Solution :
From the triangle,
[tex]$x^2 = s^2 + 90^2$[/tex]
[tex]$x = \sqrt{s^2 + 90^2}$[/tex]
Now differentiating w.r.t "t", we get
[tex]$\frac{dx}{dt}=\frac{d}{dt}\left(s^2 +90^2 \right)^{1/2}$[/tex]
[tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{\frac{1}{2}-1} \cdot 2s \cdot \frac{ds}{dt}$[/tex] [chain rule]
[tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{-\frac{1}{2}} \cdot 2s \cdot \frac{ds}{dt}$[/tex]
[tex]$=\frac{s}{\left(s^2 + 90^2\right)^{\frac{1}{2}}} . \frac{ds}{dt}$[/tex]
But given that [tex]$\frac{ds}{dt}$[/tex] = 100 ft/s
When all the ball crosses the third base, this means that s = 90. So substituting the value of s and [tex]$\frac{ds}{dt}$[/tex] in [tex]$\frac{dx}{dt}$[/tex] , we get
[tex]$\frac{dx}{dt} = \frac{90}{\left(90^2 +90^2\right)^{1/2}} \times 100$[/tex]
[tex]$\frac{dx}{dt} = \frac{90}{\sqrt{8100+8100}} \times 100$[/tex]
[tex]$\frac{dx}{dt} = 50\sqrt2$[/tex]
= 70.710 ft/s
For homework, a teacher instructs her students to choose a county in their state for a social
studies project. Since they live in a small state, repeats are allowed.
Are these two events dependent or independent?
Answer:
they are dependent
Step-by-step explanation:
You have a goal to save $250. You have saved $160? What percent of your goal have you reached?
help pls, i’ll mark as brainliest if correct
Answer: -11/12
Step-by-step explanation:
Can someone pleaseeee help if you’re correct I’ll give u brain list
Answer:
45 degrees / 2 miles
Step-by-step explanation:
All the sides are equivalent, therefore each side has the same value.
Hopefully this helped you make sure to make it brainliest! :D
Answer:
Step-by-step explanation:
2√2
Which two numbers multiply to 20 and add to 9
Answer: 5x4=20
And 5+4=9
Step-by-step explanation:
The required two numbers are 4 and 5.
What is equation?"It is a statement which consists of equal symbol between two mathematical expressions."
For given example,
We need to find two number such that if multiply then we get 20 and add to get 9.
Let 'a' and 'b' be two numbers.
According to given conditions,
a × b = 20 .........................(i)
a + b =9 .......................(ii)
So, from given conditions we have two equations (i) and (ii).
From equation (ii) we have,
a = 9 - b ...............(iii)
Substitute above value of 'a' in equation (i),
⇒ (9 - b) × b = 20
⇒ 9b - b² = 20
⇒ b² - 9b + 20 = 0
Now we solve this quadratic equation to find b.
⇒ b² - 9b + 20 = 0
⇒ b² - 5b - 4b + 20 = 0
⇒ (b - 5) (b - 4) = 0
⇒ b = 5 or b = 4
Find the value of 'a' from equation (iii)
When b = 5
⇒ a = 9 - 5
⇒ a = 4
When b = 4
⇒ a = 9 - 4
⇒ a = 5
Therefore, the required two numbers are 4 and 5.
Learn more about equation here:
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Calvin evaluated Negative two-thirds times 5 and one-sixth using the steps below.
Step 1: Negative two-thirds time (5 + one-sixth)
Step 2: (Negative two-thirds + 5) times (Negative two-thirds + one-sixth)
Step 3: 4 and one-third times negative one-half
Step 4: Negative 2 and one-sixth
Which describes Calvin’s error?
In step 1, he incorrectly broke up 5 and one-sixth.
In step 2, he distributed the Negative two-thirds instead of the 5.
Answer:
The answer is C on Edge 2021
Step-by-step explanation:
In step 2 he confused the multiplication and addition signs
Answer:
C
Step-by-step explanation:
got it right
Can u help me please
I'll help
The sum of the prices for the items(That's 2large baskets and small gift baskets) for the first customer is $57. So assuming the price of a large basket is x and small basket is y, then an expression for the first sentence is;
2x + 5y= 57
The sum of the prices for the second customer is $6 less than the first customer ( that's 57-6 which is $51). Since he bought 1 large basket and 10 small baskets and the price of each large basket is the same and the price of each small basket is the same they assume the same variable of x and y. So the expression of the second sentence is;
x+10y=51.
So the expressions will be;
2x+5y=57
x+10y=51
That's Option C
Can someone tell me what the slope is ?
Answer:
-5/4
Step-by-step explanation:
rise/run = -5/4
hope this helps <3
Answer:
-5/4
calculator lol (and rise over one)
There were 4983 students going on the field trip. Each bus could hold 60 students. How many buses did they need to transport all of the students?
