The numbers are 77 , 177 and 308 .
Numbers are the building blocks in mathematics. It is an arithmetic value that is used to represent a quantity. Real numbers , integers , natural numbers, whole numbers , irrational numbers are are various types of numbers.
Let us consider the first number to be x . Then the second number is 4x+100 , and the third number is 100 more than the first number. Therefore the the sum of the three numbers will be:
x+4x+(x+100)=6x+100
Now the sum of all the numbers is 562.
Therefore we can write a linear equation in x to find the values of x.
∴ 6x+100=562
or, 6x = 562 - 100
or, 6x = 462
or, x = 462 ÷ 6
or, x = 77
Therefore the second number is 4x = 4 × 77 = 308 and the third number is x + 100 = 77 + 100 = 177 .
So the numbers are 77 , 177 and 308 .
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Answers:
a.) 17t + 200
b.) 93 minutes
Explanation:
The initial volume of the pond is 200 gallons, so that is the y-intercept and included in the equation. The rate of 17 gal/min is written as 17t if t = time.
The full equations is 17t + 200.
To find when the pond will fill up you simply make 1781 equal to the equation:
1781 = 17t + 200
Then solve for t:
1781 – 200 = 17t + 200 – 200
1581 = 17t
1581 ÷ 17 = 17t ÷ 17
93 = t
Answer:
√52 units
Step-by-step explanation:
The segment MN is the hypotenuse of a right triangle that is 6 units wide and 4 units high. The Pythagorean theorem tells you its length is ...
MN = √(6² +4²) = √(36 +16)
MN = √52
Answer:
-3.5 x 0.2 = -0.7 - 7.0 -33
-0.7 = -40.7
= -40
Hope this helps.
Answer:
a) 
.
b) 
Step-by-step explanation:
Given a function 
, this function has the following gradient:
.
(a) find the gradient of f
We have that 
. So
.
.
(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.
The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.
We have that:
.
The vector is 
To use v as an unitary vector, we divide each component of v by the norm of v.
So
Now, we can calculate the scalar product that is the directional derivative.
