If v(t) and h(t) denote the ball's velocity and height at time t, respectively, then we have h(0) = 1.2 m and v(0) = 58 m/s.
The ball is in free fall after being tossed, so its acceleration is constant at any time t :
[tex]a(t) = -9.8 \dfrac{\rm m}{\mathrm s^2}[/tex]
By the fundamental theorem of calculus, the velocity function is given by
[tex]\displaystyle v(t) = v(0) + \int_0^t a(u) \, du[/tex]
Compute the integral:
[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) \int_0^t du[/tex]
[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t - 0)[/tex]
[tex]\displaystyle \boxed{v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t}[/tex]
Similarly, the height function is given by
[tex]\displaystyle h(t) = h(0) + \int_0^t v(u) \, du[/tex]
[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \int_0^t \left(58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t\right) \, du[/tex]
[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) (t - 0) - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t^2 - 0^2)[/tex]
[tex]\displaystyle \boxed{h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) t - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t^2}[/tex]
Answer:
V(t) = 58-9.8t
h(t)=1.2+58t-4.9[tex]t^{2}[/tex]
Step-by-step explanation:
Using the standard formula
a=V f-Vi/t --rearrange
at=V f-Vi
V f=V i + a t
therefore
V(t)=58-9.8t
same with height
H= Hi+Vit+1/2at^2
therefore
h(t)=1.2+58t-4.9t^2
A cell phone company charges a monthly fee plus $0.25 for each text message you send. The monthly fee is $30.00 . You owe $59.50. How many text messages did you send?
Answer:
Excluding the monthly fee of $30 dollars.
Step-by-step explanation:
$30-$59.50 = $29.50
multiply $0.25 by 118 and you'll get exactly $29.50
the answer is " I sent 118 Text messages "
I NEED THE ANSWER ASAP. IM BEING TIMED
The following information is known about a savings account.
Time = 6 years
Interest rate = 1.9%
Principal = $850
What amount of total interest will be earned at the end of year 6?
Answer:
96.90
Step-by-step explanation:
I = PRT
T = 6
P = 850
I = 1.9% = 0.019
I = (850)(0.019)(6) = 96.90 <==
-5(2x -3) + 4x = - 3x + 6
Help me please
You need to find the measure of angle A
Most people don’t do this when I ask these questions
Answer:
Step-by-step explanation:
6x + 5 = 4x + 45
6x - 4x = 45 - 5
2x = 40
x = 20
6x + 5 = 6.20 + 5 = 125°
When a cold drink is taken from a refrigerator, its temperature is . After minutes in a room its temperature has increased to . What is the temperature of the drink after minutes
Answer:
Step-by-step explanation:
5) Which table does NOT represent a function?
Answer: D does not represent a function.
Step-by-step explanation: I hope this helps you out.
19. There are 1,200 students at Thomas School, Each
day, students take 5 classes and teachers teach 4 classes. If each class
has 30 students and 1 teacher, how many teachers teach at the school?
Answer: 40 teachers
Step-by-step explanation:
Do 1,200 Divided by 30 because thats the amount of students
Identify the slope and y-intercept of the
equation 2x + 5y = 20
Answer:
Slope = - ⅖
Y-intercept = (0, 4), where b = 4
Step-by-step explanation:
Given the linear equation in standard form, 2x + 5y = 20, where A = 2, B = 5, and C = 20:
Start by transforming the standard equation into its slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.
Subtract 2x from both sides:
2x -2x + 5y = - 2x + 20
5y = -2x + 20
Divide both sides by 5 to isolate y:
[tex]\frac{5y}{5} = \frac{-2x + 20}{5}[/tex]
y = - ⅖x + 4 ⇒ This is the slope-intercept form where the slope, m = -⅖, and the y-intercept, b = 4. The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. Therefore, the y-intercept is (0, 4).
How many pounds is a pepper?
I really need to know.
Answer:
4-5 ounces or 113-142 grams
Step-by-step explanation:
Blue10
Brown15
Green5
Red10
Yellow12
The table shows how many of each color candy came out of a bag. What is the probability of choosing a brown candy?
a dress which sosts $180 is being sold at a discoundof 10% the amount of the discount is
Answer:
The discount is $18.
NEED ASAP PLSS
5+2x = 2x+6
You want to simplify ? or just find the value ?
1) Order the numbers from least to greatest.
