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3 years ago

13

the area of a childrens rectangular playground is 680 square meters. the length is 14 meters longer than the width. determine th

e length and width of the playground.

1 answer:

Vilka [71]3 years ago

6 0

Uvgtfc 247 -3555- 42.21 , Jon. 9087

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Sarah kicked a ball in the air. The function

Aleksandr-060686 [28]

Answer: The ball hits the ground at 5 s

Step-by-step explanation:

The question seems incomplete and there is not enough data. However, we can work with the following function to understand this problem:

$f=30 t- 6t^{2}$ (1)

Where $f$ models the height of the ball in meters and $t$ the time.

Now, let's find the time $t$ when the ball Sara kicked hits the ground (this is when $f=0 m$ ):

$0=30 t- 6t^{2}$ (2)

Rearranging the equation:

$6t^{2}-30 t=0$ (3)

Dividing both sides of the equation by $6$ :

$t^{2}-5 t=0$ (4)

This quadratic equation can be written in the form $at^{2}+bt+c=0$ , and can be solved with the following formula:

$t=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$ (5)

Where:

$a=1$

$b=-5$

$c=0$

Substituting the known values:

$t=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(0)}}{2(1)}$ (6)

Solving we have the following result:

$t=5 s$ This means the ball hit the ground 5 seconds after it was kicked by Sara.

6 0

3 years ago

Which logarithmic equation is equivalent to the exponential equation below?

anzhelika [568]

Answer:

$log_e^{67.21}= a$

Step-by-step explanation:

The equation is ,

$\implies 67.21 = e^a$

Here e is the Euler's Number . The log which are defined on the base e are called Natural logarithms.

Say if we have a expoteintial equation ,

$\implies a^m = n$

In logarithmic form it is ,

$\implies log_a^n = m$

Similarly our required answer will be ,

$\implies\boxed{ log_e^{67.21}= a }$

3 0

2 years ago

What are the coordinates of the point on the directed line segment from (-6, -3) to

melamori03 [73]

Given:

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.

To find:

The coordinates of that point.

Solution:

Section formula: If point divides a line segment in m:n, then the coordinates of that point are

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get

$Point=\left(\dfrac{6(5)+5(-6)}{6+5},\dfrac{6(8)+5(-3)}{6+5}\right)$

$Point=\left(\dfrac{30-30}{11},\dfrac{48-15}{11}\right)$

$Point=\left(\dfrac{0}{11},\dfrac{33}{11}\right)$

$Point=\left(0,3\right)$

Therefore, the coordinates of the required point are (0,3).

3 0

3 years ago

How many solutions ? ( 1 solution , no solution , infinite solutions ) I WILL MAKE U BRAINLIST NEED ASAP

tangare [24]

Answer:

#4 = ∞

#5= no solution

#6= no solution

Step-by-step explanation:

GOOD LUCK!!!!

4 0

2 years ago

6) -4(3 + 5x) + 10(8x + 4)

MrRissso [65]

Answer:60x+28

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers