13. If a toy rocket is launched vertically upward from ground level with an initial
velocity of 100 feet per second, then its height h after t seconds is given by the
equation h(t) = - 16+ + 100t (if air resistance is neglected).
Answers
Check the picture below.
how long will it take for it to hit the ground, or namely, what is "t" when h(t) is 0.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&100\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases}[/tex]
[tex]h(t)=-16t^2+100t+0\implies h(t)=-16t^2+100t\implies \stackrel{h(t)}{0}=-16t^2+100t \\\\\\ 16t^2-100t=0\implies 4t(4t-25)=0\implies \begin{cases} 4t=0\\ t=0\\[-0.5em] \hrulefill\\ 4t-25=0\\ 4t=25\\ t=\cfrac{25}{4}\\[1em] t=6\frac{1}{4} \end{cases}[/tex]
so h(t) is 0, as you saw on the picture, at two instances, once it was on the ground, 0 seconds, or t=0, and then t = 6.25, or 6 seconds and some change later.
Related Questions
I need help finding x
Answers
Answer:
Step-by-step explanation:
#19.
(7x - 2)° + (10 - 3x)° = 180°
(7x - 3x) + (10 - 2) = 180
4x = 172
x = 43
#21.
(6x - 144)° = (2x)°
4x - 2x = 144
2x = 144
x = 72
Please help me due today
Answers
Answer:
if m∠1 = 30° then m∠3 = 30° as they are parallel to each other and that is why they will have same angles.
therefore m∠3 = 30°
extra's:
→ m∠2 = m∠4 =
→ (360-30*20)/2
→ 150°
...............................
See here
m<1 and m<3 are opposite angles to eachother.
And we know that opposite angles are equal
so
m<1=m<3 m<3=30°1. A pound of fertilizer pellets will cover about 300 square feet of lawn. Find how many pounds of fertilizer will be
needed for a rectangular patch of grass that measures 45 feet by 45 feet.
Answers
Answer:
6.75 if exact 7 if rounding up
Step-by-step explanation:
1lb=300ft^2
45x45=2,025
2,025/300=6.75
Lainley wraps a cube-shaped present in a box that has a volume of 729 inches. Neglecting any overlap, how many square inches of wrapping paper does Lainey use to cover all of the sides of the box? Marking brainliest
A. 81 in.^2
B. 162 in^2
C. 324 in^2
D. 486 in^2
Answers
The area of a cube-shaped present in a box Lainley wraps is A. 81 in²
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A box that has a volume of 729 inches.
First we'll prime factorize 729.
729 = 3×243 = 3×3×81 = 3×3×3×3×3×3.
If we take the cube root of 729 it would be 3×3 = 9.
So, It is a cube with a side length 9.
Now, We know area of a cube is side².
Therefore, The area of this cube is 9² = 81 in².
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Which set of points is a function?
A- (0,3),(2,4),(0,6)
B- (1,2),(2,2),(3,2)
C- (1,4),(2,5),(1,6)
D- (2,3),(-2,4),(2,6)
Answers
Answer:
B
Step-by-step explanation:
This is a really simple topic. All you need to do when seeing these ordered pairs is see which has x-values that don't repeat. Over here, we can see that that is B, so B is the correct option.
Alexandra is following a recipe that requires three fourths cup of water. She needs to make 10 servings. How many cups of water does Alexandra need?
one and one fifth cups
three and one fourth cups
seven and two fourths cups
eight and two thirds cups
Answers
3/4 • 10 = 30/4 = 7 2/4
So she needs seven and two fourths cups of water.
Answer:
3/4 • 10 = 30/4 = 7 2/4
What are the factors of x2 – x – 6? Check all that apply. X – 6 x 6 x – 3 x – 2 x 2 x 1 x – 1.
Answers
Answer:
The factors are x-3 and x+2, and the roots are 3 and -2.
Step-by-step explanation:
x^2-x-6 can be factored in the following way:
(x-3)(x+2)
The factors are x-3 and x+2, and the roots are 3 and -2.
Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: (x-3) and (x+2)
How to factorize a quadratic polynomial with single variable?Quadratic polynomial with single variables are expressible in the form
[tex]ax^2 + bx + c[/tex]
where x is the variable and a,b,c are constants.
