All categories

3 years ago

CAN SOMEONE PLEASE ANSWER THE FOLLOWING IT URGENT

Mathematics

1 answer:

emmasim [6.3K]3 years ago

8 0

Answer:

See bolded below.

Step-by-step explanation:

As you said, you only need help with no. 2:

a) Check the attachments for the lines

b) The equations are, respectively:

y = -4x + 1 [intersects parabola at 1 point]

Check:

$\begin{bmatrix}y=\left(x-2\right)^2-3\\ y=-4x+1\end{bmatrix}$

$\begin{bmatrix}-4x+1=\left(x-2\right)^2-3\end{bmatrix}$

$\begin{bmatrix}-4x+1=x^2-4x+1\end{bmatrix}$

$x^2=0, x = 0$

$y=-4\cdot \:0+1 = 1$

$y=1,\:x=0$

The point of intersection would be (0, 1)

y = -4x + 3 [intersects parabola at 2 points]

Check:

$\begin{bmatrix}y=\left(x-2\right)^2-3\\ y=-4x+3\end{bmatrix}$

Subtract the 2 equations,

$y=\left(x-2\right)^2-3\\-\\\underline{y=-4x+3}\\y-y=\left(x-2\right)^2-3-\left(-4x+3\right),\\0=x^2-2\\x = \sqrt{2}, x = - \sqrt{2} \\\\\mathrm{Plug\:the\:solutions\:}x=\sqrt{2},\:x=-\sqrt{2}\mathrm{\:into\:}y=\left(x-2\right)^2-3$

$\begin{pmatrix}x=\sqrt{2},\:&y=3-4\sqrt{2}\\ x=-\sqrt{2},\:&y=3+4\sqrt{2}\end{pmatrix}$

Therefore the points of intersection are (√2, 3-4√2) and (-√2, 3+4√2) respectively

And finally we have the equation y = - 4x. It doesn't intersect the parabola.

c) The y-intercepts of such graphs are all less than or equal to 0.

You might be interested in

The radius of a cone is 5cm the heigth of the cone is 18 cm what is the volume of the cone

nikitadnepr [17]

6-8 cm is the answer!! Hope this helps!

3 0

3 years ago

One half liter of lemonade concentrate is added to 3 liters of water. how many one thirds liter servings of lemonade are made.

uysha [10]

So, 3 liters of water, add 1/2 liter of lemonade, that's 3 and 1/2 liters of lemonade.

so in short, how many times does 1/3 go into 3 and 1/2?

let's change the mixed to "improper" and divide then.

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\
-------------------------------\\\\
\cfrac{\quad \frac{7}{2}\quad }{\frac{1}{3}}\implies \cfrac{7}{2}\cdot \cfrac{3}{1}\implies \cfrac{21}{2}\implies 10\frac{1}{2}$

8 0

4 years ago

Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

4 0

3 years ago

Is 14 200 000 in scientific notation 1.42 10x,5

Elan Coil [88]

Yes, the rules of scientific notation are:

1. All non-zero digits are significant

2. Zeros in between non-zeros are significant.

3. Zeros to the left of the first non-zero number are NOT significant.

4. Zeros to the right of non-zero numbers are significant IF a decimal point is present.

P.S: if you need help with sig fig rounding, let me know.

6 0

3 years ago

What is the scale factor very urgent

alisha [4.7K]

Answer:

The scale factor of the triangle if of 3.

Step-by-step explanation:

All you have to do is use figure A and either multiply or divide by a number to get figure B. In this case, the straight vertical side of Figure A is 6 units, and the straight vertical side of Figure B is 2. So 6 divided by 2 is 3. That means that the scale factor of the triangle is of 3. The triangle contracted it's size by 3.

4 0

3 years ago