Given:
The distance s (in feet) of the ball from the ground after t seconds is
[tex]s=64t-16t^2[/tex]
To find:
(a) At what time t will the ball strike the ground?
(b) For what time t is the ball more than 48 feet above the ground?
Solution:
(a)
We have,
[tex]s=64t-16t^2[/tex]
Substitute s=0, to find the time t when the ball strike the ground.
[tex]0=64t-16t^2[/tex]
[tex]0=16t(4-t)[/tex]
Using zero product property, we get
[tex]16t=0\Rightarrow t=0[/tex]
[tex]4-t=0\Rightarrow t=4[/tex]
Therefore, the ball strike the ground in initial condition (t = 0) and after 4 seconds (t = 4).
(b)
Now, s > 48, to find the time t when the ball will be more than 48 feet above the ground.
[tex]64t-16t^2\geq 48[/tex]
[tex]0> 16t^2-64t+48[/tex]
Divide both sides by 16.
[tex]0> t^2-4t+3[/tex]
[tex]0> t^2-t-3t+3[/tex]
[tex]0> t(t-1)-3(t-1)[/tex]
[tex]0>(t-1)(t-3)[/tex]
Related equation is [tex](t-1)(t-3)=0[/tex]. Zeroes are t=1,3. These two number divide the number line is three parts. (-∞,1),(1,3),(3,∞)
[tex]0>(t-1)(t-3)[/tex] inequality is true for only (1,3).
It is only possible when t lies in the interval (1,3).
Therefore, the ball will be more than 48 feet above the ground between 1 and 3 seconds.
At a convenience store, you have a choice of five diet drinks, 10 regular drinks, six bags of fat-free chips, and 10 bags of regular chips. What is the probability that you will buy a regular drink and a regular bag of chips?
Answer:
I guess that the purchase is at random, then let's see the possible options:
5 diet drinks.
10 regular drinks.
Total drinks = 15
6 bags of fat-free chips
10 bags of regular chips.
Total chips = 16.
Probability of buying at random, a regular drink is equal to the number of regular drinks divided the total number of drinks:
p1 = 5/15 = 1/3
Probability of buying at random a regular bag of chips, we use the same reasoning as before.
p2 = 6/16 = 3/8
The joint probability will be equal to the product of the individual probabilities:
P = p1*p2 = (1/3)*(3/8) = 1/8.
Answer:
the answer is 5/12
Step-by-step explanation:
If r varies directly as t and r = 6 when
t = 11, find the value of t when r= 24
Answer:
t=44
4.6=24
4.11=44
r=6
t=11
4r=24
4t=44
Cypress Middle School wants to have a fundraiser to buy art supplies. Fundraiser A will give the school $1.50 for each order placed plus $75 as a bonus. Fundraiser B will give the school $3.00 for each order placed, but no bonus. How many orders must be placed in order for the total amount of money earned by each fundraiser to be the same? a 150 b.5 c.17 d.50
Answer:
50
Step-by-step explanation:
Let the number of orders required be x
Fund raiser A , 1.50 for each other plus bonus of 75
for x orders, we have 1.50 * x = 1.50x
Add the bonus = 1.50x + 75
Fund raiser B, $3 for each other , no bonus
Total from fund raiser B is 3 * x = 3x
So to make them equal, we ensure that e equate both values;
3x = 1.5x + 75
3x -1.5x = 75
1.5x = 75
x = 75/1.5
x = 50
50 orders will make both funds equal
find the slope of a secant line with the intervals of [0,1]
Answer:
m = N/A
Step-by-step explanation:
Can you give me a curve or something?
Line / passes through the origin and the point (3, 4). What is the slope
a line parallel to linel?
Answer: 4/3
Step-by-step explanation:
Slope of the line = (y2 - y1) / ( x2 - x1)
= (4 - 0) / ( 3 - 0 )
= 4 / 3
Suppose that a number written as a decimal has an infinite number of non-repeating digits after the decimal point. What is this number called?
