Answer:
Chris will take 0.75 seconds to return to his starting height of 10 feet.
Step-by-step explanation:
Let the height of Chris be represented by [tex]h(t) = -16\cdot t^{2}+12\cdot t +10[/tex], where [tex]h(t)[/tex] is the height in feet and [tex]t[/tex], the time in seconds. First, we equalize the formula to a height of 10 feet and simplify the resulting expression, that is:
[tex]-16\cdot t^{2}+12\cdot t +10 = 10[/tex]
[tex]-16\cdot t^{2}+12\cdot t = 0[/tex]
Then, we simplify the expression by algebraic means:
[tex]-16\cdot t\cdot \left(t-\frac{3}{4} \right) = 0[/tex]
Roots of the polynomial are, respectively:
[tex]t = 0\,s\,\lor \,t = 0.75\,s[/tex]
First root represents the initial height of Chris, whereas the second one represents the instant when Christ returns to the same height above the surface of the water. Hence, Chris will take 0.75 seconds to return to his starting height of 10 feet.
what is the value of x?
Answer:
The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa" See: Coordinates.
The Polygons are similar. Find the value of x.
Answer:
13
Step-by-step explanation:
8/2=16/4
=4
x-3=2.5*4
x=10+3
x=13
Write the series using summation notation: -1 +4-9+ 16 - 25+ ...
A cylindrical well has a radius of 10 feet and a height of 15 feet. What
volume of water will it take to fill in the well?
Answer:
Look below.
Step-by-step explanation:
We can use the information provided to plug it into a...
Fomula to find a volume of a cylinder:
V=πr^2h
V=π(10)^2(15)
V≈4712.39ft
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue
Answer:
Use 1.75 cups of blue and 1 cup of yellow
Step-by-step explanation:
The given problem can be placed in the category of ratios and proportions. There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too. Hence adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.
Write the equation of the line which passes through (1, 2) and with slope of −1/3
in standard form.
Answer:
x + 3y = 7Step-by-step explanation:
The equation of a line which passes through (x₁, y₁) and with slope of m in point-slope form:
y - y₁ = m(x - x₁)
m = -¹/₃
(1, 2) ⇒ x₁ = 1, y₁ = 2
Therefore, the equation of the line which passes through (1, 2) and with slope of −1/3 in point-slope form:
y - 2 = -¹/₃(x - 1)
y - 2 = -¹/₃x + ¹/₃ {add ¹/₃x to both sides}
¹/₃x + y - 2 = ¹/₃ {add 2 to both sides}
¹/₃x + y = 2¹/₃ {multiply both sides by 3}
x + 3y = 7
mathematical literacy
[tex]79 \times 85[/tex]
Answer:
6715
Step-by-step explanation:
I hope this helps, :)
Solve for y. 2(2y+6)=28
Answer:
y=4
Step-by-step explanation:
2(6 + 2y) = 28
(6 x 2 + 2y x 2) = 28
(12 + 4y) = 28
12 + 4y = 28
12 + -12 + 4y = 28 + -12
12 + -12 = 0
0 + 4y = 28 + -12
4y = 28 + -12
28 + -12 = 16
4y = 16
16\4
y = 4
A middle school has 200 boys and 300 girls enrolled in the seventh-grade. The principal randomly selects 45 seventh-grade students to take a lunch survey. How many of the seventh-grade students selected for the survey should the principal expect to be boys?
Answer:18
Step-by-step explanation:
Given
The school has 200 boys and 300 girls
The ratio of boys and girls is 2:3
If 45 seventh grade students are selected then the ratio of boys and girls remain the same
suppose there are 2x boys and 3x girls, such that ratio is 2:3
[tex]\Rightarrow 2x+3x=45\\\Rightarrow 5x=45\\\Rightarrow x=9[/tex]
No of the boys are [tex]2x=2\times 9=18[/tex]
Answer:
18
Step-by-step explanation:
what the another person said
3x = -6у + 3
2y = -x+1
Answer:
3x = -6у + 3 and 2y = -x+1 are the same
i dont know what the question is but this should help. they are the same line on a graph
Step-by-step explanation:
3x = -6y + 3
2y = -x + 1 adding x on both sides and subtracting 2y on both sides
x = -2y + 1 multiply by 3
3x = -6y + 3
Rewrite the following problems using exponent rules. Then, solve using logarithms.
