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3 years ago

Please help if you can

Mathematics

1 answer:

umka21 [38]3 years ago

7 0

Answer: 80, 1/12, 5/6

Step-by-step explanation:

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Write the expression that shows "3 times the sixth power of ten."

KIM [24]

3 x 10 (with a small 6 at the top right of the ten). Hope this helped

8 0

3 years ago

Read 2 more answers

Find the value of n, correct to 4 significant figures.

Law Incorporation [45]

Answer:

6.708

Step-by-step explanation:

Y varies directly as the square of x (Given)

$\implies y\:\alpha \:x^2$ ......(1)

Y varies inversely as the square root of z (Given)
$\implies y\:\alpha\: \frac{1}{\sqrt z}$ ......(2)

Combining (1) & (2), we find:

$y\:\alpha \:\frac{x^2}{\sqrt z}$

$\implies y=\frac{kx^2}{\sqrt z}$ (Where k is constant of proportionality).....(3)

Now, when y = 2, x = 3 and z = 4, we find the value of k i.e. constant.

$2=\frac{k(3)^2}{\sqrt 4}$

$\implies 2=\frac{k(9)}{2}$

$\implies k =\frac{4}{9}$

Plugging the value of k in (3), we find:

$y=\frac{4x^2}{9\sqrt z}$ ....(4)

Next, in equation (4), plug y = 5, x = n and z = 16 and obtain the value of n by solving it.

$5=\frac{4(n)^2}{9\sqrt {16}}$

$\implies 5=\frac{4(n)^2}{9(4)}$

$\implies 5=\frac{(n)^2}{9}$

$\implies 5(9)=(n)^2$

$\implies 45=(n)^2$

$\implies n=\sqrt{45}$

$\implies n=6.70820393$

$\implies n\approx 6.708$

7 0

1 year ago

Evaluate -1(5)(2)(-4)

wariber [46]

Answer:

Step-by-step explanation:

-1 × 5 = -5

-5 × 2 = -10

-10 × -4 = 40

6 0

2 years ago

4/8 as a mixed number

Tpy6a [65]

Answer:

8/4

Step-by-step explanation:

8/4

5 0

3 years ago

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What are the answers to these 2 question 4&5 PLZ HELP

Ahat [919]

The first problem:

y = -2 x² ⇒⇒⇒ x² = -y/2 →(1)33 x² + y² = 27 → (2)
By substitution from (1) at (2) with the value of x²
∴ 33 (-y/2) + y² = 27
∴ y² - 16.5 y - 27 = 0
a = 1 , b = -16.5 , c = -27
∴ $y= \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \frac{16.5 \pm \sqrt{(-16.5)^2-4*1*(-27)} }{2*1}$
∴ y = 18 or y = -3/2
By substitution from at (1) with the value of y
for y = 18 ⇒⇒⇒ x² = -18/2 = -9 (unacceptable)
for y = -3/2 ⇒⇒⇒ x² = -(-3/2)/2 = 3/4
∴ $x= \pm \sqrt{ \frac{3}{4} } = \pm \frac{ \sqrt{3} }{2} 
$
The correct options are 2 , 7
Solution of the system of equations is
$( \frac{ \sqrt{3} }{2} , \frac{-3}{2} )$
and
$( -\frac{\sqrt{3} }{2} , \frac{-3}{2} )$
==================================
The second problem:
The general equation of the hyperbole is
$\frac{x^2}{a^2} - \frac{y^2}{b^2} =1

Transverse axis is horizontal 

The equation if the asymptotes are y = \pm \frac{b}{a}x$
For the given equation:
$\frac{x^2}{225} - \frac{y^2}{36} = 1$
a² = 225 ⇒⇒⇒ a = √225 = 15
b² = 36 ⇒⇒⇒ b = √36 = 6
∴ the slope of the asymptotes = b/a and -b/a

b/a = 6/15 = 2/5

-b/a = -6/15 = -2/5

∴ m = 2/5 and m = -2/5

3 0

2 years ago