Answers
Related Questions
Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.
Answers
Answer:
31√2 feet
Step-by-step explanation:
The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.
SetupLet h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...
h² +(17√2)² = 50²
SolutionSubtracting the constant on the left gives ...
h² = 2500 -578 = 1992
h = √1992 = 31√2
The height of the square pyramid is exactly 31√2 feet.
__
Read more about the Pythagorean theorem here:
https://brainly.com/question/27707750
The eccentricity of the conic section shown is
Answers
Answer:
1
Step-by-step explanation:
This is a U shaped graph, so the shape is a parabola
Eccentricity of any parabola is 1.
Answer:
Step-by-step explanation:
Just for some extra confrontation indeed the correct answer is 1.
Which of the following is The function f(x)=2x2−1 is/has
A. order 2 rotational 2 symmetry about the origin
B. symmetry about the y-axis
C. neither symmetric about the y-axis nor has order 2 rotational symmetry about the origin
D. odds a good way to get someone to participate in a group?
Answers
The given function has symmetry about the y - axis.
Symmetry of the Function
If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.
The given function is,
f(x) = 2x² - 1
It is an even function since the function remains same for both x and -x.
Putting f(x) = 0, we get,
2x² - 1 = 0
2x² = 1
x² = 1/2
x = ±1/2
⇒ Axis of symmetry is, x=0
Hence, the function f(x) is symmetric about y-axis.
Learn more about a function here:
https://brainly.com/question/12431044
#SPJ1
An artist is making a sketch based on a 12 inch by 30 inch poster. She divides the poster into grid squares. What are the greatest size grid squares she can make?
Answers
The greatest size grid squares she can make is; 12 inch by 12 inch.
What are the greatest size grid squares she can make?Since, it follows from the task content that the poster at the artist's disposal is 12 inch by 30 inch, it follows that the smaller dimension of the poster is; 12inch.
It is the limiting dimension and hence, the greatest size grid squares she can make is; 12in by 12 inch.
Read more on grid squares;
https://brainly.com/question/27892243
#SPJ1
What is the slope of the line that contains the points (9,-4) and (1,-5)?
OA. 1
OB.1/5
O C.-1/8
O D. -1
Answers
Answer:
Step-by-step explanation:
hello .....
note : the slope of the line (AB) is :
m = (YB -YA)/(XB - XA)
given : A(9,-4) and B (1,-5)
m= ((-5)-(-4))/(1-9)
m= 1/8
A genetic experiment with peas resulted in one sample of offspring that consisted of 427 green peas and 161 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
O Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
a. Construct a 90% confidence interval. Express the percentages in decimal form.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
Sub
Answers
Using the z-distribution, we have that:
a) The confidence interval is: (24.33%, 30.37%).
b) The correct option is: No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]n = 427 + 161 = 588, \pi = \frac{161}{588} = 0.2735[/tex]
Then the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 - 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.2433[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 + 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.3037[/tex]
As a percentage, the interval is: (24.33%, 30.37%).
25% is part of the interval, hence the correct statement is:
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that "sin a sin b = 1/2[cos(a-b)-cos(a+b)]" is an identity. Use the definitions of sum and difference formulas for cosine.
Answers
The equations which completes the left-hand column of the table are;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Which equations and identities complete the left-hand column of the table?The given expression on the right is written as follows;
First row;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
The definition of the sum and difference of cosine are;
cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)
cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)
Therefore;
Second row;
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)
Which gives;
[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
Third row;
sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Learn more about trigonometric functions here:
https://brainly.com/question/1143565
#SPJ1
In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Answers
Using the normal distribution, there is a 0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given, respectively, by:
[tex]\mu = 42.5, \sigma = 4.8[/tex]
The probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 35, hence:
X = 48:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48 - 42.5}{4.8}[/tex]
Z = 1.15
Z = 1.15 has a p-value of 0.8749.
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 42.5}{4.8}[/tex]
Z = -1.56
Z = -1.56 has a p-value of 0.0594.