Its factored form is
[tex]\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})[/tex]
For the given case, the expression given to us is [tex]x^2 - x - 6[/tex]
Comparing it with the standard form of quadratic expression [tex]ax^2 + bx + c[/tex], we get: a = 1. b = -1. and c = -6
Using the aforesaid formula, we get:
[tex]=\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})\\\\=\dfrac{1}{4}\times(2x -1 - \sqrt{1 +24})(2a -1 + \sqrt{1 + 24})\\\\=\dfrac{1}{4} \times (2x - 1-5)(2x - 1 + 5)\\\\=(x -3)(x+2)[/tex]
Thus, The factors of given expression are: (x-3) and (x+2)
Learn more about factors here;
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Grace got a haircut for $26.95, bought three shirts on sale for $18.50 each and a pair of jeans for $48, and purchased two CDs for $18.50 each. Round each amount to the nearest ten dollars to find a reasonable estimate of how much Grace spent.
Answers
26.95 + 18.5 * 3 + 48 + 18.5 * 2
18.5 * 3 = 55.5
18.5 * 2 = 37
37 + 55.5 + 48 + 26.95 = 167.45
= $167.5
The question is in the picture please give me all the answers
Answers
a) 1/4
b) 1/8
c) 1/81
Step-by-step explanation:
I used the negative exponent rule:
b^-n = 1/b^n
What is the surface area of the sphere, in square meters?
Possible answers:
A. Not enough information is given to calculate this surface area.
B. 804
C. 2144
D. 201
Answers
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies SA=4\pi (8)^2\implies \stackrel{using~\pi =3.14}{SA\approx 804}[/tex]
∠1 and ∠2 are vertical angles. ∠2 has a measure of 63°.
What is the measure of ∠1?
Answers
Answer:
63 degrees
Step-by-step explanation:
vertical angles are conruent
Hope this helps! :)
A small airplane can hold 13 people per trip. How many trips would it take the airplane to transport 9,165 people?
Answers
You have to divide
its 9,165 divided by 13
[tex]\frac{9165}{13}[/tex] = 205
Teddy it takes 205 trips
to transfer 9,165 in a plane that can hold 13 people per trip
Hope I helped ^-^
The Hamden board of education wants to know how the community feels about building a new media center for the middle school. They called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. Which of the following are true of the sample of 40 voters? Check all that apply.
Answers
Answer:
The true statements about the sample described in the scenario above are:
The sample should be larger to give more reliable information.
The sample size is too small to represent the population.
The sample size is too small and can lead to false inferences.
Step-by-step explanation:
The sampling technique employed is a systematic random sampling where samples are chosen at every specified interval. Hence, the sample is randomly selected.
Help !! To avoid working with messy fractions when solving a quadratic equation by completing the square, the b value should be:
negative
zero
odd
even
Answers
Answer
Even
Step-by-step explanation:
I got the answer from my teacher.
How many solutions exist for the given equation?3x + 13 = 3(x + 6) + 1
Answers
Answer:
0
Step-by-step explanation:
3x+13=3(x+6)+1
Expand:
3x+13=3x+18+1
Simplify:
3x+13=3x+19
Subtract 13 from both sides:
3x+13-13=3x+19-13
Simplify:
3x=3x+6
Subtract 3x from both sides:
3x-3x=3x-3x+6
0=6
Since the sides are not equal there are no solutions to this problem
Please help me asap
I will give you 50 points
Answers
Answer: C
Step-by-step explanation:
Find the value of x if the figure is a regular polygon.
Answers
taking a peek at this regular polygon hmm is has 6 sides, so is a hexagon, ok.
[tex]\textit{sum of all interior angles in regular polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies 6\theta =180(6-2) \\\\\\ 6\theta =180(4)\implies 6\theta =720\implies \theta =\cfrac{720}{6}\implies \boxed{x=\theta =120}[/tex]
Learning Task 5 : In your answer sheet , prove the theorem , using the given below . if a quadrilateral is inscribed in a circle , then its opposite angles are supplementary." Given : Quadriateral ABCD is inscribed in OE Prove : ∠ABC and ∠ABC are supplementary ∠DAB and ∠DCB are supplementary
Answers
Answer: quadrilateral is inscribed in a circle , then supplementary . " its opposite angles are Given : Quadriateral ABCD is inscribed in OE Prove : ABC
Step-by-step explanation:
i am not smart pls help!!!
