Answer:
Step-by-step explanation:
d(t) = 4t + 382 - 16t²
where d is the distance (in feet) between the rock and ground t seconds after thrown. Ground is 0 feet. As a note, I'm not clear why the "4t" term is in this equation. It has the effect of adding an increase in height at the rate of 4 feet/sec. I'll assume this is to accommodate any increase in height due to the throw, but it is a bit curious.
<u>a. How long after the rock is thrown is it 370 feet from the ground?</u>
The 382 in the equation represents the starting height of the rock (382 feet). To find the time to reach 370 feet:
370 = 4t + 382 - 16t²
Solve using the quadratic equation. There will be two answers, one negative, which we'll discard until we can go backwards in time. The positive value is 1, which would mean the rock will be at 370 feet in 1 second after throwing.
<u>b. After how many seconds will the rock reach the ground?</u>
Ground is 0 feet:
0 = 4t + 382 - 16t²
t = 5 seconds
<u>c. What is the height of the rock when it is halfway to the ground?</u>
The initial height is 382 feet, as per the equation, since when t = o (initial), d(t) is 382 feet. Halfway to the ground would be (382/2) or 191 feet.
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2.74 and 137/50 should be correct
Let 'a' be the number of ounces of 2%-solution in the 25-ounce mixture
and 'b' be the number of ounces of 5%-solution in the 25-ounce mixture.
Since, fluid ounces of each concentration should be combined to make 25 fl oz.
So, a+b=25 (Equation 1)
And, a container of 2% acid solution and a container of 5% acid solution should be combined to make 25 fl oz of 3.2% acid solution.
So, a of 2% + b of 5% = 3.2% of 25
Multiplying the above equation by 100, we get
(Equation 2)
Substituting the value of a=25-b in equation 2, we get
Since, a=25-b
a= 25-10
a=15.
So, 15 fluid ounces of 2% solution combined with 10 ounces of the 5% solution to create a 25-ounce mixture at 3.2% concentration of acid.
Answer:
can be written in scientific notation as
Step-by-step explanation:
A number is written in scientific notation if it can be written as where p has value greater than or equal to 1 and less than 10 and x is an integer.
Given -
First applying
We get,
using property of exponents
Thus, we have to write in scientific notation,
Multiply and divide by 10 , we get
Thus, can be written in scientific notation as
Answer:
x = 1
Step-by-step explanation:
7x + 16 = 8x + 15
<u>Step 1</u> : Subtract 15 on both sides
7x + 16 - 15 = 8x
7x + 1 = 8x
<u>Step 2</u> : Subtract 7x on both sides
1 = 8x - 7x
1 = 1x
x = 1