -21 - 2y and x = -39 - 4y intersect? (i need the answer)
Answers
ANSWER
The lines intersect at (-3, -9)
EXPLANATION
The point where the lines intersect is the solution to the system of equations
[tex]\begin{cases}x=-21-2y \\ x=-39-4y\end{cases}[/tex]We can solve it using the elimination method, which consists in subtracting one equation from the other in order to eliminate one of the variables and obtain only one equation with only one variable:
[tex]\begin{gathered} x=-21-2y \\ - \\ x=-39-4y \\ \text{ ------------------------------} \\ (x-x)=(-21-2y)-(-39-4y) \end{gathered}[/tex]Solving for y:
[tex]\begin{gathered} 0=-21+39-2y+4y \\ 0=18+2y \\ 2y=-18 \\ y=-9 \end{gathered}[/tex]Now we have to replace y = -9 into one of the equations and solve for x:
[tex]\begin{gathered} x=-21-2y \\ x=-21-2(-9) \\ x=-21+18 \\ x=-3 \end{gathered}[/tex]The lines intersect at (-3, -9)
Write an addition fact that corresponds to the following sentence, and then answer the questionOn three consecutive passes, a football team gains 10 yards, loses 19 yards, and gains 21 yards. What number represents the total net yardage?The addition fact that corresponds to the sentence is_____The total net yardage is yards______
Answers
Given:
On three consecutive passes, a football team gains 10 yards, loses 19 yards, and gains 21 yards.
To find:
An addition fact that corresponds to the given sentence and the number represents the total net yardage.
Solution:
It is given that first football gains 10 yards then loses 19 yards and then again gains 21 yards.
The gaining is shown by a positive sign and the loss is shown by a negative sign.
So, the addition fact is given below:
[tex]+10-19+21[/tex]Now, the resultant of the above expression is the total net yardage.
[tex]\begin{gathered} +10-19+21=+31-19 \\ =+12 \end{gathered}[/tex]Thus, the total net yardage is 12 yards.
I need help with this problem. Please show work and simplify the answer!
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PLEASE HELP!!!!! I WILL GIVE BRAINLIEST!!!!
Evaluate the expression . Write your answer as a simplified mixed number, or as a decimal. Show your work
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Answer:
[tex]-3\frac{15}{16}[/tex]
Step-by-step explanation:
Given:
[tex](-\frac{1}{4}+2.875)\div(-\frac{2}{3})[/tex]
First, convert 2.875 to an improper fraction:
[tex]2.875=2\frac{875}{1000}=2\frac{7}{8}=\frac{23}{8}[/tex]
The expression becomes:
[tex](-\frac{1}{4}+\frac{23}{8})\div(-\frac{2}{3})[/tex]
Then, add the terms in the parentheses:
[tex]-\frac{1}{4}+\frac{23}{8}=-\frac{2}{8}+\frac{23}{8}=\frac{21}{8}[/tex]
The new expression is:
[tex]\frac{21}{8}\div-\frac{2}{3}[/tex]
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. Therefore:
[tex]\frac{21}{8}\times-\frac{3}{2}[/tex]
Next, multiply the numerators and denominators:
[tex]-\frac{63}{16}[/tex]
Finally, simplify to a mixed fraction:
[tex]-3\frac{15}{16}[/tex]
How do I write five hundred and eight hundredths as a decimal number.
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start by writing the whole part, sine there us only hundreds we can write it as
[tex]500[/tex]then write the decimal part, we can see that there are no tenths in this expression so we start with a 0, then for the hundredths, we can put the number 8
[tex].08[/tex]The complete number should be
[tex]500.08[/tex]Find the angle between the vectors u = 5i – 2j and v = 2i + 3j.
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STEP - BY - STEP EXPLANATION
What to find?
The angle between the given vectors.
Given:
u = 5i – 2j and v = 2i + 3j.
To solve the given problem, we will follow the steps below:
Step 1
Write the formula that can be use to solve the above.
