The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.
Find or approximate the time when the object hits the ground. Explain your method.
The approximate time when the object hits the ground will be 10 seconds.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
h(t) = (49 + 4.9t)(10 - t)
The time when the object hits the ground is calculated as,
h(t) =
(49 + 4.9t)(10 - t) = 0
If (49 + 4.9t) = 0, then the value of 't' is given as,
49 + 4.9t = 0
t = - 10
The value of time is an absolute value. Thus, this can be neglected.
If (10 - t) = 0, then the value of 't' is given as,
10 - t = 0
t = 10 seconds
The approximate time when the object hits the ground will be 10 seconds.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ3
PLS HELP Find the value of x.
A. 4
B. 2
C. 7
D. 14
Answer:
ANSWER IS B
Step-by-step explanation:
5x - 3 = 3x + 1
5x - 3x = 1 + 3
2x = 4
x = 4/2
x = 2
Answer:
B. 2
Step-by-step explanation:
The sides 5x - 3 and 3x + 1 are the same length, so you can put an equal sign: 5x - 3 = 3x + 1, x = 2:
5(2) - 3 = 3(2) + 1
10 - 3 = 6 + 1
7 = 7
So x is 2
A car bought for $13,000 despreciates at 12% annually. What will the car be worth after 10 Years ?
Answer:
I think $3620.51
Step-by-step explanation:
If i did it right, the equation should be something like this?
13,000(.88)^10
3/4x × 12/11 ÷ 3x/22
Answer:
242/48
Step-by-step explanation:
279 students went on a field trip. Five buses were filled and 9 students traveled in cars. How many students were in each bus? PLEASEEEEE HELPPPPP ME you get 60 points i dont know if anyone cares but hey
Answer:
90 students.
Step-by-step explanation:
279-9=270, and 270 divided by 9 is 90.
what is the measure of x
Answer:
56.25°
Step-by-step explanation:
cos x° = b/h = 15/27 = 5/9
x° = cos^(-1) (5/9) = 56.25°
A quadrilateral is a parallelogram if each____ divides a parallelogram into two____.
Answer:
diagonal, congruent triangles
Step-by-step explanation:
The object below is made with six identical cubes. Each cube edge is 3 inches long.
As
3 in.
What is the surface area of the object in square inches?
Answer:
306 square inches.
Step-by-step explanation:
All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).
6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.
Each face of one cube = 3*3 = 9 in^2.
Therefore the surface area = 9 * 34 = 306 in^2.
Drag and drop the correct angle measures onto the diagram
Answer:
Here you go!
Hope this helps!
Please help?? I have an exam tomorrow
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²
= x(x - 3y) - 2y(x - 3y)
= (x - 3y)(x -2y)
x² - 4xy + 3y² = x² -xy - 3xy + 3y²
= x(x - y) - 3y(x - y)
= (x - y)(x - 3y)
x² - 3xy + 2y² = x² - xy - 2xy + 2y²
= x(x - y) - 2y(x - y)
= (x - y)(x - 2y)
Least common denominator = (x-y)(x - 2y)(x - 3y)
[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]
Let z be inversely proportional to the cube root of y. When y =.064, z =3
a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.
Given:
z be inversely proportional to the cube root of y.
When y =0.064, then z =3.
To find:
a) The constant of proportionality k.
b) The value of z when y = 0.125.
Solution:
a) It is given that, z be inversely proportional to the cube root of y.
[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]
[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, z=3 when y=0.064. Putting these values in (i), we get
[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]
[tex]3=k\dfrac{1}{0.4}[/tex]
[tex]3\times 0.4=k[/tex]
[tex]1.2=k[/tex]
Therefore, the constant of proportionality is [tex]k=1.2[/tex].
b) From part (a), we have [tex]k=1.2[/tex].
Substituting [tex]k=1.2[/tex] in (i), we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]
We need to find the value of z when y = 0.125. Putting y=0.125, we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]
[tex]z=\dfrac{1.2}{0.5}[/tex]
[tex]z=2.4[/tex]
Therefore, the value of z when y = 0.125 is 2.4.
Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n}[/tex]
or
[tex]n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For the given case, it is given that:
[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]
Let the constant of proportionality be k, then we have:
[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]
It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:
[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]
Thus, the constant of proportionality k is 1.2. And the relation between z and y is:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]
Putting value y = 0.0125, we get:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]
Thus, for the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4Learn more about proportionality here:
https://brainly.com/question/13082482
There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
helpppp pleaseee its hard
Answer:
Ten thousands
Step-by-step explanation:
Replace all other digits with zero
This gives 40,000
Ten thousand (10,000) has the same amount of digits
A bag contains balls of five different colors. Two are red, three are blue, ten are white, four are green and three are black. Balls are taken from the bag without looking, and not returned. What is the smallest number of balls that should be taken from the bag to be sure that two balls of the same color have been taken? please explain with the answer
Answer:
6
Step-by-step explanation:
The worst scenario is that of a slight possibility, the first 5 balls you took are completely different color. The chance of this happening is tiny, but if you want to be sure, then you should consider about it.
But, after taking out the sixth ball, you can be sure that the ball, now right on your hand, must share a same color with at least one of the balls you took out, since there are only five colors.
help solving inequalities true or false (middle school) first person to answer i’ll give brainliest please!!!
Answer:
aef true and bcd false
hope u get well in your exams
Step-by-step explanation:
15 point question!
Hi can you help? Thanks! *if you are gonna answer, actually answer please!*
Brainly if you get it right!