0.8749 - 0.0594 = 0.8155.
0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.
Answers
The wheelchair ramp must have a height of approximately 1.553 meters. One tree is approximately 310.309 meters taller than the other one.
How to determine measures with trigonometric functions
In this problem we have two cases in which geometric diagrams and trigonometric functions are utilized to determine side lengths. Based on all informations presented in the images attached below, we proceed to find the side lengths:
Case A
h = (6 m) · sin 15°
h ≈ 1.553 m
Case B
Δh = 60 m /cos 36° - 60 m /cos 52°
Δh ≈ 310.309 m
To learn more on trigonometric functions: https://brainly.com/question/6904750
#SPJ1
Which equation has no solution?
O 1-x-31=5
O 12x-11=0
O15-3x = -8
O|-x+91=0
Answers
Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)
What linear equation has no solution?
Herein we must check each choice to find if a solution exists or not by algebra properties. Now we proceed to check each case:
Choice A
1/(x - 31) = 5
1 = 5 · (x - 31)
1 = 5 · x - 155
5 · x = 156
x = 31.2
Choice B
12 · x - 11 = 0
12 · x = 11
x = 11/12
Choice C
15 - 3 · x = - 8
3 · x = 23
x = 23/3
Choice D
- x + 91 = 0
x = 91
Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)
RemarkThe statement presents typing mistakes and is incomplete. Correct form is shown below:
Which equation has no solution?
A. 1/(x- 31) = 5
B. 12 · x - 11 = 0
C. 15 - 3 · x = - 8
D. - x + 91 = 0
E. Neither of all
To learn more on linear functions: https://brainly.com/question/21107621
#SPJ1
Explain the difference between using area and volume with 2-D and 3-D figures.
Answers
The difference between using Area and Volume with 2D and 3D figures is that Area is a measure of square units while Volume is a measure of cubic units.
What is the difference between Area and Volume?The area of an object is the measure of space occupied by the two-dimensional object (flat) in a plane. Volume on the other hand is the quantity of space occupied by the object, 3-dimensional object in this case. The unit of area is in square units. The unit of volume is in cubic units.
Read more on Area and Volume;
https://brainly.com/question/15612720
#SPJ1
Deondra has 57 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 340 square meters. List each set of possible dimensions
(length and width) of the field.
Answers
(L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters. This can be obtained by forming quadratic equation for the data.
Calculate the set of possible dimensions (length and width) of the field:
Let length be L and width be W.
Given that,
three sided fence has a length of 57m,
⇒ 2W + L = 57 m ⇒ L = 57 - 2W
the area of the land is 340 square meters
length × width = 340 ⇒ L × W = 340
(57 - 2W)W = 340
57W - 2W² = 340
2W² - 57W + 340 = 0
Solve for W using quadratic formula,
a = 2, b = -57, c = 340
W = (-b±√b²-4ac)/2a
= (57±√3249-2720)/4
= (57±√529)/4
= (57±23)/4
W = 20 m and W = 8.5 m
For W=20, L=57-2(20) = 17
For W=8.5, L=57-2(8.5) = 40
Hence (L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters.
Learn more about quadratic equations:
brainly.com/question/5975436
#SPJ1
A catering service offers 11 appetizers, 7 main courses, and 4 desserts. A customer is to select 9 appetizers, 5 main courses, and 2 desserts for a banquet. In how many ways can this be done?
Answers
Based on the various meals offered by the catering service, the ways that the order can be done is 6,930 ways..
How many ways can the food be served?This can be found as:
= (11! / (9!2!)) x (7! / (5!2!)) x (4! / (2!2!)
= 55 x 21 x 6
= 6,930 ways
In conclusion, the order can be made in 6,930 ways.
Find out more on permutations at https://brainly.com/question/1216161.
#SPJ1
I need help with b and c please and thank you!!
Answers
Answer:
rjdjdj shiejd shsuisis shusisos
In AABC, m/A = 15°, a = 9, and b = 12. Find c to the nearest tenth.