[tex]cos\theta=\frac{\vec{a}\vec{.b}}{\vec{|a}\vec{||b}|}[/tex]Step 2
Determine;
→ →
a. b
[tex]\begin{gathered} \vec{a}\vec{.b}=(5)(2)+(-2)(3) \\ \\ =10-6 \\ \\ =4 \end{gathered}[/tex]Step 3
Determine;
→ →
|a| and | b|
[tex]\begin{gathered} \vec{|a|}=\sqrt{5^2+(-2)^2} \\ \\ =\sqrt{25+4} \end{gathered}[/tex][tex]=\sqrt{29}[/tex][tex]\begin{gathered} \vec{|b|}=\sqrt{2^2+3^2} \\ \\ =\sqrt{4+9} \\ \\ =\sqrt{13} \end{gathered}[/tex]Step 4
Substitute the values into the formula.
[tex]\begin{gathered} cos\theta=\frac{4}{\sqrt{29}\times\sqrt{13}} \\ \\ =\frac{4}{\sqrt{377}} \end{gathered}[/tex]Step 5
Take the arc cos of both-side.
[tex]\theta=cos^{-1}(0.20601)[/tex][tex]\theta=78.1\degree[/tex]ANSWER
θ = 78. 1°
Convert the following mixed number to an improper fraction: 28 1 / 8 What is the numerator of this improper fraction? State the answer without reducingAll negatives must be included in your final answer:ie. if the question asks for the whole number portion, numerator, or denominator of the answer and it has a negative, you must include that negative.Be sure to reduce all fractions fully and convert improper fractions to mixed numbers before stating your final answer
Answers
Given the mixed number:
[tex]28\frac{1}{8}[/tex]Let's convert the mixed number to an improper fraction.
To convert a mixed number to improper fraction, multiply the denominator by the whole number, then add the result to the numerator.
Thus, we have:
[tex]\begin{gathered} 28\times8=224 \\ \Longrightarrow224+1=225 \end{gathered}[/tex]Therefore, the improer fraction is:
[tex]\frac{225}{8}[/tex]The numerator is the number at the top of the fraction.
Therefore, the numerator of this improper fraction is = 225
ANSWER:
[tex]\frac{225}{8}[/tex]Numerator = 225
Answer: To convert a mixed number to improper fraction multiply the whole number and the denominator and then add the numerator. This gives the numerator of the improper fraction. The denominator is the same as the denominator of the given mixed number.
Step-by-step explanation:
[tex]28\frac{1}{8}[/tex] = [28x8+1] / 8 = [tex]\frac{224+1}{8}[/tex] = [tex]\frac{225}{8}[/tex]
The numerator of [tex]\frac{225}{8}[/tex] is 225
To learn more about conversion of mixed number to improper fraction:
https://brainly.in/question/28231026
Z (7x+3)° m n (6x+11)
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In this problem, the two angles are equal because of the properties, so:
[tex](7x+3)=(6x+11)[/tex]and we can solve for x
[tex]\begin{gathered} 7x-6x=11-3 \\ x=8 \end{gathered}[/tex]So the angles are:
[tex]\begin{gathered} 7(8)+3=59 \\ 6(8)+11=59 \end{gathered}[/tex]Which of the following has a graph that is an ellipse centered at (−2, 3)
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Solution:
The vertex equation of an ellipse is;
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Thus, given the center;
[tex](h,k)=(-2,3)[/tex]Then, the equation whose graph is an ellipse centered at (-2,3) is;
[tex]\frac{(x+2)^2}{12}+\frac{(y-3)^2}{18}=1[/tex]
The remains of an ancient ball court include a rectangular playing alley with a perimeter of about 18m. The length of the alley is two times the width. Find the length and the width of the playing alley.The width is ? m and the length is ? m.
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Given:
Perimeter = 18 m
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]Where:
l = lenght
w = width
In this case, we have that:
l = 2w
Therefore, we substitute the values in the formula:
[tex]\begin{gathered} P=2l+2w \\ 18=2(2w)+2w \end{gathered}[/tex]And solve for w:
[tex]\begin{gathered} 18=4w+2w \\ 18=6w \\ \frac{18}{6}=\frac{6w}{6} \\ w=3 \end{gathered}[/tex]For the length:
[tex]l=2w=2(3)=6[/tex]Answer:
The width is 3 m
The length is 6 m
-4(-7x-6) help me please
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multiply each term by -4 and sum
[tex]\begin{gathered} (-4\times-7x)+(-4\times-6) \\ =28x+24 \\ \end{gathered}[/tex]Use the appropriate form of the percentage formula.30% of what number is 21?
