Answer:
Greatest height: 45 meters
Time for greatest height: 3 seconds
Height after 5 seconds: 25 meters above the cliff
Time for height of 40 meters: 7.123 seconds
Height after 7 seconds: -35 meters (35 meters below the cliff)
Step-by-step explanation:
to find the maximum height, we need to calculate the derivative of y in relation to t and then find when dy/dt = 0:
dy/dt = 30 - 10t = 0
10t = 30
t = 3 seconds
In this time, the height is:
y = 30*3 - 5*3^2 = 45 meters
After 5 seconds, the height is:
y = 30*5 - 5*5^2 = 25 meters
The time for the height of 40 meters is:
40 = 30t - 5t^2
t^2 - 6t - 8 = 0
Using Bhaskara's formula, we have:
Delta = 6^2 + 4*8 = 68
sqrt(Delta) = 8.246
t1 = (6 + 8.246) / 2 = 7.123 seconds
t2 = (6 - 8.246) / 2 = -1.123 seconds (negative value for time is not valid)
So the time when the rocket reaches 40 meters is 7.123 seconds
After 7 seconds, the height is:
y = 30*7 - 5*7^2 = -35 meters
The rocket will be 35 meters below the cliff.
evaluate the expression 10(x+2)+10x2 for x=2
Answer:
60
Step-by-step explanation:
10(2+2)+10x2
10(4)+20
=60
Answer: 60
Step-by-step explanation:
I need help asap lol
Answer:
13/38
Step-by-step explanation:
the number of kids who have 1 sibling is 13
the total is 38
13/38
Find the surface area AND the volume of the triangular prism
Answer:
SA=1200 in squared. V=2160 in cubed.
Step-by-step explanation:
Let's start with the surface area. The area of of a triangle is 1/2 x b x h. But we have 2 congruent triangle on the prism, so we have this.
2 x 1/2 x b x h.
The 2 and 1/2 cancel so we are left with b x h.
The other sides are easy.
Find the area of the sides we know that have base times height.
16 x 30 + 16 x 9 + 30 x 9...
To find the last side, we need to find the hypotenuse.
To find it, we use the pythagorean theorem.
a²+b²=c²
Use the values of the right triangle's dimensions and plug them in.
16²+30²=c²
256+900=c²
c²=1156
c=34
now using this, we have
16 x 30 + 16 x 9 + 30 x 9 + 9 x 34.
Now solve!
SA = 1200 in squared
The volume is easy.
All we need is the area of the triangular side and multiply it by the depth, 9.
16 x 30 x 1/2 =
240
240 x 9=
2160. in cubed
HELP ASAP!!!!!
A 13 ft ladder is resting on a wall. The angle the ladder makes with the floor is 45 degrees. How high off the ground is the top of the ladder?
Use the function y=13cos(theta) to find the answer
Answer:
The height would be 9.1923 ft
PLEASE HELP WILL GIVE BRAINLIEST
select the equation for the line described
the line crossing the point (2,7) and with slope = -2
Answer:
Here is your answer
Step-by-step explanation:
y - 7 = -2(x-2)
y - 7 = -2x + 4
+7 +7
y = -2x + 11
a) When 3 is subtracted from a
number, the result is 8.
Answer:
11
Step-by-step explanation:
check:
3+8=11
11-3=8
Please help me!!!!!!!! :)
Answer:
Step-by-step explanation:
the 30 year olds are more likely to pick chocolate as their favorite ice cream because the fraction of people who like chocolate is 14/20 where the other 3 are 4/20 and 2/20. this can be converted into percentages as well by multipling by 5. 70% of people who are in their 30s like chocolate opposed to the 20% and 10%.
The point-stope form of the equation of the line that passes through (-5. -1) and (10.-7) is y+7= -2/5(x-10). What is the standard form of the equation for this line?
