Answer:
Step-by-step explanation:
There are 2 different ways to do this: calculus and by completing the square. In this particular instance, calculus is WAY easier, and since I don't know for what class you are doing this, I'll do both ways. First the calculus way. We know the position equation, and the first derivative of the position is velocity. We also know that when the velocity is equal to 0 is when the object is at its max height. So we'll find the derivative first, then solve it for t:
If [tex]s(t)=-3t^2+20t+2[/tex] then the first derivative is
v(t) = -6t + 20 Solving for t requires that we set the velocity equal to 0 (again, this is where the object is at its max height), so
0 = -6t + 20 and
-20 = -6t so
t = 3.3 seconds. Now that we know that at 3.3 seconds the object is at its highest point, we sub that time into the position function to see where it is at that time:
s(3.3) = [tex]-3(3.3)^2+20(3.3)+2[/tex] and
s(3.3) = 35.3 meters.
Now onto the more difficult way...completing the square. Begin by setting the position function equal to 0 and then move over the constant to get:
[tex]-3t^2+20t=-2[/tex] Since the leading coefficient is not a 1 (it's a 3), we have to factor out the 3, leaving us with:
[tex]-3(t^2-\frac{20}{3}t)=-2[/tex] Now the rule is to take half the linear term, square it, and add it to both sides. Our linear term is [tex]\frac{20}{3}[/tex] and half of that is [tex]\frac{20}{6}[/tex]. Squaring that:
[tex](\frac{20}{6})^2=\frac{400}{36}=\frac{100}{9}[/tex]. We will add that in to both sides. On the left it's easy, but on the right we have to take into account that we still have that -3 sitting out front, refusing to be ignored. So we have to multiply it in when we add it to the right. Doing that gives us:
[tex]-3(t^2-\frac{20}{3}t+\frac{100}{9})=-2-\frac{100}{3}[/tex] We will clean this up a bit now. The reason we do this is because on the left we have created a perfect square binomial which will give us the time we are looking for to answer this question. Simplifying the right and at the same time writing the perfect square binomial gives us:
[tex]-3(t-\frac{20}{6})^2=-\frac{106}{3}[/tex] Now the last step is to move the constant back over and set the quadratic back equal to y:
[tex]y=-3(t-\frac{20}{6})^2+\frac{106}{3}[/tex]. The vertex of this quadratic is
[tex](\frac{20}{6},\frac{106}{3})[/tex] where
[tex]\frac{20}{6}=3.3[/tex] as the time it takes for the ball to reach its max height of
[tex]\frac{106}{3}=35.3[/tex] meters.
I'd say if you plan on taking calculus cuz you're not there yet, you'll see that many of these types of problems become much simpler when you know it!
How??????????????????????
Answer:
y=-1/3x+7
Step-by-step explanation:
y=mx+c
m=-1/3, c=7
y=-1/3x+7
Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
the height of a tree is 170m the lower and upper bound of it's height is
9514 1404 393
Answer:
[165, 175) meters
Step-by-step explanation:
The rule with respect to questions like this is that the bounds are ±1/2 of the place value of the least-significant digit. Here, the integer portion of the number has trailing zeros, and there is no decimal point or fractional part. Ordinarily, this combination of characteristics would signal that the trailing zeros are not significant, so the only significant digits are 1 and 7. The place value of the least significant digit is 10, so the bounds on the measurement are this number ±1/2(10) = ±5.
Of course, 175 rounds up to 180, so the upper bound is a limit, rather than an actual value. The height should be interpreted in this context as ...
165 m ≤ height < 175 m
The lower and upper bounds are 165 m and 175 m, respectively.
_____
Additional comment
The best way to avoid any ambiguity as to whether trailing zeros are significant is to use scientific notation. If a zero in the ones place is significant, that is conventionally indicated by a decimal point: "170.". If scientific notation is used, the number would be reported as 1.70×10² to indicate the trailing zero is significant.
For reference, Earth's tallest tree is a redwood just under 116 meters high.
look at the image for the question
9514 1404 393
Answer:
246.6 in²
Step-by-step explanation:
The surface area is the sum of the base area and the areas of the four triangular faces. The relevant area formulas are ...
A = s² . . . . . . area of a square of side length s
A = 1/2bh . . . . area of a triangle with base b and height h
Then the surface area of this figure is ...
A = (9 in)² + 4×(1/2)(9 in)(9.2 in) = 81 in² +165.6 in² = 246.6 in²
What is the midpoint between A(-6,1) and B(0,2)?
Answer:
(-3, 3/2)
Step-by-step explanation:
To find the midpoint between two points you are going to add the X1 and X2, then divide by two. Then you are going to add the Y1 and Y2, and divide by two.
A(-6,1) B(0,2)
= (-6+0, 1+2)
= (-6, 3)
=(-6/2, 3/2)
=(-3, 3/2)
Given the function f ( x ) = { 6 x − 4 x < 0 6 x − 8 x ≥ 0 Calculate the following values: f ( − 1 ) = f ( 0 ) = f ( 2 ) =
Answer:
[tex]f(-1) = -10[/tex]
[tex]f(0) =- 8[/tex]
[tex]f(2) = 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6x - 4[/tex] --- [tex]x < 0[/tex]
[tex]f(x) = 6x - 8<0[/tex] -- [tex]x \ge 0[/tex]
Solving (a); f(-1)
Here [tex]x= -1[/tex]
[tex]-1 < 0[/tex], so:
[tex]f(x) = 6x - 4[/tex]
[tex]f(-1) = 6 *-1 -4[/tex]
[tex]f(-1) = -10[/tex]
Solving (b); f(0)
Here [tex]x = 0[/tex]
[tex]0 \ge 0[/tex], so:
[tex]f(x) = 6x - 8[/tex]
[tex]f(0) = 6*0 - 8[/tex]
[tex]f(0) =- 8[/tex]
Solving (c) f(2)
Here [tex]x = 2[/tex]
[tex]2 \ge 0[/tex], so:
[tex]f(x) = 6x - 8[/tex]
[tex]f(2) = 6*2 - 8[/tex]
[tex]f(2) = 4[/tex]
Please help to solve this.
Find sin5x,if sinx+cosx=1,4
Answer:
Hello,
Step-by-step explanation:
we must first remember that:
[tex]\boxed{sin(5x)=5sin(x)-20*sin^3(x)+16*sin^5(x)}\\\\[/tex]
Let say t=sin(x)
[tex]sin(x)+cos(x)=1.4\\\\t+\sqrt{1-t^2}=1.4\\\sqrt{1-t^2}=1.4-t\ we\ square\\1-t^2=1.4^2+t^2-2.8*t\\2t^2-2.8*t+0.96=0\\\Delta=2.8^2-4*2*0.96=0.16=0.4^2\\\\t=\dfrac{2.8-0.4}{4} =0.6\ or\ t=\dfrac{2.8+0.4}{4}=0.8\\\\t^3=0,216\ or\ t^3=0,512\\\\t^5=0,07776\ or\ t^5=0,32768\\\\\boxed{sin(5x)=5*0.6-20*0.216+16*0.07776=-0,07584}\\\\or\\\\\boxed{sin(5x)=5*0.8-20*0.512+16*0.32768=-0,99712}[/tex]
What is the smallest three-digit odd numb
that can be made from 2, 8,5, 1, 3?
Answer: 101
Step-by-step explanation:
.
Please help! Identify which of the following is not equivalent to a1/4
Answers (images below)
no links please!
Answer: B
Step-by-step explanation:
A) [tex]a^\frac{3}{4}[/tex]÷[tex]a^\frac{1}{2}[/tex] cannot be the answer. When a to the power of x is divided by a to the power of y it is a to the power of x-y. Ex: [tex]a^x[/tex]÷[tex]a^y=a^x^-^y[/tex]
So 3/4-1/2 is 1/4 giving us [tex]a^{\frac{1}{4} }[/tex]
B is the answer because taking the square root of a is the same as [tex]a^\frac{1}{2}[/tex] which isn't the same as [tex]a^\frac{1}{4}[/tex]
C is not the answer because when a to the power of x is multiplied by a to the power of y it is a to the power of x+y. Ex: [tex]a^x[/tex]·[tex]a^y[/tex]=[tex]a^{x+y}[/tex]
1/8+1/8=1/4 so it is [tex]a^\frac{1}{4}[/tex]
D can't be the answer. [tex]a^\frac{1}{8}[/tex] squared is the same as [tex]a^\frac{1}{8}[/tex]·[tex]a^\frac{1}{8}[/tex] so the same explanation of c applies to d
How many hours will it take to complete a 45-km bike ride if you go 12km per hour the whole time?
Answer:
3.75 hours
Step-by-step explanation:
d = rt
where d is the distance, r is the rate and t is the time
45 = 12 t
Divide each side by 12
45/12 = t
3.75 hours = t
Find the area of the triangle with the following measurements:
Answer:
56.25
Step-by-step explanation:
(9x12.5)÷2
just use a c calculator
200m^4+80m^3+8m^2=0
I got m = 0, -5 but I could be wrong
Answer:
m= 0, -0.2
Step-by-step explanation:
that's what I got when I did it
Answer:
m = 0m = -1/5m = -1/5Step-by-step explanation:
200m^4 + 80m^3 + 8m^2 = 0
~Factor
8m²(5m + 1)(5m + 1) = 0
~Set everything to equal 0 and solve
8m² = 0 → m² = 0 → m = 0
5m + 1 = 0 → 5m = -1 → m = -1/5
5m + 1 = 0 → 5m = -1 → m = -1/5
Best of Luck!
Which is a direct proportion
y = -4
y = 2x + 1
y = 6
y = 2/3x
Answer:
y=2x+1
Step-by-step explanation:
y is directly proportional to x if it increases as x increases
HELP PLEASE AND BE CORRECT
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Each point moves to 3 times its original distance from P.
A is 2 up and 1 left of P, so A' will be 6 up and 3 left of P.
B is 1 down and 2 left of P, so B' will be 3 down and 6 left of P.
C is 2 right of P, so C' will be 6 right of P.
Three construction companies have bid for a job. Max knows that the two companies with which he is competing have probabilities 1/3 and 1/9, respectively, of getting the job. What is the probability that Max will get the job?
Answer:
0.5555 = 55.55% probability that Max will get the job.
Step-by-step explanation:
What is the probability that Max will get the job?
The sum of all probabilities is 100% = 1, so, considering Max's probability as x:
[tex]x + \frac{1}{3} + \frac{1}{9} = 1[/tex]
[tex]\frac{9x + 3 + 1}{9} = 1[/tex]
[tex]9x + 4 = 9[/tex]
[tex]9x = 5[/tex]
[tex]x = \frac{5}{9}[/tex]
[tex]x = 0.5555[/tex]
0.5555 = 55.55% probability that Max will get the job.
The max has probability of getting this job is x= 0.5555 and 55.55%
Suppose that ;
Max has probability of getting this job is = x
and other two companies have probability to get job is [tex]\frac{1}{3} or \frac{1}{9}[/tex].
Sum of the probability have bid a job is 100% which is equal to 1.
The sum of the probabilities in a probability distribution is always 1. A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment. Based on this definition, a probability distribution has two important properties that are always true:According to given question ;
Sum of all the companies having probability to get the job = 1
[tex]x + \frac{1}{3} + \frac{1}{9} = 1[/tex]
[tex]\frac{9.x+1.3+1.1}{9} = 1\\9x+3+1 = 9.1\\9x+4 =9\\9x = 9-4\\9x = 5\\x = \frac{5}{9}[/tex]
x = 0.5555
The Max has probability of getting this job is x= 0.5555 or 55.55%
For the more information about probability click the link given below
https://brainly.com/question/14210034
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. If required enter negative values as negative numbers.
In a regression analysis involving 30 observations
Interpret b1, b2, b3, and b4 in this estimated regression equation (to 1 decimal). Assume that for each coefficient statement, the remaining three variables are held constant. Enter negative values as negative numbers.
b1 = estimated change in y per 1 unit change in x1
b2 = estimated change in y per 1 unit change in x2
b3 = estimated change in y per 1 unit change in x3
b4 = estimated change in y per 1 unit change in x4
Predict y when x1 = 10, x2 = 5, x3 = 1, and x4 = 2 (to 1 decimal).