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If 30% of a number x is equal to 21, then x is to 100% as 21 is to 30%:
[tex]\frac{x}{100}=\frac{21}{30}[/tex]Solve for x:
[tex]x=\frac{21}{30}\times100=70[/tex]Then, 30% of 70 is 21.
Therefore, the answer is 70.
i only need the final answers, i do not need an explanation i am just double checking my final answer
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5) A ball is dropped from a height of 400 feet. Each time it hits the ground, it rebounds 75% of the distance it has fallen. How far will the ball travel before coming to rest?
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Initial height: 400 m
Each time it hits the ground, it rebounds 75% the distance it has fallen. Let us say this distance is d, then the new height is:
[tex]\begin{gathered} h=75\text{\% of }d=\frac{75}{100}\cdot d \\ \Rightarrow h=\frac{3}{4}d \end{gathered}[/tex]If the initial height is 400 m, then the subsequent heights are given by the recurrence equation:
[tex]\begin{gathered} h_0=400 \\ h_n=(\frac{3}{4})^n\cdot h_0 \\ \Rightarrow h_n=400\cdot(\frac{3}{4})^n \end{gathered}[/tex]And the total distance traveled D is:
[tex]\begin{gathered} D=h_0+2\cdot\sum ^{\infty}_{n\mathop=1}\lbrack(\frac{3}{4})^n\cdot h_0\rbrack \\ \Rightarrow D=400+800\cdot\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n \end{gathered}[/tex]Now, let us analyze the sum term:
[tex]\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=\frac{3}{4}+(\frac{3}{4}_{})^2+(\frac{3}{4})^3+\cdots_{}[/tex]From the infinite geometric sequence:
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop=0}r^n=\frac{1}{1-r} \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}r^n=\frac{1}{1-r}-1 \end{gathered}[/tex]Where r < 1. From our problem, r = 3/4 < 1, then:
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=\frac{1}{1-\frac{3}{4}}-1=\frac{1}{\frac{1}{4}}-1=4-1 \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=3 \end{gathered}[/tex]Finally, using this result:
[tex]D=400+800\cdot3=400+2400=2800[/tex]Simplify. In the form of a paragraph, explain in complete sentences the steps necessary to simplify the expression andinclude the final answer in your explanation. Complete your work in the space provided or upload a file that can displaymath symbols if your work requires it.
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1. When dividing with exponents, the exponent of a variable in the denominator is subtracted from the exponent in the numerator for the same variable. Then, first step to simplify is subtract the exponents of x and y in the fraction in parentheses:
[tex]\begin{gathered} =(x^{3-1}y^{1-2})^{-2} \\ =(x^2y^{-1})^{-2} \end{gathered}[/tex]2. To remove the parentheses you multiply each exponent in the parentheses by the exponent out of the parentheses:
[tex]\begin{gathered} =x^{2\cdot(-2)}y^{(-1)\cdot(-2)} \\ \\ =x^{-4}y^2 \end{gathered}[/tex]3. When you have a negative exponent (as the x powered to -4) you divide 1 in to the term with negative exponent (after you divide the exponent turns into a positive exponent):
[tex]=\frac{1}{x^4}\cdot y^2[/tex]4. Then, the given expression simplified is:
[tex](\frac{x^3y}{xy^2})^{-2}=\frac{y^2}{x^4}[/tex]Hi, can you help me answer this question please, thank you
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From the given z-value z=1.841, we can find the corresponding P-value by means of a z-table:
Then, by rounding to 4 decimal places, the p-value is 0.9672
what is the slope of the equation y = - 7x + 9
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EXPLANATION
The slope of a line is given by the following expression:
[tex]\text{Slope = }\frac{rise}{run}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]In this case, we have that the slope is represented by the generic form:
y = mx + b
Where m is the slope and b is the y-intercept.
So, the slope is -7.
Answer: m=-7
Find the equation of the line
Use exact numbers
Answers
Answer:
y = (1)x +(-5)
Step-by-step explanation:
You want the slope-intercept equation of the line graphed with y-intercept -5 and x-intercept +5.