1. 3(0.99)4t = 15
2. 4(1.01)3 + t = 8
9514 1404 393
Answer:
1. 3(0.96059601^t) = 15; t = -40.03
2. 4.121204(1.01^t) = 8; t = 66.66
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
The solution for an exponential problem using logarithms is ...
a·b^x = c ⇒ log(c/a)/log(b) = x
_____
1. Rewrite: (3)(0.99^4)^t = 15 ⇒ 3(0.96059601^t) = 15
Solution: t = log(15/3)/log(0.96059601) ≈ -40.03
__
2. Rewrite: 4(1.01^3)(1.01^t) = 8 ⇒ 4.121204(1.01^t) = 8
Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66
Please help I really don’t understand this question
Answer:
I will explain it to you in a jiffy ok? Can you wait a sec
The equation that describes the relationship is y =
Answer:
Y=4/6X ( or u can write it as Y=1.5X) .
Hope it was helpful for you .
An athlete consumed 4,000 calories yesterday. Today, she consumed 3,800 calories. What is the percent change in number of calories consumed. Was this a percent increase or decrease? Round to the nearest percent.
finding the area, ty
Tell me if you can’t see it I’ll tell you the answers!!
Answer:
I can't see it
Step-by-step explanation:
Answer:C
Step-by-step explanation: it’s 3/15, meaning, for example, taking 3 chocolate bars from a bunch of 15
Ram gives his son 100 naira on one day, 50 naira on the second day, 25 naira on the third day and so on. What will be the total amount given by Ram to his son starting from the first day, if he lives forever?
Answer:
175+(25*∞d)
Step-by-step explanation:
So d will represent the days which we don't know yet
100 + 50 + 25 + 25d
175+25d
and in this case it will be infinite the amount of days so
175+(25*∞d)
The total amount given by Ram to his son starting from the first day, if he lives forever is 200 nairas.
Given,
Ram gives his son 100 nairas on one day, 50 nairas on the second day, 25 nairas on the third day, and so on.
We need to find what will be the total amount given by Ram to his son starting from the first day if he lives forever.
What is a geometric sequence?It is a sequence where each term after the first term is found by multiplying the previous terms by a common ratio.
Example:
2, 4, 8, 16, 32
Common ratio = 4/2 = 8/4 = 16/8 = 2
The sum of the nth term of a geometric sequence is given by:
S = a [ [tex]r^{n}[/tex]- 1 ) / ( r - 1 ) ] if r > 1 ______(1)
S = a [ 1 - [tex]r^{n}[/tex] ) / ( 1 - r ) ] if r < 1 _______(2)
We see that,
Ram gives his son 100 nairas on one day, 50 nairas on the second day, 25 nairas on the third day, and so on.
This is a geometric sequence.
Find the sequence.
100, 50, 25, ,,,,,,, ∞
Here,
The common ratio is:
r = 50 / 100 = 25/50 = 1/2
i.e r < 1
Find the sum of at ∞.
Now,
a = 100
r = 1/2
n = ∞
From (2)
S = a [ 1 - [tex]r^{n}[/tex] ) / ( 1 - r ) ]
S = 100 [ 1 - 0 ] / (1 - 0.5 ) ]
S = 100 [ 1 / 0.5 ]
S = 100 / 0.5
S = 200
Thus the total amount given by Ram to his son starting from the first day, if he lives forever is 200 nairas.
