13. Yah umm whoever gets the answer right wins a cookie

Pls show full working out

sweet-ann [11.9K]

Answer:

Question 1a. i) $x=1.8m$

Question 1a. ii) $Volume=27.6m^3$

Question 1b) $Volume=65.9m^3$

Explanation:

Question 1 a. i) Find the value of x.

$tan(\theta )=\dfrac{opposite\text{ }leg}{adjacent\text{ }leg}$

For the smalll triangle you can write:

$tan(\theta )=\dfrac{x}{1m}$

For tthe big triangle:

$tan(\theta )=\dfrac{x+2.7m}{2.5m}$

Substitute:

$\dfrac{x}{1m}=\dfrac{x+2.7m}{2.5m}$

Solve for x:

$2.5x=x+2.7m\\\\2.5x-x=2.7m\\\\1.5x=2.7m\\\\x=2.7m/1.5\\\\x=1.8m$

Question 1a ii) Find the volume of the frustrum

Find the volume of a cone with height = 2.7m + 1.8m = 4.5m, and radius = 2.5m

Formula:

$Volume=(1/3)\pi \times radius^2\times height$

Substitute:

$Volume=(1/3)\pi \times (2.5m)^2\times 4.5m=9.375\pi m^3$

Find the volume of a cone with heigth = 1.8m and radius = 1m

$Volume=(1/3)\pi \times (1m)^2\times 1.8m=0.6\pi m^3$

Subtract the volume of the small cone from the volume of the big cone

$Volume\text{ }of\text{ }frustrum=9.375\pi m^3-0.6\pi m^3=8.775\pi m^3\approx 27.6m^3$

Question 1b. Calculate the volume of the bin

i) Upper frustrum

This is the same frustrum from the equation of above, thus ist volume is 27.6m³.

ii) Lower frustrum

$\dfrac{x}{2.0m}=\dfrac{x+2.4m}{2.5m}$

$2.5x=2(x+2.4m)\\\\2.5x=2x+4.8m\\\\0.5x=4.8m\\\\x=9.6m$

$Volume=(1/3)\pi \times (2.5m)^2\times (9.6m+2.4m)-(2.0m)^2\times (9.6m)$

$Volume=38.3m^3$

iii) Add the volume of the two frustrums

$Volume=27.6m^3+38.3m^3=65.9m^3$

6 0

3 years ago

How can we isolate the variable c

Vlada [557]

Well depending on the equation you look at both sides and eliminate everything from both using addition, subtraction, multiplication, and division.

Ex:

3c-4=7 first add the 4 because you use the opposite type of operation so you add it to 7 which gives you:

3c=11 next you have to divide to get it alone

3c/3=11/3

which gives you

c= 3.66666666667

8 0

3 years ago

Curtis rides his bike 9 miles one way then turns around and rides back. On the return trip, his speed is increased 20% because t

k0ka [10]

Answer:

The expression that represents his total time is given by "t = 7.5/s" where s is his speed against the wind.

Step-by-step explanation:

In order to solve this problem we will assign a variable to Curtis speed on the first leg of the trip, this will be called "s". Since the speed on the first part is "s" and the speed on the second part is 20% higher, then the speed on the second part is "1.2s". Each leg of the course is 9 miles long, therefore the time it took to go each way is given by:

time = distance/speed

First part:

t1 = 9/s

Second part:

t2 = 9/1.2s = 7.5/s

The expression for the whole course is the sum of each, so we have:

t = t1 + t2

t = 9/s + 7.5/s

t = (9 + 7.5)/s = (16.5)/s

7 0

3 years ago

Which one is a linear function?

Lubov Fominskaja [6]

y + 3 + 2x

explanation:

Linear functions are those where the independent variable x never has an exponent larger than 1. So for example they would not have a var such as 3x2 in them. The linear function on this page is the general way we write the equation of a straight line. It is of the form

y = ax + b Where:

x,y are the coordinates of any point on the line

a is the slope of the line

b is the y-intercept (where the line crosses the y-axis)

The a var is the slope of the line and controls its 'steepness'. A positive value has the slope going up to the right. A negative slope goes down to the right.

The b var is the y intercept - the point where the line crosses the y axis. Adjust the sliders above to vary the values of a and b, and note the effects they have on the graph.

Another form

The more common form of the linear function is written y = mx+b, using m for the slope instead of a. This version is included to be consistent with the quadratic and cubic explorers. If you prefer it the usual way use Linear explorer (mx+b).

Things to try

The simplest case. Y = constant. (y = b)

Click 'zero' below each slider

Since a and b are both set to zero, this is the graph of the equation y = 0x+0. This simplifies to y = 0 and is of course zero for all values of x. Its graph is therefore a horizontal straight line through the origin.

Now move the rightmost slider for b and let it settle on, say, 5.

This is the graph of the equation y = 0x+5. This simplifies to y = 5 and so the function has the value 5 for all values of x. It is therefore a straight horizontal line through 5 on the y axis. Play with different values of b and observe the result.

Linear equation. (y = ax+b)

Click 'reset'

Click 'zero' under the right b slider.

The value of a is 0.5 and b is zero, so this is the graph of the equation y = 0.5x+0 which simplifies to y = 0.5x. This is a simple linear equation and so is a straight line whose slope is 0.5. That is, y increases by 0.5 every time x increases by one. Since the slope is positive, the line slopes up and to the right. Since b is zero, the y-intercept is zero and the line passes through the origin (0,0). Play with the a slider and observe the results, including negative values.

Click on 'reset' and move the b slider to, say, 8.

The value of a is 0.5 and b is 8, so this is the graph of y = 0.5x+8. The effect of changing b from zero to 8 is that the graph has moved upwards and now passes through 8 on the y axis.

Move both sliders and observe the overall effects of these two coefficients (a and b) working together.

Try it yourself

Press "reset", then "hide details"

Adjust the sliders until you see a line that appeals to you

Estimate the slope and y-intercept of the line and write down the equation for the line

Click on "show details" and see how close you got

Hints

The point where the line crosses the (vertical) y-axis is the y-intercept - b

For each increase of one on the (horizontal) x-axis, how much does the line go up or down?

This is a, the slope of the line

If the line goes down and to the right, the slope (a) will be negative.

Coordinate Geometry

In coordinate geometry, the equation for a straight line is usually written y = mx+b. That is, the letter m is used to indicate the slope. See Equation of a line (coordinate geometry).

8 0

2 years ago

Write the fraction as a decimal. Round to the nearest hundredth, if necessary. 7/8

labwork [276]

Answer:

0.875

Step-by-step explanation:

We know that

7/8

is the same as

7÷8

Then using

Long Division for 7 divided by 8

and rounding to a Max of 3 Decimal Places gives us

=0.875

hope this helps:)sorry if it doesnt

plz give brainliest

4 0

3 years ago

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