Answer:
The answer is 129
Step-by-step explanation:
5(exponent 4)/5 = 125 +4 equals 129
I think
Answer:
129
Step-by-step explanation:
5^4 / 5 + 4
We know that a^b / a^c = a^(b-c)
5^(4-1) +5
5^3 +4
125 +4
129
A silo in the shape of a cylinder is partially filled with corn to feed cows. The corn fills 25% of the height of the silo. What is the approximate volume of the part of the silo that is filled with corn if the silo is 12 feet in diameter and 60 feet high?
- PLEASE HELP im in the middle of an exam
Answer:
1695.6 cubic feet
Step-by-step explanation:
Given that,
The corn fills 25% of the height of the silo.
The diameter of silo, d = 12 feet
Radius, r = 6 feet
Height, h = 60 feet
The volume of the part of the silo that is filled with corn is given by :
[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]
So, the required volume is equal to 1695.6 cubic feet.
find the length of arc RS. Use 3.14 for pie. Round to the nearest tenth.
3.10
Step-by-step explanation:
If you round 3.14 to the nearest tenth 4 is nearer to 10 than 20. Therefore, the answer is 3.10
what is the answer to this question
Answer:
[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]
How many marble do you need to balance to scale
A. 4
B. 3
C. 2
D. 1
Answer: its B.
Step-by-step explanation:
have a good day hope this help
Answer:
B.3
Step-by-step explanation:
just divide 6 by 2
Can someone please help me!!!
Answer:
Option C
Step-by-step explanation:
same logic as in 2D problems. if C wasn't true, then the two planes couldn't be parallel
(Please help!) What is the value of x?
B
(x + 5) ft 910
8 ft
more
91°
А
38°
P.
38°
13 ft
13 ft
R
X=
Answer:
x = 5.1
Step-by-step explanation.
Our first step is to find all the angles. If b = 91 degree and c is 38, a. has to be 51 because all triangles add up to 180 degree. Because we have both B and b, we can use sine law.
a/A 13/sin91 c/38
we can use b in this situation.
The legnth of a is 10.1.
So, x-5 would be 5.1
If line a has a slope of -3 and is perpendicular to line b, what would is the slope of line b?
Answer:
Slope of line B: 1/3
Step-by-step explanation:
To find a slope perpendicular to another slope, you take its negative reciprocal.
Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3
in a math final please help asap
find the angle r show ur work
Answer:
The measure of angle R is 112 degrees
Step-by-step explanation:
Using the given markings, we can see that we have an isosceles triangle
so RT is also 3x-2
Mathematically, the sum of the interior angles of a triangle is 180:
Thus;
9x + 4 + (3x-2) + (3x-2) = 180
9x + 3x +3x + 4-2-2 = 180
15x = 180
x = 180/15
x = 12
Recall; Angle R is 9x + 4
= 9(12) + 4 = 108 + 4 = 112
On the coordinate plane, point T is located at (0,7) and point U is located at (x,-5). The distance between points T and U is 15 units.
What are the two possible values of x?
Answer:
x = 9 or x = -9
Step-by-step explanation:
The parameters of the given points are;
The location of the point T = (0, 7)
The location of the point U = (x, -5)
Then distance between points T and U = 15 units
The distance between points A and B, 'd', given their coordinates, A(x₁, y₁) and B(x₂, y₂) is found using the following formula;
[tex]d=\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, for the given points, T(0, 7) and U(x, -5), we get;
[tex]15 = \sqrt{\left ((-5) - 7 \right )^{2}+\left (x - 0 \right )^{2}}[/tex]
Squaring both sides, gives;
[tex]15^2 = \left ((-5) - 7 \right )^{2}+\left (x - 0 \right )^{2}} = (-12)^2 + x^2[/tex]
∴ x² = 15² - (-12)² = 81 = 9²
x² = 9²
∴ x = ±√(9²) = ± 9
The possible values of x are x = 9 or x = -9
helpppp meee pleaseeeeewee
We can't see what you are talking about. send another one.
What is the explicit formula for the geometric sequence 2, 6, 18, 54, …?
Answer:
3x
Step-by-step explanation:
You multiply the pervious number with 3 to get the next number
For example 2 times 3 = 6
6 times 3 = 18
18 times 3 =54
54 times 3= 162
So on and so forth
the sum of 25 and x is 48 find x. . Solve.
Answer:
x = 23
Step-by-step explanation:
Sum of 25 and x = 48
25 + x = 48
Subtract 25 from both sides
25 - 25 cancels out
48 - 25 = 23
We would be left with x = 23
Answer:
[tex]x =23[/tex]
Step-by-step explanation:
Sum of 25 and x
[tex]25 + x[/tex]
Sum of 25 and x is 48
[tex]25 + x = 48[/tex]
Now lets simply Solve the equation
[tex]25 + x = 48 \\ x = 48 - 25 \\ x =23[/tex]
Hope this helps you.
Have a nice day!
how do you find x in this? I need help asap!!
Answer:
Step-by-step explanation:
According to the theorem, the angle measuring 110 is one-half the measure of the arc it intercepts. That means that the major arc (this arc of which I'm speaking) measures 110 * 2 = 220.
Since the outside of a circle, regardless of how big or small the circle is, has a degree measure of 360, then x = 360 - 220 so
x = 140°
Latoya has b decks of cards . Each deck has 52 cards in it , what is the expression for the total numbers of cards latoya has
Answer:
52b
Step-by-step explanation:
She has 52 cards per deck, and b decks.
This means she has 52b cards.
How this works:
For 1 deck, she has 52 cards, or 52×1 cards.
For 2 decks, she has 104 cards, or 52×1 cards.
For 5 decks, she has 260 cards, or 52×5 cards.
For 10 decks, she has 520 cards, or 52×10 cards.
Therefore, for b decks, she has 52×b, or 52b cards.
**This content involves writing algebraic expressions, which you may wish to revise. I'm always happy to help!