The values of t for which the ball's height is 20 feet, after solving the quadratic equation using the appropriate values for a, b, and c, are approximately t = 3.79 seconds and t = 0.54 seconds. These values represent the time it takes for the ball to reach 20 feet on its way up and on its way down.
Explanation:To find all values of t for which the ball's height is 20 feet, we need to set the ball's height equation h = 7 + 30t - 16t2 equal to 20 and solve for t. This means solving the quadratic equation: 16t2 - 30t + (7 - 20) = 0, which simplifies to 16t2 - 30t - 13 = 0.
We can solve this quadratic equation using the quadratic formula, t = (-b ± √(b2 - 4ac)) / (2a), where a = 16, b = -30, and c = -13. After applying the quadratic formula, we find two potential solutions for t, which are t = 3.79 seconds and t = 0.54 seconds. Since time cannot be negative, both of these times represent the moments when the ball is at 20 feet: once on the way up and once on the way down.
The values of t for which the ball's height is 20 feet are approximately [tex]\(t \approx 2.76\)[/tex] seconds and [tex]\(t \approx 0.14\)[/tex] seconds (rounded to the nearest hundredth).
To find the values of [tex]\(t\)[/tex] when the ball's height is 20 feet, you can set the equation for height [tex]\(h\)[/tex] to 20 and solve for [tex]\(t\)[/tex]:
[tex]\[h = 7 + 30t - 16t^2\][/tex]
Setting [tex]\(h\)[/tex] to 20:
[tex]\[20 = 7 + 30t - 16t^2\][/tex]
Rearranging the equation:
[tex]\[16t^2 - 30t + 7 = 0\][/tex]
Now, you can solve this quadratic equation for t. You can use the quadratic formula:
[tex]\[t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\][/tex]
In this case, the coefficients are [tex]\(a = 16\), \(b = -30\), and \(c = 7\)[/tex].
[tex]\[t = \frac{30 \pm \sqrt{(-30)^2 - 4(16)(7)}}{2(16)}\][/tex]
[tex]\[t = \frac{30 \pm \sqrt{900 - 448}}{32}\][/tex]
[tex]\[t = \frac{30 \pm \sqrt{452}}{32}\][/tex]
[tex]\[t = \frac{30 \pm 2\sqrt{113}}{32}\][/tex]
Now, you have two possible solutions for t:
[tex]\[t_1 = \frac{30 + 2\sqrt{113}}{32} \approx 2.76 \text{ seconds}\][/tex]
[tex]\[t_2 = \frac{30 - 2\sqrt{113}}{32} \approx 0.14 \text{ seconds}\][/tex]
Find an implicit and an explicit solution of the given initial-value problem. (use x for x(t).) dx dt = 2(x2 + 1), x(π/4) = 1
I thought of a number, doubled it, then decreased by 17. Then I divided the result by 3. I got 15. What was my number?
The number person thinking about is 14.
Given that, I thought of a number, doubled it, and then decreased it by 17. Then I divided the result by 3. I got 15.
What is the equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number be x.
Double it=2x
Decreased it by 17=2x+17
Divided the result by 3=(2x+17)/3
The result is equal to 15.
(2x+17)/3=15
⇒2x+17=45
⇒2x=28
⇒x=14
Therefore, the number person thinking about is 14.
To learn more about the equations visit:
https://brainly.com/question/10413253.
#SPJ2
E=mc2 is one of the most recognizable equations in the world. In this task, you’ll attempt to understand it better. Let’s start with what the letters mean. The letter E stands for energy, the letter m stands for mass, and the letter c stands for the speed of light. The meaning of this equation is that you can completely convert mass into energy. a. Rewrite the equation to solve for the speed of light, c. Use rational exponents instead of roots.
A number is K units to the left of 0 on the number line. Describe the location of its opposite
Two kinds of thread are being compared for strength. fifty pieces of each type of thread are tested under similar conditions. brand a has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand b has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. construct a 95% confidence interval for the difference of the population means.
