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3 years ago

11

Sam built a ramp to a loading dock. The ramp has a vertical support 2 m from the base of the loading dock and 3m from the base o

f the ramp. If the vertical support is 1.2 m in height, what is the height of the loading dock?

1 answer:

blsea [12.9K]3 years ago

5 0

Answer:

tan angle = x/5.

Step-by-step explanation:

If I understand your description,

tan angle at bottom of ramp = 1.2/3.

Then tan angle = x/5.

Check my thinking.

You might be interested in

A: P = 2L + 2W solve for W<br><br>B: C = 5/9(F - 32) solve for F

aliya0001 [1]

Answer:

A. P/2 - L = W

B. 9/5C + 32 = F

Step-by-step explanation:

A. P = 2L + 2W

P = 2(L+W)

P/2 = L + W

(P/2)-L = W

B. C = 5/9(F - 32)

9/5C = F - 32

9/5C + 32 = F

7 0

3 years ago

DochEvi [55]

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve " $curve_{big}$ " and the three smaller curves " $curve_1$ " " $curve_2$ " " $curve_3$ " in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

<u>Parts of a circle</u>

Since values in the diagram are diameters, use the formula for the Perimeter of a circle $P=\pi d$ (where d is the diameter).

Let's call the diameters of each of our curves " $d_{big}$ " " $d_1$ " " $d_2$ " " $d_3$ ", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: $Length(curve_{big})=\frac{1}{2} \pi d_{big}$

Substituting back into the main equation above:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ $P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}$

Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

The diameter for the large Curve, is the sum of the three small diameters, so $d_{big}=12cm$ , and $d_{1}=d_{2}=d_{3}=4cm$

Substituting and simplifying (in terms of pi):

$P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm$

<u>Additional Understanding</u>

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve $d_{1} + d_{2} + d_{3} =d_{big}$ , one could make a different substitution into one of our formulas above:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

$P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))$

$P_{overall}=\frac{1}{2} \pi (2d_{big})$

$P_{overall}=\pi d_{big}$

Notice that $\pi d_{big}$ is just the full perimeter of a circle with the big diameter.

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.

7 0

2 years ago

A ball is launched upward from a height 40 feet above ground level. The ball’s height at t seconds is given by -16t^2=128=40 .

Nesterboy [21]

Answer:

The ball will be at 100 feet at time x=0.5 sec and at time x=7.5 sec

Step-by-step explanation:

<u><em>The correct question is</em></u>

A ball is launched upward from a height 40 feet above ground level. the ball's height at t seconds is given by h(t)=-16t^2+128t+40 At what time(s) will the ball be at 100 feet?

we have

$h(t)=-16t^{2}+128t+40$

so

For h(t)=100 ft

substitute in the equation and solve for x

$-16t^{2}+128t+40=100$

$-16t^{2}+128t-60=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+128t-60=0$

so

$a=-16\\b=128\\c=-60$

substitute in the formula

$x=\frac{-128(+/-)\sqrt{128^{2}-4(-16)(-60)}} {2(-16)}$

$x=\frac{-128(+/-)\sqrt{12,544}} {-32}$

$x=\frac{-128(+/-)112} {-32}$

$x=\frac{-128(+)112} {-32}=0.5$

$x=\frac{-128(-)112} {-32}=7.5$

therefore

The ball will be at 100 feet at time x=0.5 sec and at time x=7.5 sec

7 0

3 years ago

John recieves £173 per week after working for 25 hours. How much does he get per hour

inessss [21]

Answer:

Amount John gets paid per hour $6.92$ Dollars per hour ,

Step-by-step explanation:

To find how much he gets paid per hour we need to divide the total payment he received by the total number of hours he worked.

Amount John gets paid per hour = $\frac{173}{25}$ Dollars per hour.

= $6.92$ Dollars per hour

4 0

4 years ago

Starting at the same point, Tom and Juanita go biking in opposite directions. If Tom rides at a speed of 18 mph, and Juanita rid

adell [148]

72 miles
one hour= 18+18
second hour= 18+18

3 0

3 years ago