Answer:
eighty four 84 84 84 84 84
Answer:
84
Step-by-step explanation:
Hooke’s Law of Elasticity states that the force applied, y, varies directly with the distance a spring stretches, x (assuming the spring is not stretched past its elastic limit). If a force of 160 newtons stretches a spring 800 cm, how far will a force of 368 newtons stretch the same spring? Justify your answer.
Group of answer choices
F. It will stretch the same spring 73.6 cm because the equation is y equals 5x.
G. It will stretch the same spring 73.6 cm because the equation is y equals one fifth x..
H. It will stretch the same spring 1,840 cm because the equation is y equals 5x.
J. It will stretch the same spring 1,840 cm because the equation is y equals one fifth x..
Answer:
H: It will stretch the same spring 1,840 cm because the equation is y equals 5x.
Step-by-step explanation:
800=y
160and368=x
You find the answer by dividing,
⁸⁰⁰⁄₁₆₀= ʸ⁄₃₆₈800 divided by 160 equals 5 which means the equation is y equals 5x
and 368x5=1,840
also, do you go to college park?
What expression is equivalent to 11x-6x+x
Answer:
6 x
Step-by-step explanation:
The picture below has the steps
SOME ONE HELP PLS Jenny has finished 15 of the 20 lessons in her piano book. Liam has finished the same percent of lessons from his piano book. His book contains 40 lessons. How many lessons has Liam finished?
Answer:
30
Step-by-step explanation:
15/20 is 75%
75% of 40 is 30
can I please have some help
Step-by-step explanation:
6.-3
8.-36
10.11
make it braintliest please
Answer:
6) q = -3
8) d = -4
10) y = 10
Step-by-step explanation:
6) -7q = 21
divide by -7 on both sides
q = -3
8) -1/3d = 12
divide both sides by -1/3
d = -4
10) -88 = -8y
divide both sides by -8
10 = y
or
y = 10
50 points and a Brainliest.
Answer:
1a. 64=4(7+x)
1b. x=9
2a. 64=7+4x
2b. x=57/4
Step-by-step explanation:
1a. To represent this situation, all of the weight for each package must be in the equation. Since each package has 4 boxes, and only the objects in one box are detailed, everything must be multiplied by 4. Now, the values that must be multiplied by 4 are a bag of rice and beans. Since the beans weigh 7 pounds, they can be represented using the constant 7, and the rice can be represented with the variable x. Combining all of this information, the equation 64(total)=4(7+x)
1b. Now, the equation above must be solved. First, divide both sides by 4 in order to get 16=7+x. Now, subtract 7 from both sides to find that x=9
2a. This problem is similar to the first problem, except instead of multiplying both the beans and rice by four, only the rice needs to be multiplied. With this knowledge the equation 64=7+4x is created.
2b. To solve the above equation, 7 must be subtracted from both sides. This leaves 57=4x. Now, both sides must be divided by 4, giving the final answer of x=57/4.
Answer:
1a. 64=4(7+x)
1b. x=9
2a. 64=7+4x
2b. x=57/4
Step-by-step explanation:
For her science project, Sylvia collected flowers and measured their length. The line plot displays the lengths of the flowers. If
the flowers were laid end to end, what is the total length of all the flowers?
Length of Flowers
Number
of Flowers
OA. 5 feet
OB. 5 feet
OC. 54 feet
OD. 58 feet
Answer:
5 3/4
Step-by-step explanation:
I have this problem too and in the same website too. It told us the total length of all of the flowers, so we add 1/8 + 1/4 + 3/8 + 3/8 + 3/8 + 3/8 + 1/2 + 1/2 + 5/8 + 5/8 + 3/4 + 7/8 and it was equal to 5 3/4
Answer: the answer is 5 3/4
Step-by-step explanation: i took the quiz
-5x+35=40
It's 2-step-equations btw :)
Answer:
x = - 1
Step-by-step explanation:
Given
- 5x + 35 = 40 ( subtract 35 from both sides )
- 5x = 5 ( divide both sides by - 5 )
x = - 1
17 - 4x = 33
What does X=?
Answer:
x = -4
Step-by-step explanation:
17 - 4x = 33
Subtract 17 from each side
17-17 - 4x = 33-17
-4x = 16
Divide each side by -4
-4x/-4 =16/-4
x = -4
help me with this please.
Answer: i know this already is late but ,8 13 18 just adding 5
Step-by-step explanation:
Is (-1,2) a solution to the following linear equation:
2x + y = 2
Answer:
No
Step-by-step explanation:
plug in the variables into the equation
(x,y)
(-1,2)
2(-1)+2=2
2*-1=-2
-2+2=0
2 does not equal 0 so therefore no, it is not a solution
30pts PLEASE HELP I WILL GIVE BRAINLIEST TO RIGHT ANSWER
The distance of a golf ball from the hole can be represented by the right side of a parabola
with vertex (-1,8). The ball reaches the hole 1 second after it is hit, at time 0.
What is the equation of the parabola, in vertex form, that represents the ball's distance
from the hole, y, at time x?