Answers
Answer:
yes, the 10 ft wave is an outlier
Step-by-step explanation: smarts
hope this helps :))
Answer:
the 10ft wave is the outlier
Step-by-step explanation:
hope this helps
Helpppp asapppppppppppp
Answers
Answer:
the first one
4a + 3a =7a
the second one
4a+4b
Answer:
1. 7a
2. 4a + 4b
Step-by-step explanation
1. (a x 4) = 4a
(a x 3) = 3a
4a + 3a = 7a
2. question 2 is correct
The height of a cone is 10ft. The area of the base is 22ft. Compute the volume of the cone
Answers
[tex] {73.33ft}^{3} [/tex]
Step-by-step explanation:
[tex]v = \pi {r}^{2} \frac{h}{3} [/tex]
[tex]\pi {r}^{2} = {22ft}^{2} [/tex]
[tex]v = 22 \times \frac{10}{3} [/tex]
[tex]v = 22 \times 3.33[/tex]
[tex]v = {73.33ft}^{3} [/tex]
The answer for y = -x + 4
Answers
Answer:
x=4
y=4
m=-1
b=4
no relatibe extrema
no horizontal asymtotes
netheir even nor odd
Step-by-step explanation:
please help me quick with it
Answers
Answer:
is there any examples/
Step-by-step explanation:
what does "what is the difference between ½+¼ and ¾+¼" mean
Answers
Answer:
It means: 1/2+1/4 - 3/4+1/4
Find the two numbers whose sum is 67 and whose difference is 3.
Answers
Answer:
32;35
Step-by-step explanation:
a+b=67
a-b=3 => a=3+b
=>instead of a we write 3+b =>
a+b=67 => 3+b+b=67 => 2b=64 => b=32
=> a = 3+b=> a=32+3=35
I need help asap the question is in the picture.
Answers
Answer:
The second one between 2 and 3
Step-by-step explanation:
Sq root of 7 = 2.65
Answer:
2nd number line represents √7 best
Step-by-step explanation:
Method 1
√7 ≈ 2.65
Therefore, the 2nd number line represents √7 best
(the one with the dot between 2 and 3)
Method 2
√1 = 1
√4 = 2
√9 = 3
Therefore, as √7 is between √4 and √9, the solution is somewhere between 2 and 3.
What is the range of the function F(x)= 2cos(x-3)?
Answers
Answer:
The range is −5≤y≤−1 - 5 ≤ y ≤ - 1 .
range: [-2, 2]
Solving Steps:
Find properties of the trigonometric
function: → range: [-2, 2]
I hope this helps you :)
(SHOW UR WORK I DONT FEEL LIKE DOING THIS XDD BUT THANKSS) 98.73 ÷ 15 =
Answers
Answer:
Answer 6.582
Step-by-step explanation:
0 6. 5 8 2
1 5 9 8. 7 3 0
− 0
9 8
− 9 0
8 7
− 7 5
1 2 3
− 1 2 0
3 0
− 3 0
0
Hope its understandable ._.
how much is 20 cookies for 15.25 dollars
Answers
Answer:
305 cookies
Step-by-step explanation:
Well, we know that each cookie is $15.25( that is expensive!?) so we multiply it and get 305 (15.25 x 20)
YW!! Have a nice day!
There were 24 teams at a soccer tournament. In all, 12 teams wore red shirts, 6 teams wore blue shirts, 4 teams wore orange shirts, and 2 teams wore white shirts.
Answers
Answer:
1rst one is 3:2 the second one is 1:2 and third is 1:12 if i remember
Step-by-step explanation:
The total number of teams at the soccer tournament was 24.
The information about the number of teams and the shirts they wore at the soccer tournament.
To summarize:
12 teams wore red shirts
6 teams wore blue shirts
4 teams wore orange shirts
2 teams wore white shirts
To find the total number of teams, add up the number of teams for each shirt color:
Total Teams = 12 (Red) + 6 (Blue) + 4 (Orange) + 2 (White) = 24 teams
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