A. 20.0 B. 17.4 C. 8.4 D. 11.5
Answers
Answer:
Step-by-step explanation:
This is a Law of Sines problem. The expanded formula is
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] where the capital letters are the angles and the lowercase letters are the side lengths. We only use 2 of these ratios at a time. And in order to do that, we can only have one unknown per set of ratios. I have angle A and side a, so I'll use that ratio, but I don't have angle C to help me find side c. I also don't have angle B. But I do have side b, so I'll use the A and B sin stuff and then solve for C indirectly.
[tex]\frac{sin15}{9} =\frac{sinB}{12}[/tex] to solve for angle B. Cross multiply:
[tex]sinB=\frac{12sin15}{9}[/tex]
[tex]sinB=.3450926061[/tex] Use the inverse and sin keys on your calculator (in degree mode) to get that
B = 20.2°. Now that we have that, we can find the measure of angle C:
180 - 15 - 20.2 = 144.8°
Now we can use the sin ratio involving the angle C, side c (our unknown), and angle A and side a:
[tex]\frac{sin144.8}{c}=\frac{sin15}{9}[/tex] and cross multiply to solve for c:
[tex]c=\frac{9sin144.8}{sin15}[/tex] gives us that
c = 20.0
What is the correct classification for each given angle?
Drag and drop the answer into the box to match each angle.
Answers
Answer:
∠AFB = Acute
∠DFB = Obtuse
∠CFD = Right
Step-by-step explanation:
∠AFB is acute b/c its less than 90°
∠DFB is obtuse b/c it more than 90°
∠CFD is right b/c it's exactly 90°
Ayayai inc. Has a customer loyalty program that rewards a customer with 1 customer loyalty point for every $10 of purchase. Each point is redeemable for $3 discount on any future purchases . On july 2, 2020 customers purchase pro for $370000 (with a cost of $210900 )and earn 37000 points redeemable for future purchases. Ayayai is expected 31500 points to be redeemed. Ayayai estimates a standalone selling price for $2.50 per point (or $92500 total ) on the basis of the likelihood of redemption . The points provide a material right to customers that they would not receive without entering into a contract. As a result. Ayayai concludes that the points are separate performance obligation. Determine the transaction price for the product and the customer loyalty points. Product purchases, loyalty points, total transaction price
Answers
The transaction price for Ayayai's product and the customer loyalty points are $92500 and 37000 points respectively.
How to determine the transaction price?Based on the information provided about Ayayai inc., the transaction price for their product and the customer loyalty points would be allocated as follows:
SSP PA TTP AA____
Product purchases $370,000 80% $370,000 $296,000
Loyalty points $92,500* 20% $370,000 $74,000__
$462,500 $370,000
*37,000 × 2.50 = $92,500
Note:
SSP means Standalone selling prices.PA means Percent allocated.TTP means Total transaction price.AA means Allocated amounts.Read more on transaction price here: https://brainly.com/question/15874481
#SPJ1
What is the missing exponent in the equation 3 TO THE SEVENTH POWER EQUALS 27
Answers
Answer: 3 to the 3rd power equals 27
Step-by-step explanation: Because a exponent is the number times itself 3x3 equals 9 that's already 2 then 9x3 equals 27 so anything above is to much
car travels 22 miles for every gallon of gasoline used. The table below represents this relationship.
Gas Mileage
Distance Traveled
(miles)
Gasoline Used
(gallons)
22
1
44
2
x
3
88
4
Answers
The equation that shows a pair of equivalent ratios that can be used to find the unknown is [tex]\frac{22}{1} =\frac{x}{3}[/tex]
Writing an EquationFrom the question, we are to determine which equation shows a pair of equivalent ratios that can be used to find the unknown
In the given table, the unknown is x
Consider the given values in the table,
The equation that shows a pair of equivalent ratios that can be used to find the unknown is
[tex]\frac{22}{1} =\frac{x}{3}[/tex]
Hence, the equation that shows a pair of equivalent ratios that can be used to find the unknown is [tex]\frac{22}{1} =\frac{x}{3}[/tex]
Here is the complete question:
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship. Gas Mileage Distance Traveled (miles) Gasoline Used (gallons) 22 1 44 2 x 3 88 4. Which equation correctly shows a pair of equivalent ratios that can be used to find the unknown.