Let's suppose that the hole is at y = 0m, where x is the time variable.
we know that:
The vertex is (-1s, 8m).
(i suppose x in seconds and y in meters)
At x = 1s, the ball reaches the hole, so we also have the point:
(1s, 0m).
Remember that the vertex of a quadratic equation y = a*x^2 + b*x + c is at:
x = -b/2a,
then we have:
-1 = -b/2a.
Then we have tree equations:
8m = a*(-1s)^2 + b*-1s + c
0m = a*(1s)^2 + b*1s + c
-1s = -b/2a.
First we should isolate one variable in the third equation, and then replace it in one of the other two:
1s*2a = b.
So we can replace b in the first two equations bi 1s*2a.
8m = a*1s^2 - 1s*2a*1s + c
0m = a*1s^2 + 1s*2a*1s + c
We can simplify both equations and get:
8m = a*( 1s^2 - 2s^2) + c = -a*1s^2 + c.
0m = a*(1s^2 + 2s^2) + c = a*3s^2 + c.
Easily we can isolate c in the second equation and then replace it into the first equation:
c = -a*3s^2
The first equation becomes:
8m = -a*1s^2 - a*3s^2 = -a*4s^2
a = 8m/-4s^2 = -2m/s^2.
Now with a, we can find the values of c and b.
c = -a*3s^2 = -(-2m/s^2)*3s^2 = 6m.
b = 1s*2a = 1s*(-2m/s^2) = -2m/s.
Then the equation is:
y = (-2m/s^2)*t^2 + (-2m/s)*t + 6m
James wants to buy a new cell phone package there are three packages available for each offering a different deal which package offers the best deal
Answer:package 3
Step-by-step explanation:
Hope I am right it is there cheapest
 what number when added to 1 1/3 gives 2
last one i need help with
Answer: 10 sq units
Step-by-step explanation:
3 + 4.5 + 0.5 + 2 = 10 sq units
Rationalize the denominator and simplify. √a+1 - 2 / √a+1 + 2
Answer:
5+a-4√a+1 / a-3
The rationalization of given expression is a+5-4√(a+1)/(a+5).
What is Rationalization?Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction. That is, remove the radicals in a fraction so that the denominator only contains a rational number.
The given expression is √(a+1)-2/√(a+1)+2.
Multiply both numerator and denominator by (a+1)-2, we get
√(a+1)-2×(a+1)-2/√(a+1)+2×(a+1)-2
= (√(a+1)-2)²/(√(a+1))²+2²
= (√(a+1))²-2×√(a+1)×2+2²/a+1+4
= a+1-4√(a+1)+4/(a+5)
= a+5-4√(a+1)/(a+5)
Therefore, the rationalization of given expression is a+5-4√(a+1)/(a+5).
Learn more about the rationalization here:
https://brainly.com/question/1980047.
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A square has a perimeter of 8x - 10 units, Each side is x units long. What is the value of x?
Answer:
They want you to recognize that you can make 2 equations that both are equal to P.... the perimeter.... and then set them equal to each other and solve for x .. as below
Step-by-step explanation:
P = 8x-10
P = 4x
4x = 8x-10
10 = 4x
2.5 = x
7th grade math please help
Answer:
3.8 x 4.5
+
3.8 x 5.1 divided by 2!
Step-by-step explanation:
You can turn it into 2 squares, or follow the hints!
What is 60 percent of 20
Answer:
The answer is 12. Hope this helped :-)
Step-by-step explanation:
60% of 20
6.2=12
Michael needs to memorize words on a vocabulary list for German class. He has 12 words to memorize,and he is one-fourth done. How many words has Michael memorized so far?
Answer:
3
Step-by-step explanation:
12 divided by 4 equals 3
Hope this helped!! :)
Brainliest?!?!
PLEASE HELP ME I WILL GIVE YOU BRAINIEST
Answer:
2.68 × [tex]10^{26}[/tex] Km³
Step-by-step explanation:
Using the given formula for volume V, then
V = [tex]\frac{4}{3}[/tex] π × (4 × [tex]10^{8}[/tex] )³
= [tex]\frac{4}{3}[/tex] π × 4³ × ([tex]10^{8}[/tex] )³
= [tex]\frac{4}{3}[/tex] π × 64 × [tex]10^{24}[/tex]
= 268 × [tex]10^{24}[/tex]
= 2.68 × 10² × [tex]10^{24}[/tex]
= 2.68 × [tex]10^{26}[/tex] Km³
pleaze help
Plot the ordered pair in a coordinate plane. Describe the location of the point. 32. A(1,3)
33. B(0, -3)
34. C(-4,-2)
35. D(-1 1/4, 2)
and explain it if u can
Answer:
Well, there are 4 quadratic spots on the graph. A(1,3) would be in the top right. B(0,-3) would be on the line on the bottom half of the graph. C(-4,-2) would be in the left bottom half of the graph. and D(-11/4,2) would be in the top right. Connect the dots and just say the shape it makes.
Step-by-step explanation: