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2 years ago

14

Show that the equation 2x + 3 cos x + e ^ x = 0 has a root on the interval [- 1, 0]

1 answer:

ExtremeBDS [4]2 years ago

5 0

If <em>x</em> = -1, you have

2(-1) + 3 cos(-1) + <em>e</em> ⁻¹ ≈ -0.0112136 < 0

and if <em>x</em> = 0, you have

2(0) + 3 cos(0) + <em>e</em> ⁰ = 4 > 0

The function <em>f(x)</em> = 2<em>x</em> + 3 cos(<em>x</em>) + <em>eˣ</em> is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < <em>c</em> < 0 such that <em>f(c)</em> = 0.

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Convert 34.0 dm to km. Show all work.

larisa [96]

Step-by-step explanation:

Convert 34 Decimeters to Kilometers (dm to km) with our conversion calculator and conversion tables. To convert 34 dm to km use direct conversion formula below.

34 dm = 0.0034 km.

You also can convert 34 Decimeters to other Length (popular) units.

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2 years ago

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Max can type 160 words in 5 minutes. How long would it take him to type 400 words? * A. 12.50 minB. 13 minC. 10.50 minD. 12 min

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To find how long it would take him, one has to divide 400 by 160 and then multiply 5 by what that number is. You multiply 5 by the quotient because that is the number that would make it proportional. 400/160 x 5 is 12.5, meaning that the answer is 12.5 minutes, or A.

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3 years ago

Consider the right triangle below.

MaRussiya [10]

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15 feet, 7.5 square feet

Step-by-step explanation:

Perimeter = 6.5 + 2.5 + 6

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Area = ½ × 2.5 × 6

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3 years ago

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Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court

Ksju [112]

Answer:

$(a)\dfrac{92}{117}$

$(b)\dfrac{8}{39}$

$(c)\dfrac{25}{117}$

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

$P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}$

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed) $=P(MW)+P(WM)$

$=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}$

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.
Two women are appointed

P(at least one woman is appointed) $=P(MW)+P(WM)+P(WW)$

$P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}$

In Part B, $P(MW)+P(WM)=\frac{8}{39}$

Therefore:

$P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}$

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2 years ago

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gtnhenbr [62]

Answer:

1176in^2

Step-by-step explanation:

find the surface area of the cube

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14*14 is finding the area of one side and then we multiply it by six because that's how many congruent sides there are

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3 years ago

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