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3 years ago

Match the following items help me plz ASAP

Mathematics

2 answers:

irina [24]3 years ago

8 0

1 proper fraction (fraction is normal)
2 mixed number example 1.5 of a cup it’s not a even number
3 equivalent fraction because it’s a whole number (3/3 = 1)
4 improper fraction (36/2)
5 denominator (_/this)
6 numerator (this/_)

Y_Kistochka [10]3 years ago

3 0

1. Proper Fraction
2. Mixed Number
3. Equivalent Fractions
4. Improper Fraction
5. Denominator
6. Numerator
This should help.

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9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

If a quadrilateral has vertices a(-2,2) b(2,3) c (3,-4) d(-3,-2) find the slope of AB,BC,CD,DA

FrozenT [24]

Slope AB=0.25
BC=-7
CD=-1/3
DA=4

4 0

3 years ago

How hard must someone pull on the unkown line and inwhat direction to keep the knot from moving

dolphi86 [110]

Answer:

4.4N, 263.4°

Step-by-step explanation:

The sum of all forces must add to zero:

The forces in the x-plane:

∑F = 3N + (cos 120°)*5N + x = 0

x = -(3N + (cos 120°)*5N)

x = -0.5N

The forces in the y-plane:

∑F = (sin 120°)*5N + y = 0

y = -(sin 120°)*5N = -√(3/4)*5N = -4.3N

The magnitude of the unknown force U is:

U = √(x² + y²) = √19 = 4.4N

The direction is given by:

tanФ = y/x

Ф = 263.4°

4 0

3 years ago

!!!!!!!!!!!!!!!! x= and y=

kap26 [50]

Answer:

Y=16

X=32

Step-by-step explanation:

ï just know you need to do more meth

7 0

3 years ago

X|−10|=3<br><br>find all possible values of x

hram777 [196]

Answer:

x=13

Step-by-step explanation:

so,x-10=3

or,x=3+10

or,x=13

therefore, x=13

4 0

3 years ago

Read 2 more answers