Learn more on Writing an equation here: https://brainly.com/question/18815248
#SPJ1
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 316 people entered the park, and the admission fees collected totaled 924.00 dollars. How many children and how many adults were admitted
Answers
Answer: pretty sure
There were 108 children and 175 adults.
Name a pair of complementary angles in this figure.
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
angles DEH and HEJ
angles DEH and DEJ
angles DEH and DEK
angles DEF and DEH
Answers
The answer choice which represents a pair of complementary angles in the task content is; angles DEH and DEJ.
Which pair of angles represent complementary angles?It follows from the concept of angle geometry that two or more angles are said to be complementary when the sum of their measures is 90°.
It follows from the task content therefore that since, DEJ = 90° and the sum of the measures of angles DEH and DEJ amounts to 90°.
Hence, the pair of angles are complementary.
Read more on complementary angles;
https://brainly.com/question/16281260
#SPJ1
Solve for x in sin xtan x + tan x – 2sin x + cos x = 0 for 0 ≤ x ≤2π rads.
Answers
The value of x = 4.71, 0.41, or 5.89 radian value
Specification:
sinxtanx + tanx -2sinx + cosx = 0
tanx = sinx / cosx
sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0
cosx to remove the fraction
sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0
sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1
sinx -2sinxcosx + 1 = 0
sinx (1-2cosx) = -1
1-2cosx = -1 / sinx
-2cosx = -1 / sinx -1
2cosx = 1 / sinx + 1
cosx = 1 / 2sinx + 1/2
sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2
Squared on both sides
1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4
4sin ^ 2 (x) Multiply
4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)
4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0
y = sinx
4y ^ 4 -3y ^ 2 + 2y + 1 = 0
sinx = y = -1 or -0.3478
x = 270, 180-22.61 or -22.61 degrees
x = 270, 157.39 or 337 .39 degrees
or
x = 3pi / 2, 0.13pi or 1.87pi radians
or
x = 4.71, 0.41 Or 5.89 radians
For more information about trigonometry, visit https://brainly.com/question/24349828
#SPJ1
Which graph represents the function f(x) =3(2)*?
Answers
I assume you meant [tex]f(x)=3(2)^x[/tex].
Find the Simple Intrest on
#60,000.00 for 3 years at
5% per annum
Answers
Answer:
the ans is 9000
Step-by-step explanation:
simple interest= 60000*3*5/100
Your friend is helping to raise money for a local charity by participating in a cartwheel-a-thon. Your
friend is 70 inches tall with your friend's arms raised in the air. Your friend is able to complete a
cartwheel in 15 seconds. The charity sponsor supplies a wristband to each participant to assist in
counting the number of cartwheels completed. The wristband is 4 inches from the end of your friend's
arm. Write a model for the height h (in inches) of the wristband as a function of the time (in minutes)
given that the wristband is at the highest point when ; = 0.
Answers
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
How can the height of the wristband be modeled?The model for the height can be emanated from the general formula of the sine function, then
y = A sin(Bt - C) + D
Maximum point = 70 - 4 = 66 at t = 0
Minimum point = 4
Amplitude, A = (66 - 4) ÷ 2 = 31
D = 4 + 31 = 35
At t = 0, we have;
66 = 31 × sin(B × 0 - C) + 35
31 = 31 × sin(- C)
sin(- C) = 1
C = -π/2
1 minute = 60 seconds
1 second = 1 minute/60
15 seconds = (15/60) minutes
Period = 15 seconds = 15/60 minutes
Period = 2π/B
Therefore, 15/60 = 2π/B
1/4 = 2π/B
B = 2π/(1/4) = 8π
y = Height of the function
Let h denote the height of the wristband.