Learn more about geometric sequences here:
https://brainly.com/question/11266123
#SPJ2
Such as 0.5, has a finite number of digits.
a. terminating decimal
b. repeating decimal
Answer: terminating decimal
Step-by-step explanation: :)
help please again...
Answer:
84
Step-by-step explanation:
Ab = 7 x 2 = 14
V = 14 x 6 = 84
Please help me give Brain
Answer:168
Step-by-step explanation:
What value of x is in the solution set of -2(3x + 2) > -8x + 6?
-6
-5
5
6
Answer:
hello as I think the answer is X= 6
Answer:
6
Step-by-step explanation:
Given
- 2(3x + 2) > - 8x + 6 ← distribute parenthesis on left side
- 6x - 4 > - 8x + 6 ( add 8x to both sides )
2x - 4 > 6 ( add 4 to both sides )
2x > 10 ( divide both sides by 2 )
x > 5
The only value on the list greater than 5 is 6
Then 6 is in the solution set
A girl walks 5,000 meters in one hour. If the girl walks at the same speed for 4 hours, how many kilometers will she have walked?
Item 19 The staircase has three parallelogram-shaped panels that are the same size. The horizontal distance between each panel is 4.25 inches. What is the area of one panel?
Answer:
[tex]Area = 287\ in^2[/tex]
Step-by-step explanation:
Given
[tex]Length = 20.5[/tex]
[tex]Space = 4.25[/tex]
[tex]Panels = 3[/tex]
See attachment
Required
The area of one panel
From the attachment, the total width is 50.5in.
i.e.
[tex]Total\ Width = 50.5[/tex]
Given that there are 2 spaces between the 3 panels and each space has a length of 4.25 in.
The reduced width is:
[tex]Reduced\ Width = 50.5 - 2 * 4.25[/tex]
[tex]Reduced\ Width = 42[/tex]
At this point, we can calculate the width of one panel by dividing the reduced width by the number of panels (3).
[tex]Width = \frac{42}{3}[/tex]
[tex]Width = 14[/tex]
The area of one is:
[tex]Area = Length * Width[/tex]
[tex]Area = 20.5 * 14[/tex]
[tex]Area = 287\ in^2[/tex]
Help me out please?
Answer:
perpendicualr
Step-by-step explanation:
The mass of a dolphin is 2 × 102 kilograms. The mass of an orca is 1 × 104 kilograms. About how many times as much mass does the orca have than the dolphin?
Answer: 100
Step-by-step explanation:
2 x 102 = 204 and 1 x 104 = 104.
204 — 104 = 100.
5 less than 3 times a number y. Please help.
Answer:
3y-5 would be your equation
Step-by-step explanation:
Answer:
H-u-H?!
Step-by-step explanation:
help please :)
V74
V74
Answer:
x =10
Step-by-step explanation:
Using the pythagoras theorem om one of the right triangle;
(√74)² = (x/2)²+7²
74 = (x/2)²+49
(x/2)² = 74 - 49
(x/2)² = 25
Square root both sides
√ (x/2)² = ±√25
x/2 = ±5
x = 2 * ±5
x = ±10
Hence the value of x is 10
the perimeter of a rectangular red sticker is 34 mm. it is 8 mm tall. how wide is it?
Answer:
9 mm wide
Step-by-step explanation:
Perimeter = length x 2 + width x 2
34 mm = 16 mm + ?
34mm = 16 mm + 18 mm
18/2 = 9
9 mm wide
Answer:
p=2L+2W
34mm=(2×8)+2W
34mm=16+2W
2W=34mm-16mm
2W=18mm
W=9mm
HELPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
1. +25
2. +14
3. -10
4. -3
5. +2
Step-by-step explanation:
I hope these help , please tell me if i got any incorrect or misunderstood!
The sales representative went to made a deal with the schools for a discount on the individual juice bottles the company usually sells the bottles to the distributors for $2.25 but they are selling them to the schools for 15% off for what price will they sell each bottle to the school?
Answer:
$1.91 per bottle :)
Step-by-step explanation: