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3 years ago

Mike ran 7 miles on his first day of training. The next day he ran 8/10 that distance. How far did he run the second day.

Mathematics

1 answer:

jeka57 [31]3 years ago

3 0

7 miles multiplied by 8/10 is 56/10, or 28/5 miles.

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82 decrease by 10 percent

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Answer:

Percentage decrease = 10% × 0.82

New value = 0.82 - Percentage decrease

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2 years ago

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2 years ago

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dangina [55]

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2 years ago

In a certain year, there were 88 female officials in Congress, which is comprised of the House of Representatives and the Senate

Ainat [17]

Answer:

71 in House of Representatives
17 in Senate

Step-by-step explanation:

Let h and s represent the numbers in the House and Senate, respectively. Then we have ...

h + s = 88

h - s = 54

Subtracting the second equation from the first gives ...

(h +s) -(h -s) = (88) -(54)

2s = 34 . . . . . simplify

s = 17 . . . . . . . divide by 2

h = 88 -17 = 71 . . . . find the other value using the sum equation

There were 71 females in the House of Representatives, and 17 females in the Senate.

3 0

2 years ago

Convert,the complex number into polar form: 4+4i

kow [346]

Z = a + bi
z = 4 + 4i

r² = a² + b²
r² = (4)² + (4)²
r² = 16 + 16
r² = 32
r = 4√(2)
r = 4(1.414)
r = 5.656

$cos\theta = \frac{a}{r}$
$cos\theta = \frac{4}{4\sqrt{2}}$
$cos\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$cos\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
$cos\theta = \frac{4\sqrt{2}}{4(2)}$
$cos\theta = \frac{4\sqrt{2}}{8}$
$cos\theta = \frac{\sqrt{2}}{2}$
$2(cos\theta) = 2(\frac{\sqrt{2}}{2})$
$2cos\theta = \sqrt{2}$
$2cos\theta = 1.414$

$sin\theta = \frac{b}{r}$
$sin\theta = \frac{4}{4\sqrt{2}}$
$sin\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$sin\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
$sin\theta = \frac{4\sqrt{2}}{4(2)}$
$sin\theta = \frac{4\sqrt{2}}{8}$
$sin\theta = \frac{\sqrt{2}}{2}$
$2(sin\theta) = 2(\frac{\sqrt{2}}{2})$
$2sin\theta = \sqrt{2}$
$2sin\theta = 1.414$

z = a + bi
z = rcosθ + (rsinθ)i
z = r(cosθ + i sinθ)

z = 4 + 4i
z = 5.656cosθ + (5.656sinθ)i
z = 5.656(cosθ + i sinθ)
z = 5.656(cos45 + i sin45)

$\theta = tan^{-1}\frac{b}{a}$
$\theta = tan^{-1}\frac{4}{4}$
$\theta = tan^{-1}(1)$
$\theta = 45$

The polar form of 4 + 4i is approximately equal to 5.656(cos45 + i sin45).

5 0

3 years ago