Intercept formThe intercept form of the equation for a line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
Using the given intercept values, a=5, b=-5, the equation is ...
x/5 +y/(-5) = 1
Slope-intercept formThe desired form of the equation can be found by solving for y:
-x +y = -5 . . . . . . multiply by -5
y = x -5 . . . . . . . . add x
The numbers that go in the boxes are 1 and -5.
. A town committee has a budget of $75 to spend on snacks for the volunteers participating in aclean-up day. The committeechairperson decides to purchase granola bars and at least 50 bottlesof water. Granola bars cost $.50 each, and bottles of water cost $.75 each. Write and graph asystem of linear inequalities for the number of bottles of water and the number of granola bars thatcan be purchased
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Assume that the number of granola bars is x and the number of bottles is y
Since they decided to purchase at least 50 bottles
At least means greater than or equal, so
[tex]x\ge50[/tex]Since the cost of 1 bar = $0.50, then
The cost of all bars = 0.50x
Since the cost of 1 bottle = $0.75, then
The cost of all bottles = 0.75y
Since their budget is $75
They can not exceed that, then
[tex]0.50x+0.75y\le75[/tex]The solution will be in the common part of the two colors
The red represents the second inequality
The blue represents the first inequality
Simplify 9y - 11 + 4y - 16y
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The given expression is
9y - 11 + 4y - 16y
In order to simplify the expression, we would collect like terms. The like terms in this situation are
1) the terms containing y
2) the terms that don't contain y.
By collecting the like term, we would bring them together. It becomes
9y + 4y - 16y - 11
13y - 16y - 11
- 3y - 11
choose the image that corresponds to Figure 1 after a reflection over the x-axis and a translation of one unit left
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Solution
For this case the solution would be given by:
6. For school uniforms, five shirts and three pairs of pants cost $113. 25. If a shirtcosts $3.75 less than a pair of pants, how much is a shirt and how much is a pairof pants?
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Let x be the cost of 1 pair of pants, and y be the cost of one shirt, then since five shirts and three pairs of pants cost $113. 25 we can set the following equation:
[tex]5y+3x=113.25,[/tex]also, a shirt costs $3.75 less than a pair of pants, then:
[tex]y=x-3.75.[/tex]Substituting the second equation in the first one we get:
[tex]5(x-3.75)+3x=113.25.[/tex]Solving for x we get:
[tex]\begin{gathered} 5x-18.75+3x=113.25, \\ 8x=113.25+18.75, \\ x=\frac{33}{2}=16.5. \end{gathered}[/tex]Now, substituting x=16.5 in the second equation we get:
[tex]y=16.5-3.75=12.75.[/tex]Answer:
A shirt costs $12.75, and a pair of pants cost $16.5.
At the grocery store, 3 apples cost $0.65. What is the cost of 8 apples? 7th honors it is due today help
Answers
Answer:
$1.76 for 8 apples
Step-by-step explanation:
0.65 / 3 = 0.22
0.22 * 8 = 1.76
Hello! I need some help with this homework question, please? I just need help with C or D Q2
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C) Considering that f(x)=x² we can write the composite function f(f(x)) y plugging into the x-variable the function f(x) itself:
[tex]\begin{gathered} f(f(x)) \\ f\mleft(x\mright)=x^2 \\ f(f(x))=(x^2)^2 \\ f(f(x))=x^4 \end{gathered}[/tex]Now, let's find the Domain. Considering that this is a polynomial function that has no restraints nor discontinuity we can write out the following:
[tex]\begin{gathered} The\: domain\: of\: f\circ f\: is\: all\: Real\: numbers \\ D=\: \mleft(-\infty\: ,\: \infty\: \mright) \end{gathered}[/tex]assume that y varies inversely with x. If y = -4 when x = 1/2 , find x when y=2
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it is given that x and y have inverse relation
so K = xy
put y = -4 and x = 1/2
[tex]\begin{gathered} k=\frac{1}{2}\times-4 \\ k=-2 \end{gathered}[/tex]now
y = 2
then'
[tex]\begin{gathered} -2=x\times2 \\ x=\frac{-2}{2} \\ x=-1 \end{gathered}[/tex]so the value of x = -1
[tex]\begin{gathered} x\infty\frac{1}{y} \\ x=\frac{K}{y} \\ K=xy \end{gathered}[/tex]