A radio telescope has a parabolic surface. If it is 1m deep and 16m wide how far is the focus from the vertex?

1 answer:

6 0

Basing on the description, a parabola opening up with vertex at origin, the formula with vertex at origin is used, x^2 = 4py. p is the focus and so with the dimensions given, we obtain a 0.25 and that is the distance of the focus to the vertex.

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33) Given the graphs of f(x) = x - 1 and g(x) = -x - 7, what is the solution to the equation f(x) = g(x)?

neonofarm [45]

Answer:

Step-by-step explanation:

The solution is the point of intersection of the 2 lines

The lines intersect at (- 3, - 4 ), then

f(x) = g(x) has solution x = - 3

6 0

2 years ago

I’m confused on this answer anyone know it?

slamgirl [31]

Answer:

$y=\frac{26}{7},\:x=-\frac{15}{7}$

Step-by-step explanation:

$\begin{bmatrix}4x+5y=10\\ -2x+y=8\end{bmatrix}\\\\\begin{bmatrix}-2\cdot \frac{10-5y}{4}+y=8\end{bmatrix}\\\\$

$-5+\frac{7y}{2}=8\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\-5\cdot \:2+\frac{7y}{2}\cdot \:2=8\cdot \:2\\-10+7y=16\\y=\frac{26}{7}\\$

$\mathrm{For\:}x=\frac{10-5y}{4}\\\mathrm{Subsititute\:}y=\frac{26}{7}\\x=\frac{10-5\cdot \frac{26}{7}}{4}\\\\$

$x=-\frac{15}{7}\\$

7 0

2 years ago

The population of California is approximately 38,040,000. The population of Texas is about 2.606 × 107. What is the approximate

liubo4ka [24]

Answer:

The total population of these two states is:

$3.804\times \:\:10^7+2.606\times \:\:10^7\:=10^7\times \:\:6.41$

Therefore, option C is correct.

Step-by-step explanation:

The population of California is approximately 38,040,000.

The population of Texas is about 2.606 × 10⁷.

Writing the population of California i.e.38,040,000 in scientific notation by moving the decimal point 7 places to the left and dropping the 0's on the right side as they're after the decimal point now.

i.e.

38,040,000 = 3.804 x 10⁷

So adding 3.804 x 10⁷ and 2.606 × 10⁷

i.e.

$3.804\times \:10^7+2.606\times \:10^7$