Oirational
natural
unnatural
rational
Hell yall
Answer:
Irrational
Step-by-step explanation:
The number is called an irrational number.
These numbers have some distinct properties. The number of numbers after the decimal point is infinite. What this means is that it does not terminate. It keeps on repeating.
Also, these numbers cannot be represented as a ratio of two integers i.e two whole numbers. This is because they keep on going without termination.
Lastly is that these numbers do not repeat after decimal. What I mean by this is that they do not keep repeating a particular number after the decimal point. For example in cases like 2.33333; these are infinite too, but they can be represented by the ratio of two whole numbers and in such cases, they are not irrational in their own respect
Substitute the length of the sides (7 in, 25in n)
into the Pythagorean theorem. Then, find the length of the missing side m
(Please with step by step answer)
Answer:
with 2 sides, we can assume that the 25 inch side is the hypotenuse.
7^2 + 25^2 = 49 + 625 = 674
674 is NOT a perfect square so we'll make the 25 side as the hypotenuse.
7^2 +n^2 = 625
n^2 = 625 - 49
n^2 = 576
square root (576) = 24
So the 3 sides are
7 24 and 25
Step-by-step explanation:
Please help me thanks
Answer:
A. Pair 1
Step-by-step explanation:
B is just repositioned, C is a reflection, and D is also a reflection.
Given j || k and m<8 = 150•
What is m<3?
Enter your answer in the box.
M<3=
Answer:
m<8=150
m<3=150÷3=50
|6 - 3| simplify this answer please
Answer:
3
Step-by-step explanation:
the bracket just makes it a positive number so if it was 3-6 then it would still be 3 because of brackets
If the maglev train travels at a constant speed of 480 kilometers per hour for 1/4 hour how far does the train travel ?
Answer:
120 km
Step-by-step explanation:
Multiply the distance traveled by the speed of the train.
1/4 hr × 480 km/hr = 120 km
Angle Z is 21 degrees larger than twice the measure of angle T. If ∠Z and ∠T are supplementary, what is the measure of angle T? *
angle T = x
angle Z = 2x + 21
We know that supplementary angles add up to 180 degrees.
180 = x + 2x + 21
Combine like terms.
180 = 3x + 21
Subtract 21 from both sides.
159 = 3x
Divide both sides by 3
53 = x
angle T = 53 degrees
Prove that: (1 + cos A)^2 - (1 - cos A)^2/
sin^2 A=
4cosec A. cotA
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
cosec x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex]
Consider the left side
[tex]\frac{(1+cosA)^2-(1-cosA)^2}{sin^2A}[/tex] ← expand and simplify numerator
= [tex]\frac{1+2cosA+cos^2A-(1-2cosA+cos^2A}{sin^2A}[/tex]
= [tex]\frac{1+2cosA+cos^2A-1+2cosA-cos^2A}{sin^2A}[/tex]
= [tex]\frac{4cosA}{sin^2A}[/tex]
= 4 × [tex]\frac{1}{sinA}[/tex] × [tex]\frac{cosA}{sinA}[/tex]
= 4cosecAcotA
= right side, thus proven
5. Find the 34th term in the arithmetic sequence 9, 6, 3,
A. 90
B. -90
C.-57
D. 108
Answer:
B. -90
Step-by-step explanation:
a1=9; d=-3
a34=9-3(33-1)=-90
Can somebody help me in math please ?
Answer:
sure
Step-by-step explanation:
Answer:
Sure pooh.
Step-by-step explanation:
Find x: 3x - 14 + 6 - 4 - 2x = 12
Answer:
X = 24
Step-by-step explanation:
Answer:
x = 24
Step-by-step explanation:
3x - 14 + 6 - 4 - 2x = 12
x - 12 = 12
x = 12 + 12
x = 24
HELP QUICK PLEASE
What is the slope of the line that passes through the points (-10, 9)(−10,9) and (-12, 7) ?(−12,7)?
Write your answer in simplest form.
Answer:
1
Step-by-step explanation:
(7-9)/(12-10)= 1
Triangle ABC is a right triangle.
Triangle A B C is a right triangle. Angle A C B is 90 degrees, angle C B A is 31 degrees, and angle B A C is 59 degrees.
What is the relationship between angles A and B?
They are congruent.
They are complementary.
They are supplementary.
There is no relationship between them.
Answer:
they are complementary angles and as thry both are the realeation between angle a and b
The relationship between angles A and B is that, they are complementary. option B
How to determine the relationshipFor angle ACB, the angle is at C = 90 degrees
For angle CBA, the angle is at B = 31 degrees
For angle BAC, the angle is at A = 59 degrees
Note that complementary angles are angles that sum up to 90 degrees
Angle at A = 31 degrees
Angle at B = 59 degrees
Sum of angles A and B = 31 + 59 = 90 degrees
Thus, the relationship between angles A and B is that, they are complementary. option B
Learn more about complementary angles here:
https://brainly.com/question/16281260
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I'm Giving Brainliest
Plz Help! (Don't give me just the answer explain it step by step)
Given f(r)=3r3-3r+1, what is the value of f(2)?
Is this correct? If not, please tell me the correct answer!!!
Answer:
That is correct
Step-by-step explanation:
180° rotation about origin just means that you have to flip the pre-existing image across the x-axis
Good job!
find the perimeter of a triangle on a coordinate grid where a(-3,6), B(2,-6) and C(-3,-6)
Answer:
Step-by-step explanation: AB = 6-2=4 BC = 3 ( 3- ) = 6 ∙
Calulate AC find the formula ~ d = ≅[tex]\sqrt{x} 2-x1) + (x2 - y2) = 3,2 AC = \sqrt[n]{x} (3+3)2 + ( 2 - 6 ) 2 = \sqrt[n]{x} 36 + 16 = \sqrt{} 52 P = 4 + 6 \sqrt{} 52 17.21 to dec. places\\[/tex]traslate 2 units right and 5 untis up
Answer:
The slope would be positive 5/2
Step-by-step explanation:
When finding slope you do rise over run. Or rise/run.
This is rise |
This is run __
So going up or down is a rise.
And going left or right is a run.
Did this help??
Evaluate a+4 when a=7 but how do you do it doe?
Answer:
11
Step-by-step explanation:
if a = 7
7 +4 = 11
or
a + 4 = 11
Hope this helps! Please mark Brainliest!
Write the sentence as an absolute value inequality, then solve the inequality.
Half of a number n is at most 5 units from 14.
18≤n≤38 is absolute value inequality for the problem
A square window has an area of x2 + 22x + 121 square feet. Find the length of one side of the square.
A) (x + 11) feet
B) (x – 11) feet
C) (x – 6) feet
D) (x + 6) feet
x + 11 ft
Step-by-step explanation:
x² + 22x + 121 ft² = area of square
x² + 11x + 11x + 121 ft² = side²
x(x + 11) + 11(x + 11) ft² = side²
(x + 11)(x + 11) ft² = side²
(x + 11)² ft² = side²
x + 11 ft = side²
can I have the answer for c pleaseee ASAP
Answer:
a) -1/3 b) 3 c) y=3x-10
Step-by-step explanation:
Solve for x: −2(x + 3) = −2(x + 1) − 4.
A. 2
b. 3
C. All real numbers
D. No Solutions
Answer:
I got No solution, D.
Step-by-step explanation:
i would like to keep track of how much candy i eat each day remember the y axis is vertical and axis is horizontal
Answer:then the days would be on the x axis (dependant variable) and the Amount of candy would be on the y axis(independent variable=something that can be changed)
Pls does anyone know the answer I need it fast
Answer:
The first one is 120 and the second is 200
Step-by-step explanation:
The range value is the domain value times 40
What is the equation of this line?
[tex]y = \frac{3}{4}x -3\\[/tex]
y = 4x - 3
y intercept is -3.
Slope is 4.