=2
3
3.5
2.5
2
NI
PLEASE HELP
Answer:
2, 2, 2.5, 3, 3.5
Step-by-step explanation:
Answer:
2, 2.5, 3, 3.5
Even thought there are two "2's", you only list one making it 2,2.5,3,3.5 instead of 2,2,2.5,3,3.5
PLZ ANSWER QUICK. WILL GIVE BRAINLY. NO EXPLANATION NEEDED.
Answer:
None of these are correct
Step-by-step explanation:
XZ = XY + YZ = 48 + 50 = 98
I need help with this question
Write 27% as a fraction.
Answer:
27/100
Step-by-step explanation:
27%= 0.27= 27/100 which cannot be reduced
Answer:
27/100
Step-by-step explanation:
27% = 27/100
2/3 of 40
3/5 of 45
Yeah so answer that
Hi,
[tex] \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} [/tex]
[tex] \frac{2}{3} \times \frac{40}{1} = \frac{80}{3} [/tex]
2/3 of 40:
80/3
[tex] \frac{3}{5} \times \frac{45}{1} = \frac{135}{5} = 27[/tex]
3/5 of 45:
27
✅(. ❛ ᴗ ❛.)
Answer:
A= 26.67
B= 27
Step-by-step explanation:
2/3 x 40 = 26.67
(2×40= 80÷3 = 26.67)
and...
3/5 x 45 = 27
(3×45= 135÷5=27)
Hope this helped you- have a good day bro cya)
$1.800 is invested in account that earns 6% interest compounded quarterly, how much will this
investment be worth after 6 years Given : A =
P(1 + 3) "4
8
9
$2.573.11
$1,968.20
$7,288.08
$1,252.40
Question 5 (1 point)
Dan bou
Answer:
4 better inbox
Step-by-step explanation:
2x-7=13
What is the answer for x ?
Answer:
The answer will be ( x = 10)
Define power of 10 rule
Answer:
A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.
Step-by-step explanation:
Answer:
Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.
Step-by-step explanation:
Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.
Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10 sec as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.
Write the correct order of the letters to the finish line
Answer:
Write the correct order of the letters to the finish line
Amy drove to her mother's house, which is
204 miles away. If it took her 3 hours, what was
her average speed
Answer: 68 miles per hour 2
204 miles/3 hours = 68 miles per hour
i hope this helps you ok :)
Answer:
68 Miles Per Hour
Step-by-step explanation:
[tex]\frac{204}{3} =68[/tex]
Please help I really need help if right you get Branly please help.
[1] 1/2
- It will be 1/2 as large because of the scale factor
[2] 1/4
- 1/2 * 1/2 = 1/4
[3] (1/2)n
- For every scale factor (n), there will be a chance of 1/2
Have a nice day! - I know I answered this elsewhere, I saw it twice haha
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Josh purchased a DVD for $10.80, before taxes. The price was after a 25% discount. What was the original price of the DVD?
Answer:
$
2.70
Step-by-step explanation:
can someone help me with these 3 pls?
URGENT PLEASE DO!! will give brainliest to first person to answer
29293
Step-by-step explanation:
yes yes !!
5x-4=9x+6 please put explanation
Carl ordered $28 of pizza for dinner. About how much money
does he need, rounded to the nearest ten?
Answer:
30 dollars.
Step-by-step explanation:
What is 28 closer to? 20 or 30?
30.He would have to pay 30$, and would get 2 dollars back in change.
I hope this helped at all.
I thought of a number I called this number n I multiplied my number by the sum of 12 and 18 I added 43 to the result and I got 103 what is n equal to
[tex](n \times (12 + 18)) + 43 = 103[/tex]
[tex]30n + 43 = 103[/tex]
Subtract both sides 43
[tex]30n + 43 - 43 = 103 - 43[/tex]
[tex]30n = 60[/tex]
Divide both sides by 30
[tex] \frac{30n}{30} = \frac{60}{30} \\ [/tex]
[tex]n = 2[/tex]
g(x)=(x-1)^3-1 find the inverse of this function
Answer:
G^−1(x)=3√x+1+1
Step-by-step explanation:
Answer:
[tex]g^{-1}(x)[/tex]= [tex]\sqrt[3]{x+1}[/tex]+1
Step-by-step explanation:
To find the inverse, swap x and y.
g(x)=(x-1)^3-1
-> x=(y-1)^3-1
Solve the equation in terms of y.
x=(y-1)^3-1
x+1=(y-1)^3
[tex]\sqrt[3]{x+1}[/tex]=y-1
[tex]\sqrt[3]{x+1}[/tex]+1=y