Answer:
The number of plums = 4
The number of peaches = 16
The number of nectarines = 1
Step-by-step explanation:
Let the number of peaches be = x
Let the number of nectarines be = y
Let the number of plums be = z
A box of fruit has four times more peaches than plums. This means that
The number of peaches = 4 X the number of plums.
i.e x = 4z
The box has 3 fewer nectarines than plums. This means that
Number of nectarines = number of plums - 3
i.e y = z - 3
If the box contains 21 pieces of fruit, this means that if we sum up all the peaches, nectarines, and plums in the box, we will get 21.
Peaches + Nectarines + Plums = 21
4z + z-3 + z = 21
6z =21 +3
z = 24/6
z = 4
Therefore, the number of plums = 4
The number of peaches = 4 X 4 = 16
The number of nectarines = 4 -3 = 1
Answer:
Let coordinates of vertex D be (x,y)
In parallelogram diagonals are bisect each other.
∴ Mid-point of AC= Mid-point of BD
⇒ (
2
3+(−6)
,
2
−4+2
)=(
2
−1+x
,
2
−3+y
)
⇒ (
2
−3
,
2
−2
)=(
2
−1+x
,
2
−3+y
)
⇒ (
2
−3
,−1)=(
2
−1+x
,
2
−3+y
)
Now,
⇒
2
−3
=
2
−1+x
⇒ −6=−2+2x
⇒ −4=2x
∴ x=−2
⇒ −1=
2
−3+y
⇒ −2=−3+y
⇒ 1=y
∴ y=1
∴ Coordinates of vertex D is (−2,1)
I got 6.49204 but you will need to round so D 6.5
I added all of the numbers up
Problem 1
<h3>Answer: 2/5</h3>
--------------------------
Explanation:
There are 4 green blocks out of 4+6 = 10 total. We divide the number of green over the number total to get the answer. Reduce the fraction as much as possible. The fraction 4/10 reduces to 2/5 (we divide both parts by 2).
====================================================
Problem 2
<h3>Answer: 1/6</h3>
--------------------------
Explanation:
The probability the spinner lands on red is 2/6 = 1/3. This is because there are 2 spaces that are red out of 6 total. It helps to reduce as much as possible.
The probability the coin lands on heads is 1/2 because there's 1 side labeled heads out of 2 total.
Multiply the fractions: 1/3 * 1/2 = 1/6
This works because both events are independent.
Answer:
The curvature is 
The tangential component of acceleration is 
The normal component of acceleration is 
Step-by-step explanation:
To find the curvature of the path we are going to use this formula:
where
is the unit tangent vector.
is the speed of the object
We need to find 
, we know that 
so
Next , we find the magnitude of derivative of the position vector
The unit tangent vector is defined by
We need to find the derivative of unit tangent vector
And the magnitude of the derivative of unit tangent vector is
The curvature is
The tangential component of acceleration is given by the formula
We know that and 
so
The normal component of acceleration is given by the formula
We know that and 
so
