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Katarina [22]
3 years ago
9

Diagram shows a cone and its axis of rotation which type of cross-section is formed when the cone is intersected by a plane cont

aining the axis of rotation (Plato students)

Mathematics
1 answer:
MAXImum [283]3 years ago
3 0

Answer:

The cross section will be an isosceles triangle

Step-by-step explanation:

The picture of the question in the attached figure N 1

we know that

If a plane passes through the axis of rotation of the cone, then the resultant cross-section will be a triangle with one vertex as the vertex of the cone and the two sides of the triangle through the vertex A will be equal.

Where the base of the triangle will be equal to the diameter of the circular base of cone and the two congruent sides of triangle will be equal to the slant height of the cone

therefore

The cross section will be an isosceles triangle

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What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (1, −7) and has (2, 3) as its vertex
kondaur [170]

Answer:

Vertex form: f(x) = -10(x − 2)^2 + 3

Standard form: y = -10x^2 + 40x - 37

Step-by-step explanation:

h and k are the vertex coordinates

Substitute them in the vertex form equation:

f(x) = a(x − 2)^2 + 3

Calculate "a" by replacing "f(x)" with -7 and "x" with 1:

-7 = a(1 − 2)^2 + 3

Simplify:

-7 = a(1 − 2)^2 + 3

-7 = a(-1)^2 + 3

-7 = a + 3

-10 = a

Replace a to get the final vertex form equation:

f(x) = -10(x − 2)^2 + 3

Convert to standard form:

y = -10(x − 2)^2 + 3

Expand using binomial theorem:

y = -10(x^2 − 4x + 4) + 3

Simplify:

y = -10x^2 + 40x - 40 + 3

y = -10x^2 + 40x - 37

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3 years ago
Caytee’s Confections produces white chocolate chips and milk chocolate chips at its plants in Elizabeth City and Asheville.
Zepler [3.9K]
3000x + 1000y < 30000
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x = 7.5
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3 years ago
At 3:25 p.m., a passenger train and a freight train both left Kalamazoo,
Svetlanka [38]

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4:10 PM

Step-by-step explanation:

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3 years ago
Which expression is equivalent to (x superscript four-thirds baseline x superscript two-thirds Baseline ) superscript one-third
Andrei [34K]
<h3><u>The equivalent expression is:</u></h3>

(x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = x^{\frac{2}{3}

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}

We have to find the equivalent expression

We can simplify the above expression using law of exponents

<em><u>Use the following law of exponents:</u></em>

a^m \times a^n = a^{m+n}

Therefore,

\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = (x^{\frac{4}{3}+\frac{2}{3}})^{\frac{1}{3}}\\\\Simplify\\\\\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = (x^2)^\frac{1}{3}

<em><u>Use another law of exponent</u></em>

(a^m)^n = a^{mn}

Therefore,

(x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = x^{\frac{2}{3}

Thus the equivalent expression is found

5 0
3 years ago
Read 2 more answers
For which value of theta is sine theta = negative 1?
Ivan

Answer:

1) 270 degrees

2)  pi/4 rad

Step-by-step explanation:

1.) For which value of theta is sine theta = negative 1?

Given

sintheta = -1

theta = arcsin(-1)

theta = -90degrees

Since sin is negative in the third and 4th quadrant

In the third quadrant, theta = 180 + 90 = 270degrees

In the fourth quadrant, theta = 360 - 90 = 270 degrees

Hence the required value of theta is 270degrees

2) Given the radius of the circle to be 1, the y axis value will also be 1 units

Opposite = 1

adjacent = 1

hyp = √1²+1²

hyp = √2

sin theta = opp/hyp

sin theta = 1/√2

theta = arccsin(1/√2)

theta = 45 degrees

Express in radians

45 degrees = pi/4 radians

Hence the required angle in the first quadrant is pi/4 rad

4 0
3 years ago
Read 2 more answers
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