Can someone help me with these
1 answer:
Answer:
Problem 2) : the gradient is "-2", and the y-intercept is "3"
Problem 3)
A is
B is
Step-by-step explanation:
Problem 2)
In the line given by the equation:
the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"
the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0
Problem 3)
Consider the two lines :
and
notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.
Now notice that the gradient of one of them is "1" (for ) that is the coefficient that multiplies the variable "x". While for the other line (
) the gradient is "2" and therefore steeper than the previous one.
Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation , and the line identified with "B" is the one with smaller gradient
.
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Answer:
150 minutes
Step-by-step explanation:
P.S - The exact question is -
Given - This is the pond in a shape of a prism, it is completely full of
water. Colin uses a pump to empty the pond. The level goes
down by 20 cm in the first 30 min.
To find - Work put how many minutes Colin has to wait for the pond
to completely empty.
Proof -
Given that,
Height of prism = 1 m
Also,
Base of the prism is trapezium and
Sides of the trapezium are 0.6 m and 1.4 m
Height of trapezium is 2 m
We know that,
Area of trapezium = × (sum of sides)× height
= × (0.6 + 1.4)× 2
= × (2)× 2
= 2 m²
⇒Area of trapezium = 2 m²
Now,
Volume of prism = Area of trapezium × height of prism
= 2 m² × 1 m
= 2 m³
⇒Volume of prism = 2 m³
Now,
Given that the level goes down by 20 cm in the first 30 min
We know
100 cm = 1 m
⇒1 cm = = 0.01 m
⇒20 cm = 20×0.01 m = 0.2 m
⇒The level goes down by 0.2 m in the first 30 min.
Also,
we know that height of water = height of prism = 1 m
So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m
Also,
Volume of Remaining water = Area of trapezium × height
= 2 m² × 0.8 m
= 1.6 m³
⇒Volume of Remaining water = 1.6 m³
Now,
Volume of emptied water = Total Volume - Volume of Remaining water
= 2 m³ - 1.6 m³
= 0.4 m³
⇒Volume of emptied water = 0.4 m³
Now,
0.4 m³ water will be empty in 30 minutes
⇒ 1 m³ water will be empty in = 75 minutes
⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes
∴ we get
The remaining water is empty in 120 minutes
So,
Total pond is empty in 120 + 30 minutes
⇒Total pond is empty in 150 minutes
