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sergeinik [125]

2 years ago

13

The sum of the ages of the father and his son is 42 years. The product of their ages is 185. Find the age of the father and the

son

1 answer:

Iteru [2.4K]2 years ago

4 0

Let f and s be the ages of the father and the son. We have

$\begin{cases}f+s=42\\fs=185\end{cases}$

From the first equation we derive

$f=42-s$

Substitute this expression for f in the second equation and we have

$(42-s)s=185 \iff -s^2+42s-185=0 \iff s^2-42s+185=0$

The solutions to this equation are s=5 or s=37

Since the sum of the ages must be 42, the solutions would imply

$s=5 \implies f=37,\quad s=37\implies f=5$

We can only accept the first solution, since the second would imply a son older than his father!

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The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 22

NISA [10]

Answer:

a) $v(2\,s) = 2.9\,\frac{m}{s}$ , b) $v(4\,s) = -16.7\,\frac{m}{s}$ , c) $t = 2.296\,s$ , d) $h (2.296\,s) = 27.829\,m$ , e) $t \approx 4.679\,s$ , f) $v(4.679\,s) = -23.354\,\frac{m}{s}$

Step-by-step explanation:

The velocity function can be derived by the differentiating the height function:

$v = 22.5-9.8\cdot t$

Velocities after 2 and 4 seconds are, respectively:

a) $v(2\,s) = 2.9\,\frac{m}{s}$

b) $v(4\,s) = -16.7\,\frac{m}{s}$

The maximum height is reached when velocity is zero. Then:

$22.5-9.8\cdot t = 0$

c) $t = 2.296\,s$

The maximum height is:

d) $h (2.296\,s) = 27.829\,m$

The time required to hit the ground is:

$-4.9\cdot t^{2}+22.5\cdot t +2 = 0$

Roots of the second-order polynomial are:

$t_{1} \approx 4.679\,s$

$t_{2} \approx -0.087\,s$

Only the first root is physically reasonable.

e) $t \approx 4.679\,s$

The velocity when the projectile hits the ground is:

f) $v(4.679\,s) = -23.354\,\frac{m}{s}$

7 0

1 year ago

A science experiment calls for mixing 3 and two-thirds cups of distilled water with 1 and three-fourths cups of vinegar and Two-

Vikentia [17]

Answer:

D. 6 1/12

Step-by-step explanation:

First add the like fractions.

3 2/3 + 2/3 = 3 4/3 (Don't worry about simplifying yet)

Now find the least common multiple for 3 4/3 and 1 3/4 so we can add them.

<h2>REMEMBER: You can only add and subtract fractions when they have the same denominator.</h2>

3: 3, 6, 9, 12

4: 4, 8, 12

In this case 12 is the least common multiple.

3/4 x 3/3 = 9/12 9/12

4/3 x 4/4 = 16/12

Add those two fractions then add the whole numbers and put it in front.

4 25/12

Simplify

6 1/12

7 0

1 year ago

Read 2 more answers

A neighborhood is trying to set up school carpools, but they need to determine the number of students that need to travel to the

katrin [286]

Answer:

The correct option is 1.

Step-by-step explanation:

From the given histogram it is clear that

In age group 5-10, the number of students is 7.

In age group 11-13, the number of students is 5.

In age group 14-18, the number of students is 4.

It means age of 7 students lie in the interval 5-10, age of 5 students lie in the interval 11-13 and age of 4 students lie in the interval 14-18.

Total number of elements in the data set is $7+5+4=16$

In option 3 and 4 number of elements is data set is less than 16. So, option 3 and 4 are incorrect.

In option 2 all the data set lie in the interval 5-10. So, option 2 is incorrect.

In option 1,

Class intervals elements frequency

5-10 5,6,7,8,9,10,10 7

11-13 11,11,12,12,13 5

14-18 14,14,15,16 4

From the above table we can conclude that data set 1 represented in the given histogram.

Therefore the correct option is 1.

4 0

2 years ago

Read 2 more answers

A boy had 3 apples and gained one. How many apples does he have now?

Zigmanuir [339]

Answer: 4

step by step explanation: 3+1=4

4 0

1 year ago

The graphs of f(x) = 10x and its translation, g(x), are shown. On a coordinate plane, 2 exponential functions are shown. f (x) a

cricket20 [7]

Answer:

$g(x)=(10)^{x-3}$

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- The form of the exponential function is $f(x)=a(b)^{x}$ , where

a is the initial amount (x = 0) , b is the growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- If the function translated horizontally by h units to the right , then

the new function is $g(x)=a(b)^{x-h}$

- If the function translated horizontally by h units to the left , then

the new function is $g(x)=a(b)^{x+h}$

- If the function translated vertically by k units up , then the new

function is $g(x)=a(b)^{x}+k$

- If the function translated vertically by k units down , then the new

function is $g(x)=a(b)^{x}-k$

* <em>Lets solve the problem</em>

∵ f(x) is an exponential function

∵ Points (0 , 1) , (1 , 10) , (2 , 100) belong to f(x)

- g(x) is the image of f(x) after translation

∵ Points (3 , 1) , (4 , 10) , (5 , 100) belong to g(x)

∵ point (0 , 1) on f(x) becomes (3 , 1) on g(x)

∵ point (1 , 10) on f(x) becomes (4 , 10) on g(x)

∵ point (2 , 100) on f(x) becomes (5 , 100) in g(x)

∵ All the y-coordinates of the points on the function f(x) are the same

with the y-coordinates of the points on the function g(x)

∴ There is no vertical translation

∵ The x-coordinates of the points on the function f(x) are added by

3 units to give the x-coordinates of the points on the function g(x)

∴ f(x) is translated 3 units to the right

∵ $f(x)=(10)^{x}$

∴ $g(x)=(10)^{x-3}$

- Look to the attached graph for more understand

# Red graph represents f(x)

# Blue graph represents g(x)

4 0

2 years ago

Read 2 more answers