2x - 5y = -15
2x - 5y = -17
2x + 5y = -15
2x - 5y = -17
Answer:
2x+5y = -15
Step-by-step explanation:
y+7= -2/5(x-10)
Multiply each side by 5 to get rid of the fraction
5(y+7)= 5*-2/5(x-10)
5(y+7)= -2(x-10)
Distribute
5y+35 = -2x+20
Add 2x to each side
2x+5y +35 = 2x-2x+20
2x+5y +35 = 20
Subtract 35 from each side
2x+5y+35-35 = 20-35
2x+5y = -15
Find the roots. List your steps correctly. 2 points each (Show ALL steps of work, check each answer, and state the solutions correctly for full credit) a. f (n) = n2 − 6n − 16
Answer:
use quizlet
Step-by-step explanation:
Answer:
8 and -2
Step-by-step explanation:
f (n) = n² − 6n − 16
n² − 6n − 16=0n²-2*3n+9=25(n-3)²=25n-3=5 ⇒ n=8n-3= -5 ⇒ n= -2Consider the line -5x - 3y = 9.
Find the equation of the line that is parallel to this line and passes through the point (-2, 2).
Find the equation of the line that is perpendicular to this line and passes through the point (-2, 2).
Answer:
hope this helps You
Determine whether the function below is an even function, an odd function, both, or neither.
f) = r6 + 10.04 - 11/2 + 19
O A.
both even and odd
ОВ.
odd function
O c.
even function
D.
neither even nor odd
Answer:Test to determine if a function y=f(x) is even, odd or neither: Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even. If f(-x) = - f(x), the function is odd.
Step-by-step explanation:
Answer:
Even function because the highest exponent of the variable is a 6, and 6 is an even number.
Step-by-step explanation:
The aquarium shown is a rectangular prism that is filled with water. You drop a spherical ball with a diameter of 8 inches into the aquarium. The ball sinks, causing the water to spill from the tank. How much water is left in the tank? Enter your answer to the nearest tenth. (Hint: 1 in3 = 0.00433 gal)
13 in.20 in.13 in.
The amount of water left is about
gallons.
This question is incomplete because it is not properly and correctly written.
Find attached to this answer a hand drawn sketch diagram of the Aquarium (rectangular prism) showing its dimensions.
Complete Question
The aquarium shown is a rectangular prism that is filled with water. You drop a spherical ball with a diameter of 8 inches into the aquarium. The ball sinks, causing the water to spill from the tank. How much water is left in the tank? Enter your answer to the nearest tenth. (Hint: 1 in³ = 0.00433 gal)
The dimensions of the rectangular prism is given as:
Height = 13 in
Width = 13 in
Length= 20in
The amount of water left is about ____ gallons.
Answer:
The amount of water left in the tank approximately to the nearest tenth is 13.5 gallons (gal) of water
Step-by-step explanation:
Step 1
We are given a rectangular prism with the dimensions :
Height = 13 in
Width = 13 in
Length= 20 in
The first step would be to find the Volume of the Rectangular prism
Volume of the rectangular prism = Length × Width × Height
= 20in × 13in × 13in
= 3380 in³
From the question, we are given the hint that
1 in³ = 0.00433 gal
This means that 1 in³ of an object contains 0.00433 gallons of water.
Therefore, if
1 in³ = 0.00433 gal
3380 in³ =
Cross multiply
2880 in³ × 0.00433 gal
= 14.6354 gal
This means the Aquarium (rectangular prism) contains 14.6354 gallons of water.
Step 2
A spherical ball with the diameter of 8 inches was dropped into the aquarium.
We would find the volume of the spherical ball.
Volume of the Spherical ball = 4/3πr³
Radius = Diameter ÷ 2
= 8 inches ÷ 2 = 4 inches.
Volume of the Spherical ball = 4/3 × π × 4³
Volume of the Spherical ball = 268.08in³
Step 3
We would be converting the Volume of spherical ball to gallons because this gives us the quantity of water spilled due to the sinking of the spherical ball
If , 1 in³ = 0.00433 gal
268.08in³ =
Cross multiply
268.08 in³ × 0.00433 gal
= 1.1607864 gal.
Step 4
The fourth and final step is to subtract the volume of water in the aquarium from the volume of water spilled
14.6354 gal - 1.1607864 gal
= 13.4746136 gal
Approximately to the nearest tenth = 13.5 gal
Therefore, the amount of water left in the tank approximately to the nearest tenth is 13.5 gallons (gal) of water.
Please hurry
What is the equation of the line that is parallel to the linear graph of
y = 2x – 1 and passes through the point (-1, 1)?
Answer:
y=2x+3
Step-by-step explanation:
Parallel: slope is 2
y-1=2(x+1)
y-1=2x+2
y=2x+3
SOMEONE PLEASE HELP ME ASAP PLEASE!!
[tex]\sf{Answer}\\[/tex]
→ A plane contain three non - collinear points.
-x^2+2x-5^3-4x+5 in standard form
Answer:
[tex]x^{2}[/tex]-2x-120
Step-by-step explanation:
Answer:
-5x^3 - x^2 - 2x + 5
Step-by-step explanation:
Rewrite the given expression in descending powers of x:
-5x^3 - x^2 - 2x + 5
Desmond wants to buy a card for his wife. Desmond calculates the amount of the card as $4.50. The actual price of card is $4. What is Desmond’s percent error?
Answer:
14.28 percent
Step-by-step explanation:
Round 66.3899872389 to the nearest thousandth
Answer:
66.390
Step-by-step explanation:
Answer:
66.39
Step-by-step explanation:
The thousandth place is 0.00. To round, look at the number right after it. If the number is 4 or less, the number stays the same. If the number is 5 or greater, the number is rounded up.
For 66.3899872389, the bold number is the number we are trying to round. The number after it is 9. This number is greater than 5 so you have to round up.
Your answer is 66.39.
Please help I don’t understand I need help please
Answer:
the range is from 0 to 6 , so 6
Step-by-step explanation:
Answer:
0-6
Step-by-step explanation:
i think
Solve the system of equations and choose the correct ordered pair.
Answer:
C (2,5)
Step-by-step explanation:
Adding the equations, we get 10x+y=25
Multiplying that by 2 we get 20x+2y=50
Add that with the first equation, we get 24x=48, x=2.
Plugging x as 2 in, we see y = 5
So its (2,5)
Niu has decorated x cards he started with 24 stickers and he used 4 stickers per card
Answer:
6
Step-by-step explanation:
4 stickers each x 6 cards = 24 stickers used
you can try random numbers until you get your answer
Answer:
Total number of cards = 6
Step-by-step explanation:
Number of cards = Total number of stickers/ number of stickers per card
= 24/4
= 6
what is an equation of a circle with center (-10,6) and radius 8?
Answer:
(x+10) ^2 + (y-6)^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
(x-h) ^2 + (y-k)^2 = r^2 where( (h,k) is the center and r is the radius
(x- -10) ^2 + (y-6)^2 = 8^2
(x+10) ^2 + (y-6)^2 = 64
Would you rather ... Drive a car at a rate of 40 miles per hour ***OR*** Drive a car at a rate of 50 feet per second?
Answer:
40 mph
Step-by-step explanation:
at least I won't crash in one second, and that's not that slow.
Answer:
i rather drive a car 40 miles per second however.... driving at 50ft per second sounds like fun
Step-by-step explanation:
The circle above represents the amount of fruits produced by a farmer . if 0 is the centre of the circle and the three angles at 0 are equal what fraction of the fruits produced were oranges ?
Answer:
(b) 1/3
Step-by-step explanation:
because it has 3 equal parts
Answer:
As shown in the picture, if the three angles at 0 are equal, the amount of fruits in 3 sections would be equal, too.
It means the total amount of fruits would be divided equally into 3 potions, 1 portion is pawpaw, 1 portion is mango, and 1 portion is orange.
=> Fraction of oranges: F = 1/3
=> Option C is correct
Hope this helps!
:)
3 women push a stalled car. Each woman pushes with a 425 N force. What is the mass of the
car if the car accelerates at 0.85 m/s??
Answer:
1,500 Kg
Step-by-step explanation:
Formual for froce is given by
force = mass * acceleration
Force exerted by 1 woman = 425 N
no. of women exerting force = 3
Force exerted by 3 woman = 425 * 3 N = 1275 N
Acceleration produced by 1275 N force = 0.85 m/s^2
Using formula force = mass * acceleration
1275 = mass * 0.85 m/s^2
=> mass = 1275/ 0.85 m/s^2 = 1,500 Kg
Thus, mass of car is 1,500 Kg.
What is the inverse of the function? f(x)=3x−1
Answer:
The inverse is 1/3 (x+1)
Step-by-step explanation:
y = 3x-1
Exchange x and y
x = 3y-1
Solve for y
Add 1 to each side
x+1 = 3y-1+1
x+1 = 3y
Divide each side by 3
(x+1)/3 = 3y/3
1/3(x+1) =y
The inverse is 1/3 (x+1)
PLEASE HELP Give an example of an equation that has no solution and show why:
Answer:
2x-3=2x-4
Step-by-step explanation:
2x-3=2x-4
-3=-4
Not true. Thus, no solution.
Answer:
say the equation was 2x - 5 = 2x -3
well the first thing I could do is subtract the 2x from both sides, but 2x is on both sides so there would be no x-value meaning there is no solution
John paid $100 for renting a canoe for 5 hours. Which graph shows the relationship between the cost of renting a canoe for different hours?
A graph is shown. The title of the graph is Canoe Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 20, 40, 60, 80, 100, 120. Points are plotted on the ordered pairs 1,100 and 2,100 and 3,100.
A graph is shown. The title of the graph is Canoe Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 20, 40, 60, 80, 100, 120. Points are plotted on the ordered pairs 1,20 and 2,40 and 3,60
A graph is shown. The title of the graph is Canoe Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 20, 40, 60, 80, 100, 120. Points are plotted on the ordered pairs 1,10 and 2,20 and 3,30.
A graph is shown. The title of the graph is Canoe Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 20, 40, 60, 80, 100, 120. Points are plotted on the ordered pairs 1,40 and 2,80 and 3,120.
Answer:
The answer is B.
Step-by-step explanation:
You would pay about $20 each hour
Answer:
The answer is B)
Step-by-step explanation:
Simplify the radical expression.
4 sqrt 625x^12y^8
Answer:
[tex]\sqrt[4]{625x^{12}y^8} = 5 {x^3} {y^2}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[4]{625x^{12}y^8}[/tex]
Required
Simplify
We start by splitting the roots
[tex]\sqrt[4]{625x^{12}y^8} = \sqrt[4]{625}* \sqrt[4]{x^{12}} * \sqrt[4]{y^8}[/tex]
Express 625 as exponents
[tex]\sqrt[4]{625x^{12}y^8} = \sqrt[4]{5^4}* \sqrt[4]{x^{12}} * \sqrt[4]{y^8}[/tex]
From laws of indices
[tex]\sqrt[n]{a^m} = a^{\frac{m}{n}}[/tex]
So,
[tex]\sqrt[4]{625x^{12}y^8} = \sqrt[4]{5^4}* \sqrt[4]{x^{12}} * \sqrt[4]{y^8}[/tex] becomes
[tex]\sqrt[4]{625x^{12}y^8} = {5^\frac{4}{4}} * {x^\frac{12}{4}} * {y^\frac{8}{4}}[/tex]
[tex]\sqrt[4]{625x^{12}y^8} = 5 * {x^3} * {y^2}[/tex]
[tex]\sqrt[4]{625x^{12}y^8} = 5 {x^3} {y^2}[/tex]
how much lb an oz PLEASE HELP
1 pound (lb) is in 16 ounces (oz).
Answer:
16
Step-by-step explanation:
Stay safe and wear a mask!
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
Answer:
easy, if the intercepts or roots or zeros of the equation are r₁ and r₂ then 2 factors of the equatain are (x-r₁) and (x-r₂)
so
we see it intercepts the x axis at 1 and 6
r₁=1
r₂=6
therefore 2 roots are (x-1) and (x-6)
answer is 2nd option
Step-by-step explanation:
if
Answer:
b
Step-by-step explanation:
took the quiz got it right
