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Rudik [331]
3 years ago
6

6. Sketch the region enclosed by the graphs of x =0, 6y-5x=0 and x+3y=21. Find the area

Mathematics
2 answers:
Gala2k [10]3 years ago
4 0

6. 52.5

7. 13.3

I'm still waiting for feedback but those are my answers I'm almost certain on 6 but 7 I'm unsure. I used gizmos to help me out.

kow [346]3 years ago
3 0
We can see that revolving the region formed by intersecting 3 lines, we will get 2 cones that are connected their bases.
Volume of the cone V=1/3 *πr²*h

1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
3) whole volume
5³/3 *π + 5³*π=5³π(1/3+1)=((5³*4)/3)π=(500/3)π≈166.7π≈523.6

Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
A2=(1/2)*5*15=75/2
3) whole area=A1+A2=25/2+75/2=100/2=50

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Can someone please help with this? I'll give brainliest. I don't understand this... or the explanation it gives... the page befo
tresset_1 [31]

Step-by-step explanation:

Hello!
I'd love to help you learn.
I see the formula attached is 4*(\frac{1}{2})^{x} =-2^{x}-1\\

This problem is explaining you to graph, since algebraically it's a little more harder to try and find the solution.

Since they're both equal to each other, we can assign a variable like y, so we can make them into two individual lines.

You can use your scientific calculator to graph lines like this, or otherwise there are online sources (Desmos helps alot!) which can graph two equations as so.

Now that we have the corresponding system of equations, we can graph both.

y=4*(\frac{1}{2})^x\\ y=-2^x-1
Let's graph them on Desmos on the same plane. The answers are attached. Red is the first equation, blue is the second.

What determines the solutions of a system of equations?

-No solution: the two lines will never intersect/does not intersect ever, which means that there are no set point where it satisfies both equations.

-One solution: the two lines intersect once and only once, meaning that there is that one set point where the x and y values both satisfy both equations.

-Multiple solutions: the two lines will intersect each other multiple times, meaning there are multiple set points where the x and y values satisfy both equations. You usually will not have to worry about these problem sets.

-Infinite solutions: the two lines are both the same line, which means every x and y value will satisfy both equations.

Looking at the solution attached, we can see that there are no places where a system of equations intersect, therefore ruling it that they have no solution.

And to answer your last question, an asymptote is a imaginary line in which a equation can approach closely and closely, but will never touch that imaginary line. Think of a line at y=\frac{1}{x}. When you graph it, you can see that the two lines never ever EVER intersect the y-axis, or x=0; giving that x=0 as a vertical asymptote.

5 0
2 years ago
Based on a poll of 100 citizens, a community action group claims that 38% of the population is in favor of the construction of a
tatyana61 [14]

Answer:

(0.55, 0.75)

Step-by-step explanation:

The range can be estimated to be 6 standard deviations wide.  Therefore, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

The margin of error is ±2σ, so:

ME = ±0.10

Therefore, the interval estimate is:

(0.65 - 0.10, 0.65 + 0.10)

(0.55, 0.75)

8 0
2 years ago
Limit as x approaches 0 of csc3x/cotx
jolli1 [7]
Hello Meggieh821, to find the lim as x approaches 0 we can check this by inserting a number that is close to 0 that is coming from the left and from the right.

For instance, we can find the lim by using the number -.00001 for x and solve
<span>csc(3x) / cot(x)
</span>csc(3*-.00001) / cot(-.00001) = .333333... = 1 /3

We also need to check coming from the right. We will use the number .00001 for x
csc(3x) / cot(x)
csc(3*.00001) / cot(.00001) = .333333... = 1 /3

So since we are getting 1/3 from the left and right we can say as x approaches 0 the limit is 1/3

<span>\lim_{x\to 0} \frac{csc(3x)}{cot(x)} = \frac{1}{3}</span>

6 0
3 years ago
What two fractions make 1/3
Anna11 [10]
1/6 and 1/6 equals 1/3
8 0
3 years ago
Find the unit rate.<br> 48 cupcakes in 6 boxes=cupcakes per box
natka813 [3]

Answer: 8 cupcakes per box

Step-by-step explanation: "Per box" means in 1 box, so we can rewrite the given statement using fractions as

<em>48 cupcakes/6 boxes</em> = <em>__ cupcakes/1 box</em>.

To find out what goes in the blank, notice that we

have a 1 in the denominator of our second fraction.

So we want to find a fraction that is equivalent

to 48/6 that has a 1 in the denominator.

If we divide the numerator and denominator of 48/6 by 6,

we get the equivalent fraction 8/1 or <em>8 cupcakes/1 box</em>.

So now we have <em>8 cupcakes/1 box = __cupcakes/1 box</em>.

So an 8 must go in the blank which means that the unit rate

for 48 cupcakes in 6 boxes is <em>8 cupcakes per box</em>.

6 0
3 years ago
Read 2 more answers
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