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3 years ago

Patrick decided to run every day to keep himself healthy. He ended up running

Mathematics

1 answer:

Over [174]3 years ago

5 0

Answer:

Well, you gotta take the amount a person runs per day and multiply by seven to see how much they ran per week, i dont have a value so its not possible to answer the quistion.

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

A sandwich shop offers 4 different meats and 2 different cheeses. Suppose the sandwich shop offers 24 different meat-cheese sand

Sergio039 [100]

Answer:

Step-by-step explanation:

You would do this question like this.

4 meats * 2 cheeses * x breads = 24 different kinds of sandwiches.

8x = 24

8x/8 = 24/8

x = 3

There are 3 different kinds of breads.

4 0

3 years ago

What are the coordinates of the point on the directed line segment from (-4,1) to (1,6) that partitions the segment into a ratio

Aleksandr [31]

Answer:

a segment is partitioned at a ratio of 1:3, then the point is one-fourth of the distance from (-4,-1) to (2,7).

To compute the x-coordinate of that point, you will need to compute one-fourth of the x-distance between 2 and -4 then add it to -4: (2--4)/4 = 1.5; 1.5 + -4 = -2.5.

To compute the y-coordinate of that point, you will need to compute one-fourth of the y-distance between 7 and -1 then add it to -1: (7--1)/4 = 2; 2 + -1 = 1.

The point is (-2.5,1)

3 0

2 years ago

Y=52(0.42)^x identify if it's growth or decay and determine the percentage rate of increase or decrease

Shkiper50 [21]

Answer:

58%

Step-by-step explanation:

Given the exponential relation :

Y=52(0.42)^x

Since 0.42 is less than 1, then we can infer that the expression is a Decay function ;

. General form of a exponential function :

y = A(1 - r)^x ; r = Decay rate

Comparing the general equation with the equation given ;

The percentage rate of decrease is obtained thus :

1 - r = 0.42

1 - 0.42 = r

r = 0.58

Rate = 0.58 * 100%

Rate = 58%

4 0

3 years ago

What are the sides of an angle

Serhud [2]

Terminal and Initial sides.

6 0

3 years ago

Read 2 more answers