Answer:
A.) 24.08 seconds
B.) 825.42 metres
Step-by-step explanation:
function of time is given as
h ( t ) = − 4.9 t 2 + 118 t + 115 .
Where a = -4.9, b = 118, c = 115
Let's assume that the trajectory of the rocket is a perfect parabola.
The time t the rocket will reach its maximum height will be at the symmetry of the parabola.
t = -b/2a
Substitute b and a into the formula
t = -118/-2(4.9)
t = 118/9.8
t = 12.041 seconds
Since NASA launches the rocket at t = 0 seconds, the time it will splash down into the ocean will be 2t.
2t = 2 × 12.041 = 24.08 seconds
Therefore, the rocket splashes down after 24.08 seconds.
B.) At maximum height, time t = 12.041s
Substitute t for 12.041 in the function
h ( t ) = − 4.9 t 2 + 118 t + 115
h(t) = -4.9(12.041)^2 + 118(12.041) + 115
h(t) = -4.9(144.98) + 118(12.041) + 115
h(t) = -710.402 + 1420.82 + 115
h(t) = 825.42 metres
Therefore, the rocket get to the peak at 825.42 metres
A small family home in Tucson, Arizona has a rooftop area of 1967 square feet, and it is possible to capture rain falling on about 61.0% of the roof. A typical annual rainfall is about 14.0 inches. If the family wanted to install a tank to capture the rain for an entire year, without using any of it, what would be the required volume of the tank in m3 and in gallons
Answer:
Required of volume of tank = 39.62 m3 or 10471.18 gallons
Step-by-step explanation:
Total volume of water collected = Annual Rainfall * Useful Area
Total volume of water collected = 1199.87 * 1.1667
Total volume of water collected = 1399.89 ft3
---1 ft3 = 7.48 gallons
Hence, total volume of water collected in gallons = 1399.89 * 7.48 = 10471.178 gallons
----1 ft3 = 1/35.315 m3 = 0.0283 m3
Therefore total volume of water collected in m3 = 1399.89 * 0.0283 = 39.6169 m3
Workings
Useful area = 61% of 1967
Useful area = 0.61 * 1967
Useful area = 1199.87 sq/ft.
Annual rainfall = 14 inch = 14/12 month
Annual rainfall = 1.1667 ft.
Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins to solve the equation for h but runs out of time. Her partial work is shown below:
Answer: ( L+W)
Step-by-step explanation:
is 3.45445554 rational or irrational?
Answer:
3.45445554 is irrational.
Hope this helps!
Please can you mark as Brainliest!
Step-by-step explanation:
Answer:
[tex]3.45445554[/tex]
Rational number ✔️
rational number is the number that can form a fraction
Joseph is building a doghouse. He wants it to be a replica of his house, but smaller. His house is 18 feet tall. He needs the doghouse to be between 3 and 4 feet tall. Therefore, the doghouse should be what percentage of the size of his house? (Provide a range
Answer:
19%
Step-by-step explanation:
3/18=.19 and something else
3.5/18=.19 and something else
4/18= .19 and something else
18 * 19%= somewhere in between 3 and
When 3.9 is added to 6 times a number, the result is 57.3. Find the number
Answer: 8.9
Step-by-step explanation:
Let x = the number you are finding
SOLVE:
3.9+6x=57.3 ⇔ Given
6x=53.4 ⇔ subtract 3.9 on both sides
x=8.9 ⇔ Divide 6 on both sides
ANSWER:
The number is 8.9
6 2/3 miles ➕ 4 11/16 =
Answer:Add up fractions. The answer is 11 17/48
Step-by-step explanation:
hope this helps!
Answer: 11 7/20 miles
Step-by-step explanation: Add 6 and 4 to get 10, and add 2/3 and 11/16 to get 1.35 or 1 7/20 to get 11 7/20.
Have a nice day! :)
Eliana has $2600 to invest for 6 months. If she needs the money to earn $104 in that time, at what rate of simple interest must Eliana invest?
What equation would I use to solve this?
Answer:
8%
Step-by-step explanation:
I=Pr
104=2600*r/2
r/2=104/2600
r=(104/2600)(2)
r=0.08=8%
Eliana must invest at a rate of 0.33% of simple interest to earn $104.
Given,
Eliana has $2600 to invest for 6 months.
If she needs the money to earn $104 in that time.
We need to find at what rate of simple interest must Eliana invest.
What is the formula for simple interest?It is given as:
SI = PRT / 100
P = principal amount
R = rate
T = time in years.
Find the rate of interest.
We have,
Simple interest = PRT / 100
SI = $104
T = 6 months
Convert it into years.
12 months = 1 year
6 months = 6/12 years
T = 1/2 years
$104 = ($2600 x R x 1/2) / 100
104 = (2600 x R x 1/2) / 100
100 x 104 = 2600 x R x 12
R = (100 x 104 ) / (2600 x 12)
R = 104 / 312
R = 0.33 %
Thus the rate of simple interest is 0.33%
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Which rule defines the function in the graph? Two line segments on a coordinate plane that do not meet. The first segment begins at negative 3 comma negative 4, inclusive, and ends at 1 comma zero, non inclusive. The second segment begins at 2 comma 3, inclusive, and ends at 4 comma negative 3, inclusive. Group of answer choices f(x)={ x−1, if −3 ≤ x < 1 f(x)={ −3x+9, if 2 ≤ x ≤ 4 f(x)= { x−1 , if −3 < x ≤ 1 f(x)= {−3x+9 , if 2 < x < 4 f(x)={ x−1, if −3 ≤ x < 1 f(x)={ x−3, if 2 ≤ x≤ 4 f(x)={x−1, if −3 < x ≤ 1 f(x)={x−3, if 2 < x < 4
Answer:
The correct option is;
f(x) = {x - 1 if -3 ≤ x < 1 f(x) = {-3·x + 9, if 2 ≤ x ≤ 4
Step-by-step explanation:
The given coordinates of the points are;
For the first segment
Beginning point [-3, -4] (inclusive)
Endpoint (1, 0), (noninclusive)
For the second segment
Beginning point [2, 3] (inclusive)
Endpoint [4, -3] (inclusive)
The equation of the first segment is therefore;
y - 0 = (0 + 4)/(1 + 3)×(x - 1) = 1 × (x - 1)
y = x - 1
The equation of the second segment is found as follows;
y + 3 = (-3 - 3)/(4 - 2)×(x - 4) = -3 × (x - 4)
y + 3 = -3 × (x - 4) = -3·x + 12
y = -3·x + 12 - 3 = -3·x + 9
Therefore, we have;
f(x) = {x - 1 if -3 ≤ x < 1 and f(x) = {-3·x + 9, if 2 ≤ x ≤ 4
Certain investments compound interest at different intervals. What effect does the size of the compounding interval have
on the yield of the investment?
a. Investments with smaller compounding intervals have a higher yield, because the interest
earned is reinvested more quickly and thus gains compound interest more quickly.
b. Investments with smaller compounding intervals have a lower yield, because the interest earned
is smaller at each interval.
c. The size of the compounding interval does not affect the total yearly interest percentage rate and
only exists for bookkeeping purposes.
d. Investments with smaller compounding intervals have a lower yield, because the bank charges
a small fee every time interest is compounded.
Answer:
Option A: Investments with smaller compounding intervals have a higher yield, because the interest earned is reinvested more quickly and thus gains compound interest more quickly
Step-by-step explanation:
Compounding could be done monthly, quarterly, semiannually or annually. Compound interest is simply when we add the interest to the principal sum of a loan or amount deposited. It's also referred to as interest which is accrued on interest.
The compound interest that will be earned mainly depends on the frequency of compounding. Now compounding could be done monthly, quarterly, biannually or annually. Now, If we compound monthly, we will have a higher interest return than if we compounded annually.
Thus, looking at the options, the correct one is Option A
Answer:
a
Step-by-step explanation:
A perfect square ends with the same two digits. How many possible values of this digit are there?
Answer:
A perfect square is a whole number that is the square of another whole number.
n*n = N
where n and N are whole numbers.
Now, "a perfect square ends with the same two digits".
This can be really trivial.
For example, if we take the number 10, and we square it, we will have:
10*10 = 100
The last two digits of 100 are zeros, so it ends with the same two digits.
Now, if now we take:
100*100 = 10,000
10,000 is also a perfect square, and the two last digits are zeros again.
So we can see a pattern here, we can go forever with this:
1,000^2 = 1,000,000
10,000^2 = 100,000,000
etc...
So we can find infinite perfect squares that end with the same two digits.
What is the value of y?
Answer:
A-54
Step-by-step explanation:
triangle angle total is 180° the subtract 72 is 108 and divide by 2 is 54
Answer:
A. 54°
Step-by-step explanation:
a triangle is 180°.
180-72 = 108
there's 2 y's so you'd divide by 2.
108/2 = 54
-3(-5)+7y=5(-5)+2y solve for y
Answer:
-2
Step-by-step explanation:
-15+7y=-25+2y
7y-2y=-25+15
5y= -10
5y/5= -10/5
y= -2
Answer:
y= -17/5 or -3.4
Step-by-step explanation:
-8+7y= -25+2y
5y= -17
y= -17/5 or -3.4
5n +5y+5n+6a+2d
Can You intelligent people please help me with this
Answer:
6a+2d+10n+5
Step-by-step explanation:
Answer:
I believe you're trying to simplify if so then the answer is
6 a + 2d + 10n + 5y
if thats not what you're doing lmk what it is you are doing and i will help
Step-by-step explanation:
In a triangle the first angle is greater than the second angle by 18 degree and less than the third angle by 10 grade. Express all the angles in grade.
Answer:
The 3 angles are 62 2/3, 44 2/.3 and 72 2/3 degrees.
Step-by-step explanation:
let x be the first angle then the the second angle is x - 18 and the third angle = x + 10
The 3 angles add up to 180 so:
x + x - 18 + x + 10 = 180
3x = 180 + 18 - 10 = 188
x = 188/3 = 62 2/3 degrees.
x - 18 = 44 2/3
x + 10 = 72 2/3.
If m<2 =47°, then what is m<6? How do you know?
8÷2(2+2) is 16 right or is it 1
the answers 16 if you need an explanation then ill comment one.....!
Answer:
16
Step-by-step explanation:
8 :2 ×(2 +2) =
4 ×4 =
16
Solve -6(4-x)≤-4(x+1) for x
No silly answers please.
Answer:
x≤2
Step-by-step explanation:
Answer:
x ≤ 2
Step-by-step explanation:
well, -6 x 4 = -24
-6 x X = -6x
so far, we have -24 -6x ≤-4(x+1)
-4 x X = -4x
and -4 x 1 = -4 , so we now have -24 -6x ≤ -4x + -4
now we subtract x on one side, and to the other side as well, and you do the same for the numbers!
4(3x - 3) = 12 -36x
Please solve. For a project making sure i solved it right :)!
Answer:
x=1/2, x=0.5
Step-by-step explanation:
4(3x-3)=12-36x
12x-12=12-36x
12x+36x=12+12
48x=24 (Then, divide both sides by 48)
The answer is x=1/2, x=0.5
Liam bought pizza and wings for 27.58 how much change should liam receive if he gave the clerk three $10 bills
Answer:
$2.52
Step-by-step explanation:
i did it
The area of the Pacific Ocean is more than 60 million square miles.
What is that in scientific notation?
6x 10^-7
6x10^7
60 x 10^-6
60x10^6
Answer:
60x10^6
Step-by-step explanation:
Need help please I will give brainliest
Answer:
i believe your answer would be 5 and 3, FD
Step-by-step explanation:
please help me asap
A rectangular plot of land measures .25 miles In width and .75 miles in length. Find the area of the plot in square feet
Answer:
1,875
Step-by-step explanation:
by the way next time use a calculator not in a mean way ^^
Evaluate f(x)=-2×+5 for f(-5)
f(-5) = 15 (A)
Step-by-step explanation:f(x) = - 2x + 5
replace x = - 5
f(-5) = -2(-5) + 5
(-)(-) = +
f(-5) = 10 + 5
f(-5) = 15 (A)
f(-5) = -2(-5) + 5
(-)(-) = +
f(-5) = 10 + 5
f(-5) = 15 (A)
10 times as much as blank hundred is 70 hundreds or blank thousands
Answer:
10 times as much as 7 hundred is 70 hundreds or 7 thousands.
Step-by-step explanation:
The question given is:
10 times as much as _____ hundreds is 70 hundreds or _____ thousands.
Dividing the question into two fractions, we have:
10 times what is 70 hundreds?
What is 70 hundreds in thousands?
10 x 7 hundred = 10 x 700 = 70 hundreds
Recall that 70 hundreds = 70 00
70 hundreds = 70 00 = 7 thousands = 7 000
Therefore, the question can be written as:
10 times as much as 7 hundreds is 70 hundreds or 7 thousands.
Are there any maximums or minimums on the function [tex]\sqrt[3]{x}[/tex] ?
The equation 3x − 6 = 2(x + 4) has A. one B. no C. Infinitetly many solution(s).
Answer:
x=14?
Step-by-step explanation:
2(x+4)=2x+8, so 3x-6=2x+8. Subtraxt 2x from each side to get x-6=8. Then add 6 to both sides to get x=14
Answer:
One solution
Step-by-step explanation:
3x-6 = 2(x+4)
3x-6=2x+8
3x-2x-6=8
x-6=8
x=14
Irina wants to tile her floor using the translation shown below. Which is the rule for this translation? T–3, 2(x, y) T2, –3(x, y) T3, 2(x, y) T–2, 3(x, y)
Answer:
The answer is A, -3.2(x y).
Step-by-step explanation:
I thought the answer was D but I took the test and the answer ended up being A. (Brainliest?)
The rule for this translation is: T-3.2(x y). (Option A). This rule states that the original dimensions (ABCD) must move -3 units to the left and 2 units up to form A'B'C'D'.
What is a translation?Where tach point in a figure is moved the same distance in the same direction using a sort of transformation, this is known as translation.
Thus, examining the position of the old shape and the new, it is correct to indicate that the right translation given the coordinates is option A.
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Help please its timed
Answer:
15
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
2² + 6(3) - 7
Step 2: Evaluate exponents
4 + 6(3) - 7
Step 3: Evaluate parenthesis (multiply)
4 + 18 - 7
Step 4: Add
22 - 7
Step 5: Subtract
15
NEED ANSWER ASAP
Select the graph that best represents the "FIGURE."
If a segment joins the midpoints of two sides of a triangle, its length is one-half the length of the third side.
Answer:
I pretty sure its A (the first choise)
Step-by-step explanation:
I put a comment about it later if its wrong