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
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°
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:
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.
-5(2x -3) + 4x = - 3x + 6
a dress which sosts $180 is being sold at a discoundof 10% the amount of the discount is
Answer:
The discount is $18.
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)
URGENT PLEASE DO!! will give brainliest to first person to answer
29293
Step-by-step explanation:
yes yes !!
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
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.
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
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?
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]
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
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).
5x-4=9x+6 please put explanation
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:
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]
How many pounds is a pepper?
I really need to know.
Answer:
4-5 ounces or 113-142 grams
Step-by-step explanation:
NEED ASAP PLSS
5+2x = 2x+6
You want to simplify ? or just find the value ?
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
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
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 <==
I need help with this question
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
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 "
can someone help me with these 3 pls?
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.
$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:
Write the correct order of the letters to the finish line
Answer:
Write the correct order of the letters to the finish line
2x-7=13
What is the answer for x ?
Answer:
The answer will be ( x = 10)