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Masja [62]
3 years ago
12

Ming throws a stone off a bridge into a river below.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
3 0

We have been given that Ming throws a stone off a bridge into a river below.

The stone's height (in meters above the water), x seconds after Ming threw it, is modeled by h(x)=-5(x-1)^2+45.

We are asked to find the maximum that the stone will reach.

We can see that our given equation is in vertex form of parabola y=a(x-h)^2+k with vertex at point (h,k).

We can also see that leading coefficient is negative, so our given parabola is a downward opening parabola and its maximum value be at vertex.

The maximum height will be equal to y-coordinate of vertex.

We can see that vertex of our given parabola is at point (1,45). Therefore, the maximum height will be 45 meters.

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Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights
Aleks04 [339]
A. 3 hopes this helps!
8 0
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Chicken costs $3.20 per pound, and beef costs $4.59 per pound. What is the exact cost of 3 pounds of beef?
Pie

Answer:

$13.77 for three pounds of beef

7 0
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Find the measure of arc HJ.
diamong [38]

Answer:

98 degrees

Step-by-step explanation:

HJ = (5x - 7)

Because it's a full circle:

61 + 34 + (5x - 7) + (9x - 22) = 360

95 + (14x - 29) = 360

14x = 360 - 95 + 29 = 294

x = 21

HJ = 5x - 7 = 5 * 21 - 7 = 105 - 7 = 98

6 0
3 years ago
Urgent help!
Alchen [17]

Answer:

(i) 80-x

(ii) S(x) = 40 - 0.10x

(iii) $36.5

Step-by-step explanation:

Given that:

1. Total Number of fruits = 80

2. Number of mangoes = x

3. Both mangoes and oranges are there in the basket.

Solution (i):

Only mangoes and oranges are there in the basket and the basket is full.

so, Number of mangoes + Number of oranges = Total number of fruits

x + Number of oranges = 80

Number of oranges = 80 -x

Solution (ii):

<u>Given:</u>

Cost of an orange = 50 cents = $0.50

Cost of a mango = 40 cents = $0.40

Cost for x mangoes = \$ 0.40x

Cost for (80-x) oranges = \$ 0.50 \times (80-x)

\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x

Solution (iii):

Put value of x = 35 in S(x)

S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5

Hence, answers are:

(i) 80-x

(ii) S(x) = 40 - 0.10x

(iii) $36.5

7 0
3 years ago
Can I get help solving this graph? I figured out h'(2) does not exist, but am having difficulty finding h'(1) and h'(3).
Mrac [35]
F(x) is a piecewise function defined as:
f(x) = (3/2)x when 0 <= x <= 2
or
f(x) = -(3/2)x+6 when 2 < x <= 4

g(x) is defined as: 
g(x) = -(1/4)x+1 when 0 <= x <= 4

Based on the graph or through the equations we can say:
f(1) = (3/2)*1 = 1.5
g(1) = -(1/4)*1+1 = 0.75
f(3) = (3/2)*3 = 4.5
g(3) = -(1/4)*3+1 = 0.25

And the derivative values are:
f ' (1) = 3/2 = 1.5
f ' (3) = -3/2 = -1.5
g ' (1) = -1/4 = -0.25
g ' (3) = -1/4 = -0.25
which are the slopes of each line

So...
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x) ... product rule
h ' (1) = f ' (1)*g(1) + f(1)*g ' (1)
h ' (1) = 1.5*0.75 + 1.5*(-0.25)
h ' (1) = 0.75

and,
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (3) = f ' (3)*g(3) + f(3)*g ' (3)
h ' (3) = -1.5*0.25 + 4.5*(-0.25)
h ' (3) = -1.5
7 0
4 years ago
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