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jonny [76]
2 years ago
15

Find the x-intercept of the line whose equation is 8x + 2y = 4. 04 02 1/2

Mathematics
1 answer:
bezimeni [28]2 years ago
4 0

Answer:

1/2

Step-by-step explanation:

The x-intercept is a point on the graph that is located on any point of x but must have a y-value of 0. To find the x-intercept, we must set y in the given equation equal to 0.

8x + 2y = 4

8x + 2(0) = 4

8x = 4

x = 4/8

x = 1/2

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A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On
uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

h(x)=ax(x-7)             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

4=a(3)((3)-7)

4=a(3)(-4)

\dfrac{4}{(3)(-4)}=a

-\dfrac{1}{3}=a

Putting a=-\dfrac{1}{3}, we get

h(x)=-\dfrac{1}{3}x(x-7)              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)

h(1.5)=-(0.5)(-5.5)

h(1.5)=2.75

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

6 0
2 years ago
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