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
To learn more about sine function refer to:
brainly.com/question/12102275
#SPJ9
Which of the following is NOT a criterion for making a decision in a hypothesis test?
Choose the correct answer below.
OA. If P-values a, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
OB. If the test statistic falls within the critical region, the decision is to reject the null hypothesis.
OC. If a confidence interval does not include a claimed value of a population parameter, the decision is to reject
the Inull hypothesis.
OD. If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null
hypothesis.
Answers
If the p-value less than 0.05, the decision is to reject the Null hypothesis.
What is hypothesis testing?Hypothesis testing is statistical reasoning using information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially bestguessed. Because it is the underlying assumption, the null hypothesis is often referred to as H0.For instance, you might explore and find that a specific drug effectively manages headaches. But nobody will believe what you find if you can't do that experiment again.A hypothesis seeks to provide an answer to a question. We will be forced to think about the results an experiment should try to achieve by a formulated hypothesis.The independent variable is the first variable. Results with seriousness.The following should NOT be used as a decision-making standard in a hypothesis test.
If the p-value less than 0.05, the decision is to reject the Null hypothesis.
To learn more about the hypothesis, refer to:
https://brainly.com/question/606806
#SPJ9
You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary
Answers
[tex]increase = 13.25 - 12.50 \\ increase = 0.75 \: dollars[/tex]
[tex]12.50 = 100\% \\ 0.75 = x\%[/tex]
[tex]12.50x = 100(0.75) \\ x = \frac{100(0.75)}{12.50} = \frac{75}{12.5} = 6\%[/tex]
articipation Activity #6
This is similar to Try It #11 in the OpenStax text.
A satellite is rotating around Earth at 0.2 radians per hour at an altitude of 252 km above Earth. If the radius of Earth is 6,378 kilometers, find the linear speed of the satellite in kilometers per hour.
Enter the exact answer.
The linear speed of the satellite is
Number
kilometers per hour.
Answers
The linear speed based on the information is 1326 km/h.
How to calculate the speed?The radius will be:
= 6378 + 252
= 6630 km
The angular speed is 0.2. The linear speed will be:
= 6630 × 0.2
= 1326 km/h.
Learn more about speed on:
brainly.com/question/4931057
#SPJ1
A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 ft/s. The ball's height (in feet) after t seconds is given by the following.
h=5+31t-16t^2
Find all values of t for which the ball's height is 19 feet.
t= _ seconds
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answers
Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the function is:
h(t) = -16t² + 31t + 5
The height is of 19 feet when h(t) = 19, hence:
19 = -16t² + 31t + 5
16t² - 31t + 14 = 0.
Then:
[tex]\Delta = (-31)^2 - 4(16)(14) = 65[/tex][tex]x_1 = \frac{31 + \sqrt{65}}{32} = 1.22[/tex][tex]x_2 = \frac{31 - \sqrt{65}}{32} = 0.72[/tex]More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ1
If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
Answers
Answer:
x = 51Step-by-step explanation:
If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse
x = √(85²- 68²)
x = (7225 - 4624)
x = √2601
x = 51
Answer:
x = 51
Step-by-step explanation:
The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.
What are Pythagorean triples?A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:
a² +b² = c²
The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...
{5, 12, 13}, {7, 24, 25}, {8, 15, 17}
There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.
What is this triple?The given values of the triple have the ratio ...
68/85 = (4·17)/(5·17) = 4/5
Only the values in the {3, 4, 5} triple and its multiples will have this ratio.
The value of x is 3·17 = 51, so the triple is {51, 68, 85}.
x = 51
__
Additional comments
Any primitive triple will have two odd numbers.
The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.
For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.
__
The above triple can be verified using the Pythagorean theorem:
51² +68² = 2601 +4624 = 7225 = 85²