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ehidna [41]
3 years ago
15

The distance d, in centimeters, that a diving board bends below its resting position when you stand at its end is dependent on y

our distance x, in meters, from the stabilized point. This relationship can be modeled by the function.
d(x)=â4x^3+x^2.
Evaluate d(x) for x = 1 and x = 2
Mathematics
1 answer:
kaheart [24]3 years ago
3 0

Answer:

d(1) = -3 and d(2)= -28

Step-by-step explanation:

Given that the distance d, in centimeters, that a diving board bends below its resting position when you stand at its end is dependent on your distance x, in meters, from the stabilized point

d(x)=-4x^3+x^2

For finding out the distances for x=1 and x=2

let us substitute 1 and 2 for x

d(1) = -4(1^3)+1^2 = -3

d(2) = -4(2^3)+2^2 \\= -28

d(1) = -3 and d(2)= -28

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A helicopter hovers 500 m above a long straight road. There is a truck to the left and right of the helicopter. The angles of de
vivado [14]

Answer:

1045.01 rounded to the nearest hundredth

Step-by-step explanation:

First, we can draw this out. The angle of depression is the angle formed by the object at the top and the line formed by the object at the top and the object at the bottom.

If the truck on the left is truck A and the truck on the right is truck B, with the helicopter being the circle on top, there is one 60 degree angle of depression and one 20 degree one. If we make a point at the point in the road the helicopter is straight above, and we connect the points, we can form two right triangles, as shown. If we can calculate the lengths of sides x and y, we can add them up to find the length between the two trucks.

Starting with side x, we know one angle and the side length adjacent to that angle. We want to find the length opposite that angle. One formula that encompasses this is tan(θ) = opposite/adjacent. Therefore, tan(60) = x/500

tan(60) = x/500

multiply both sides by 500 to isolate the x

tan(60) * 500 = x

x = 866.0254

Similarly, with side y, we can say that tan(20) = y/500 and

tan(20) * 500 = y

y= 181.9851

The distance between the two trucks can be shown as x+y, so x+y= 1045.01 rounded to the nearest hundredth

6 0
3 years ago
An airplane is preparing to land at an airport. It is 41,300 feet above the ground and is descending at the rate of 3,100 feet p
MissTica

9514 1404 393

Answer:

  • after 7 minutes
  • 19,600 feet

Step-by-step explanation:

Here's the "pencil and paper" solution:

  The two altitude equations are ...

  • y = 41300 -3100x
  • y = 2800x

They can be solved by setting the expressions for y equal to each other.

  2800x = 41300 -3100x

  5900x = 41300

  x = 41300/5900 = 7

  y = 2800·7 = 19600

The planes will both be at 19,600 feet after 7 minutes.

_____

Attached are solutions from a graphing calculator, and from a calculator app that is able to solve systems of equations.

I find the graphing calculator the easiest to use. I can enter equations using a keyboard, and the solution is displayed in a form that can be copied and pasted.

The calculator app on my phone requires equation entry using a small on-screen keyboard, with multiple key hits required to access some functions. (y is obtained by hitting the x key twice, for example.)

The "pencil and paper" solution is not so difficult, but requires a certain amount of writing (or good short-term memory). The solutions for x and y require separate calculations, whereas the other methods give both x and y at the same time.

3 0
4 years ago
How do I add fractions with different denominations?
nordsb [41]
1.<span>Write down the fractions.
2.</span><span>Find a common denominator.
3.</span><span>Multiply both numbers on the first fraction by the bottom number of the second fraction.</span><span> 
4.</span>Multiply both numbers on the second fraction by the bottom number of the first fraction. 
5.Line both fractions up side by side with their new numbers.<span> 
6.</span>Add together the numerators of the two fractions.<span> 
7.</span><span>Take the common denominator that you figured out in Step 2 and add it on the bottom of your new numerator.
8.</span>Put the new numerator on top and the new denominator on bottom.
9.<span>Simplify and reduce.</span>
7 0
3 years ago
Solve for x by finding the missing side of the triangle. Round your answer to the nearest tenth ​
Alika [10]

Answer:

i thought i had the answer but then i got it wrong im sorry

Step-by-step explanation:

5 0
3 years ago
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Verdich [7]

Answer:

Evaluate the expression for the given values of x and y. x-y/x+y when x = 10 and y = 8

4 0
3 years ago
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