In this, question the equation is missing that's why in the solution we define the equation and its complete solution:
Let the given equation:
[tex]\bold{\hat{h}=17.6+3.8x_1-2.3x_2+7.6x_3+2.7x_4}[/tex]
[tex]\bold{b1 = 3.8}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_1}[/tex]
[tex]\bold{b2 = -2.3 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_2}[/tex]
[tex]\bold{b3 = 7.6 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_3}[/tex]
[tex]\bold{b4 = 2.7}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_4}[/tex]
Calculating the estimated value of the y when:
[tex]\to \bold{x_1 = 10}\\\\ \to \bold{x_2 = 5}\\\\\to \bold{x_3 = 1}\\\\\to \bold{x_4 = 2}\\\\[/tex]
Put the value into the above-given equation:
[tex]\to \bold{17.6 + 3.8(10) - 2.3(5) + 7.6(1) + 2.7(2)} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{68.6-11.5}\\\\\to \bold{57.1}[/tex]
So, the final answer is "57.1".
Learn more:
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1. Use the circle shown to answer each question a. Name the circle b. Identify a radius of the circle c. Identify a diameter of the circle d. Identify a different diameter of the circle.
please help!! need answer will give brainliest
Answer:
k(3) is 7 and f(h(15)) is 43
Step-by-step explanation:
(a).
[tex]{ \sf{k(x) = h(x) + g(x)}} \\ { \sf{k(x) = (3 \sqrt{x + 1}) + ( - {x}^{2} + 3x + 1) }} \\ { \sf{k(x) = (3 \sqrt{3 + 1} ) + ( - {3}^{2} + 3(3) + 1) }} \\ { \sf{k(x) = 6 + 1}} \\ { \sf{k(x) = 7}}[/tex]
b).
[tex]{ \sf{f(h(x)) = 4(3 \sqrt{x + 1}) - 5 }} \\ { \sf{f(h(15)) = 4(3 \sqrt{15 + 1}) - 5 }} \\ { \sf{f(h(15)) = 4(3 \sqrt{16} ) - 5}} \\ { \sf{f(h(15)) = 48 - 5}} \\ { \sf{f(h(15)) = 43}}[/tex]
Subtract.
7x2-5x+3
-(2x2 + 7X - 4)
Answer:
5x^2-12x+7
Step-by-step explanation:
7x^2-5x+3-(2x^2 + 7X - 4)
Distribute the minus sign
7x^2-5x+3 - 2x^2 - 7X + 4
Combine like terms
5x^2-12x+7
Answer:
-12x + 17
Step-by-step explanation:
hope this helps!
Which of the answer choices has matrix multiplication defined?
Answer:
AB
Step-by-step explanation:
For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.
Matrix A = 2*2
Matrix B = 2*3
Matrix C = 3*3
Matrix D = 1 * 3
From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB
Please help me
(3 more coming soon so if you want points you can do those too when they come out
Answer:
The choose D. 15/16
Step-by-step explanation:
[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]
I hope I helped you^_^
A car is traveling 40 kilometers per hour. What is the speed of that car in meters per second?
We have to convert it to m/s
[tex]\boxed{\sf 1km/h=\dfrac{5}{18}m/s}[/tex]
[tex]\\ \sf\longmapsto 40km/h[/tex]
[tex]\\ \sf\longmapsto 40\times \dfrac{5}{18}[/tex]
[tex]\\ \sf\longmapsto \dfrac{200}{18}[/tex]
[tex]\\ \sf\longmapsto 11.1m/s[/tex]
km/h > m/s
when converting km/h to m/s all you need to do is divide by 3.6
and vise versa when converting m/s to km/h multiply by 3.6
so therefore,
40km/h > m/s
= 40 / 3.6
= 11.11 m/s (4sf)
An amount of $700 was invested at 7% for 7 months what is the interest? Round your answer to your nearest cent.
Answer:
$343
step by step explanation: interest=PRT/100
:I=700×7×7/100
:I=$343.
Given:
Principal, P = $700
Rate of interest, R = 7% = 0.07
Time period, T = 7 months (it is considered as a monthly investment)
∴ Simple Interest, SI = PRT
SI = 700 × 0.07 × 7
SI = $343
What is straightforward interest and model?
Straightforward Simple Interest is the strategy for working out the premium sum for a specific chief measure of cash at some pace of revenue. For instance, when an individual takes credit of Rs. 5000, at a pace of 10 p.a. for a very long time, the individual's advantage for quite some time will be S.I. on the acquired cash.
Straightforward recipes generally start with an equivalent sign (=), trailed by constants that are numeric qualities and computation administrators like in addition to (+), short (- ), asterisk(*), or forward cut (/) signs.
Learn more about Simple Interest here
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A recipe asks that the following three ingredients be mixed together as follows: add 1/2 of a cup of flour for every 1/2 of a teaspoon of baking soda, and every 1/4 of a teaspoon of salt.
Which of the following rates is a unit rate equivalent to the ratios shown above?
A. 2 teaspoons of salt per 1 cup of flour
B. 1/2 teaspoon of salt per 1 teaspoon of baking soda
C .2 teaspoons of salt per 1 teaspoon of baking soda
D. 1 teaspoon of baking soda per 2 teaspoons of salt
Answer:
all of the above
Step-by-step explanation:
the ratio between the flour, the baking soda, and the salt would = 1:1:2 (disregarding tsp or cup measurements, since all the units stay the same in the choices)
so really, all the answers are correct
hope this helps!
Answer:
B. 1/2 teaspoon of salt per 1 teaspoon of baking soda.
Step-by-step explanation:
The ratio of cups of flour to tsp. of baking soda to tsp. of salt shown above is:
1/2 : 1/2 : 1/4
An equivalent rate to the ratio of tsp. of salt to tsp. of baking soda is 1/2 : 1 because:
Ratio of tsp. of salt to tsp. of baking soda is:
1/4 : 1/2
If we were to find an equivalent rate to this, it would be 1/2 teaspoon of salt per 1 teaspoon of baking soda for:
Multiply 2 to both terms in the ratio 1/4 : 1/2:
1/4 x 2 = 1/2 (simplified)
1/2 x 2 = 1 (simplified)
The new ratio is 1/2 : 1, which also represents the rate 1/2 teaspoon of salt per 1 teaspoon of baking soda.
Hope this helps!
Please comment back if this was correct.
Find the inequality represented by the graph
I'm using khan academy btw
Answer:
Step-by-step explanation:
slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4
eq. of line is y-0=3/4(x-0)
y=3/4 x
put x=4
y=2
2=3/4×4
2=3
which is true if 2<3
2<3
so y<3/4 x
Can any one solve this.Please
Answer:
True
Step-by-step explanation:
The first derivative tells you the slope of the graph at a specific point. If f'(c) =0, then that means that at f(c), the slope of the graph is 0. It is neither going up nor down
The second derivative tells you the slope of the slope of the graph. If f''(c) < 0, this means that the slope is decreasing. This means that going from the left to f(c), the slope is greater than the slope at f(c), and going from f(c) to the right, the slope is less than the slope at f(c).
Therefore, since the slope at f(c) is 0, the slope is positive to the left of f(c) and negative to the right of f(c). This means that the graph is going up until it hits f(c) and then goes down. Because f(c) is greater than the values to the left of it (because it is going up until it hits f(c)) and the values to the right of it (because it is going down past f(c)), f(c) is a local maximum
How do I solve |10-5| ?
Answer:
5
Step-by-step explanation:
Subtract
5
from
10
.
|
5
|
The absolute value is the distance between a number and zero. The distance between
0
and
5
is
5
.
5
A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as long, half as deep, and the same width as the larger pool.
How many times greater is the volume of the swimming pool than the volume of the wading pool?
. Sipho's dad used 4/11 of the packet of oranges to make juice. The
next day he used another 4/11 of the packet of oranges.
a) How many elevenths has he used?
Answer:
8 of the 11
Step-by-step explanation:
4+4=8 of the 11
Part of oranges usef from the orange packet used on 1st day = 4/11
Part of oranges used from the orange packet used on 2nd day = 4/11
Total part of oranges used from the orange packet
= (4/11) + (4/11)
= 8/11
So, Sipho's dad used 8 elevenths of the oranges.
What number should be added to -3/2 to get -5/8
Answer: 7 / 8 should be added
Step-by-step explanation:
Let x be the number that should be added
Write the equation
-3/2 + x = -5/8
Add -3/2 on both sides
-3/2 + x + 3/2 = -5/8 + 3/2
x = -5/8 + 3/2
Change the denominator of 3/2 to 8 in order to do addition
x = -5/8 + 12 / 8
x = 7 / 8
Hope this helps!! :)
Please let me know if you have any questions