In this case, we have two different brands of thread and we have data about their tensile strength. We calculate the standard error of the difference between their means and use that to construct a 95% confidence interval. The result suggests the average tensile strength of Brand B is significantly higher than that of Brand A.
Explanation:To construct a 95% confidence interval for the difference of the population means between the two types of threads, we first need to calculate the standard error of the difference which is the square root of the sum of the squares of the standard deviations divided by the respective sample sizes. In this case, the sample sizes for brands A and B are both 50.
The standard error of the difference = sqrt[(5.6^2/50) + (6.3^2/50)] = approximately 1.18
Since we are trying to build a 95% confidence interval, we have to look at the z-score corresponding to this confidence level. A 95% confidence interval corresponds to 1.96 standard deviations either side of the mean, thus the z-score is 1.96.
We can then calculate the confidence interval as:
Lower limit = (78.3 - 87.2) - 1.96 x 1.18 = -11.52
Upper limit = (78.3 - 87.2) + 1.96 x 1.18 = -7.08
So the 95% confidence interval for the difference between the mean tensile strengths of the two thread types is approximately (-11.52, -7.08) kilograms.
Learn more about Confidence Interval here:https://brainly.com/question/34700241
#SPJ3
Using the formula in model 1, choose the correct answers for the total amount and amount of interest earned in the following compound interest problem. $500 at 4% for 5 years, compounded annually. Total Amount = $ Interest Amount =$
Answer:
608.33
108.33
Step-by-step explanation:
Found answer in above answer.
let log P/N=8 and log M/N=5
What is the relationship between P and M?
What is the place value for 5 in the number 12354897
If 2(x -1) = 14, then x =
If the given equation is represented as "2(x - 1) = 14", then the value of the variable "x" is 8.
To solve the equation 2(x - 1) = 14 for x, we use algebraic techniques to separate x.
First, we distribute the 2 to both terms inside the brackets;
2x - 2 = 14,
Next, we separate the variable x by adding 2 to both sides of the equation:
2x - 2 + 2 = 14 + 2,
Simplifying the equation:
2x = 16,
At last , to solve for x, we divide both sides of the equation by 2:
We get,
(2x) / 2 = 16 / 2,
x = 8,
Therefore, the solution to the equation 2(x - 1) = 14 is x = 8.
Learn more about Equation here
https://brainly.com/question/15339510
#SPJ6
Rotating Light A searchlight rotates through one complete revolution every 4 seconds. How long does it take the light to rotate through 90°?
whats the solution of the equation
3x+9-7x=2(x+6)
3x-7x = -4x
-4x+9 =2x+12
9=6x+12
-3 = 6x
x=-3/6 = - 1/2
x = - 1/2
Anya graphed the line (y – 2) = 3(x – 1) on the coordinate grid. The slope of her line is .
Answer:
3
Step-by-step explanation:
took quiz on edge
The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?
How to simplify?
2a - 4b - 16 + (3a + 7 ) - 8
A pallet stacked with bags of cement weighing a total of 5501 N must be pushed up a 2.30-m incline to a 75.0-cm high platform. What force, in Newtons, must be applied to get the job done?
The equation of a given circle in general form is x2+ y2 − 8x + 12y + 27 = 0. Write the equation in standard form, (x − h)2 + (y - k)2 = r2, by completing the squares in the equation. Show your work in a table.
Answer:
Step Reason
x2 + y2 - 8x + 12y + 27 = 0 given
x2 - 8x + y2 + 12y = -27 Isolate the constant term
x2 - 8x + 16 + y2 + 12y + 36 = -27 + 16 + 36 Complete the square by adding . 16 and 36 to both sides.
(x2 - 2∙4∙x + 42) + y2 + 12y + 36 = 25 Group and rearrange terms in x.
(x - 4)2 + y2 + 12y + 36 = 25 (a - b)2 = a2 - 2ab + b2
(x - 4)2 + (y2 + 2∙6∙y + 62) = 25 Group and rearrange terms in y.
(x - 4)2 + (y + 6)2 = 25 (a + b)2 = a2 + 2ab + b2
(x - 4)2 + (y + 6)2 = 52 Take the square root to find r = 5.
Step-by-step explanation:
this is the exact answer from plato
hope this helps a little bit :))
Translate the sentence into an equation. Nine more than the quotient of a number and 7 is equal to 3 . Use the variable y for the unknown number.
The equation is 9+ y/7 = 3
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S
Given statement:
Nine more than the quotient of a number and 7 is equal to 3.
let the number be y
The 9+ y/7 = 3
quotient of a number and 7 is y/7
and, nine more than= 9+ y/7
So, 9+ y/7 = 3
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ2
What related number sentence shows the commutative property addition 3+9=12
Write down all elements of ({9, 10, 11} ∩ {10, 11, 12, 13}) ∪ {14, 15}. (enter your answer in set notation.)
an architectural drawing lists the scale as 1/4"=1'. if a bedroom measures 2 1/2" by 3 3/4" on the drawing, how large is the bedroom?
Answer:
The answer is 10 ft by 15 ft
Step-by-step explanation:
2 1/2 is also 2 2/4
Since 1/4 = 1
2/4 = 2 feet
Plus the whole number being 2 from 2 2/4 equates to 8 feet
because 2 is the same as 8/4.
2 2/4 = 10 feet
Do the same with 3 3/4 and you get 15 feet total.
Resulting in 10 ft by 15ft
A local grocer wants to find out whether how many mixed flower bouquets in his inventory everyday. To that end, kept records of the daily bouquet sales for the last 27 days. The average number of bouquets sold every day was 11.8 and the sample standard deviation is 2.3. Construct a 99% confidence interval for the number of bouquets sold on a given day..
Ed ate 3/8 of the pizza and jen ate 1/4 of the pizza. How much of the pizza is left
Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.
Answer:
Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.
Step-by-step explanation:
From 512 to 68, there are a total of 444 houses, of which 222 are pairs, which is half, if it is even with the previous two, would be 224, otherwise, 222, if one yes and the other does not, 223.
if I'm going to the lake that is 60 miles away and I'm driving 40 miles per hour how long would it take for me to get there
True or false The coefficient of (x^(k)) (y^(n-k)) in the expansion of (x+y)^n equals (n choose k)
under which of the following operations are the polynomials 3x+2 and 4y-11 not closed
Prove the identity
cos(-x)/[1+sin(-x)]=secx+tanx
Tina is placing 30 roses and 42 tulips in vase for table decorations in her restaurant each vase will hold the same number of flowers each vase will have only one type of flower what is the greatest number of flowers She can place it each vase
Answer: 6
Step-by-step explanation:
Given : Tina is placing 30 roses and 42 tulips in vase for table decorations in her restaurant .
Each vase will hold the same number of flowers and each vase will have only one type of flower .
Then, the greatest number of flowers she can place it each vase will be the greatest common factor of 30 and 42.
Prime factorization of 30 and 42 :
[tex]30=2\times3\times5\\\\42=2\times3\times7[/tex]
We can see that greatest common factor of 30 and 42 = [tex]2\times3=6[/tex]
Hence, the greatest number of flowers she can place it each vase =6
A plane travel from California and back it took one hour long on the way out than it did on the way back the planes average speed was 300 miles an hour the average speed on the way back with 350 miles an hour how many hours did the trip take
Rachel pays $15.20 for a pack of 8 towels. Find the unit price in dollars per towel .
The unit price of a towel is calculated by dividing the total cost of the pack ($15.20) by the number of towels in the pack (8), which equals $1.90 per towel.
Explanation:In order to find the unit price in dollars per towel, we simply divide the total cost of the pack by the number of towels in the pack. So for Rachel who paid $15.20 for a pack of 8 towels, to find the cost per towel, you'd divide $15.20 by 8.
To calculate:
Divide the total cost by the number of items: $15.20 / 8
This equals $1.90. So, the cost per towel, or unit price, is $1.90.
Learn more about unit price here:https://brainly.com/question/32390020
#SPJ2