The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:
[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]
For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:
[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]
So, the ball reaches its maximum height at t = 1 second.
To find the maximum height, we substitute t = 1 into the function h(t) :
[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]
Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
Express the complex number in trigonometric form. -2 + 2square root of three i
Answer:
The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Step-by-step explanation:
Given : Complex number [tex]-2+2\sqrt{3}i[/tex]
To find : Express the complex number in trigonometric form?
Solution :
The complex number [tex]a+ib[/tex] trigonometric form is [tex]r(\cos\theta+i\sin\theta)[/tex]
Where, [tex]r=\sqrt{a^2+b^2}[/tex]
and [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
On comparing with given complex number [tex]-2+2\sqrt{3}i[/tex]
a=-2 and [tex]b=2\sqrt{3}[/tex]
Substitute the value,
[tex]r=\sqrt{a^2+b^2}[/tex]
[tex]r=\sqrt{(-2)^2+(2\sqrt{3})^2}[/tex]
[tex]r=\sqrt{4+12}[/tex]
[tex]r=\sqrt{16}[/tex]
[tex]r=4[/tex]
[tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
[tex]\theta=\tan^{-1}(\frac{2\sqrt3}{-2})[/tex]
[tex]\theta=\tan^{-1}(-sqrt3)[/tex]
[tex]\theta=\tan^{-1}(\tan(-60))[/tex]
[tex]\theta=-60[/tex]
Substituting all values in the formula,
[tex]r(\cos\theta+i\sin\theta)[/tex]
[tex]4(\cos(-60)+i\sin(-60))[/tex]
[tex]4(\cos(60)-i\sin(60))[/tex]
Therefore, The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
can someone please explain the steps to solve these questions.
To the nearest hundredth, what is the area of a circle with a radius of 3 units
Answer:
28.27
Step-by-step explanation:
gl on test
For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the total number of visits when the cost for a member and nonmember will be the same.
The cost for a member and a nonmember of a rock-climbing gym will be the same at 30 visits.
Explanation:To find the total number of visits when the cost for a member and a nonmember will be the same, we need to set up an equation based on the problem statement, which we can then solve.
For the member, the cost is the $360 yearly fee plus $4 per visit (for equipment rental) - so if 'x' represents the number of visits, the total cost for a member would be $360 + 4x.
For a nonmember, the cost is $10 per visit (for gym use) plus $6 per visit (for equipment rental) - so the total cost for a nonmember is $16x.
So, to find the number of visits 'x' where both costs are equal, we need to solve this equation: $360 + 4x = $16x.
Solving the equation gives us $360 = 12x, which simplifies to x = 30.
So, the cost for a member and a nonmember would be the same at 30 visits.
Learn more about Break-even point here:https://brainly.com/question/35967655
#SPJ3
How many questions can i miss on a 28 question test to get a 70%?
The height of a triangle is 8 inches more than its base. the area of the triangle is 104.5 square inches. find the base and height.
answer this question please and right
does anyone know what the measuure of Ф should be . is so i will mark brainliest.
A pretzel maker was interested in knowing the number of pretzels in each bag it sold. The results of their research are shown in the box-and-whisker plot. What is the median number of pretzels?
The median number of pretzels is 54.
What is Box and whisker plot?The lower and upper quartiles are represented by the left and right sides of the box in a box and whisker plot. The box encompasses the interquartile interval, which contains 50% of the data. The median is the vertical line that divides the box in half. On the box plot, the mean is sometimes shown by a dot or a cross.
From the given box plot we can have the following information:
Minimum = 45
Lower Quartile = 47
Median= 54
Upper Quartile= 61
Maximum = 68
Thus, the Required median is 54.
Learn more about Box- whisker plot here:
https://brainly.com/question/22812839
#SPJ3
HELP ! I've been stuck on this for over 15 mins. :(
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5?
an = 8 − 5(n − 1); all integers where n ≥ 1
an = 8 − 5(n − 1); all integers where n ≥ 0
an = 8 − 3(n − 1); all integers where n ≥ 1
an = 8 − 3(n − 1); all integers where n ≥ 0
Show work please (6th grade math)
WILL MARK BRAINLIEST
There are 50 red beans and 50 white beans in a bag. The first bean selected is red. The red bean is returned to the bag. What are the chances of the second bean selected being red?
Any answers please??
Triangle rst is circumscribed about the circle below. What is the perimeter of the triangle?
Not sure what the answer is but this guy didnt attach the dang picture so here.
given function f(x)=x^2-x+8, find each of the following. f(9) f(-6) f(0)
What is the value, after 7 years...
Answer:
13946
Step-by-step explanation:
License plates are made using 2 letters followed by 3 digits. how many plates can be made ifrepetition of letters and digits is allowed
What is log base 5(4*7 )+log base 5 of 2 written as a single log?
A.log base 5 of 21
B.log base 5 of 26
C.log base 5 of 30
D.log base 5 of 56
Answer:
D. log base 5 of 56
Step-by-step explanation:
Since, by the multiplication law of logarithm,
[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]
Given expression is,
log base 5(4*7 )+log base 5 of 2
[tex]=log_5(4\times 7)+log_5(2)[/tex]
[tex]=log_5(28)+log_5(2)[/tex]
By the above property,
[tex]=log_5(28\times 2)[/tex]
[tex]=log_5(56)[/tex]
= log base 5 of 56
Hence, Option D is correct.
help pls!!! 10 points!!!
If the person can't accommodate and the glasses is + 2.50d, at which distance will the person see clearly
Answer:
40 cm or 2/5 of a meter.
Step-by-step explanation:
A short-sighted person, at a positive diopter, will take an estimation of about 2.5 and make it the denominator by 1 as the numerator to find out the distance (in meters) that they can see clearly.
We can find the value of f, given the value for P:
P = +2.50
f = 1 / p = 1 / 2.50
(changing the units, it will be) ---> 100 / 2.50 which is equal to 40 cm.
Therefore, 40 cm which is 2/5 of a meter is the distance a person with glasses +2.5d can see clearly.
Find the following measure for this figure.
Volume =
18 cubic units
24 cubic units
36 cubic units
Answer:
So the answer is 24 cubic units
Step-by-step explanation:
l=4 units,
w=2 units,
h=3 units and
V=4×2×3=24 cubic units.
In a poll of students at basketball champoin 82% of the students say that basketball is better than fottball.
Find the area of the surface of the part of y=4x+z^2 that lies between the planes
20 PTS AND I'LL MARK BRAINLIEST
∠1 and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠2=(5+4y)∘ and m∠3=(6y−25)∘ . What is m∠1 ?
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 $1.75 for the first 1 5 15 of a mile and $ 0.25 $0.25 for each additional 1 5 15 of a mile. if the distance from one of the convention hotels to the airport is 5.8 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?
To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.
Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.
The initial cost for the first 1/5 mile is given as $1.75.
We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:
[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]
To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:
[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]
Thus, there are 28 additional 1/5 mile increments.
Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:
[tex]\[ 28 \times 0.25 = 7.00 \][/tex]
The total cost is the initial cost plus the cost for the additional distance:
[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]
Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.
Norma stopped to get gas for her car before beginning a trip. her odometer read 2587 miles, and she filled up her tank with 26 gallons. at the end of her trip, her odometer read 3295 miles. what is her car's miles per gallon?(round to the closest gallon)
Which sequence is modeled by the graph below? coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8)
a. an = 1(2)n − 1
b. an = 2(1)n − 1
c. an = 1 + (2)n − 1
d. an = (2)(n − 1)
Answer: The correct option is d.
Explanation:
From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).
The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.
The point (1,1) represents that the first term is 1. Similarly from (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.
The sequence is 1,2,4,8.
It can be written as,
[tex]2^0,2^1,2^2,2^3[/tex]
Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,
[tex]a_n=2^{n-1}[/tex]
Therefore, the correct option is d.
What is the radian measure of a 150° angle?
The radian measure of a 150° angle is (5/6) π rad, found by multiplying 150° by the conversion factor π/180.
To find the radian measure of a 150° angle, we use the relationship between degrees and radians. Recall that a full circle in degrees is 360° and in radians is 2π rad. Therefore, we can say that 360° equals 2π radians. To convert degrees to radians, we multiply the degree measure by the fraction π/180.
For a 150° angle, the calculation would be:
150° multiplied by the conversion factor π/180
150° * (π/180) = (150/180) * π = (5/6) * π rad
Thus, the radian measure of a 150° angle is (5/6) π rad.
The spoke of a wheel reaches from the center of the wheel to its room if the circumference of the rim of the wheel is 42 inches how long is each spoke
Find all solutions to the equation sin2x+sinx-2cosx-1=0 in the interval [0, 2pi)