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3 years ago

Use the given area of the base and the height to find the volume of the right rectangular prism, in cubic units.

Mathematics

2 answers:

Novosadov [1.4K]3 years ago

8 0

Cant tell because there is no picture

Semenov [28]3 years ago

7 0

You dident give us a picture of it so we cant tell

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CORRECT answer gets brainliest.

Montano1993 [528]

The answer for this question is c

6 0

2 years ago

How is this solved using trig identities (sum/difference)?

GenaCL600 [577]

FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

$cos \beta = -\frac{1}{2} \sqrt{3}$

$tan \beta= \frac{1}{3} \sqrt{3}$

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
$sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )$
$sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )$
$sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})$

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
$cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )$
$cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )$
$cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )$

Find tan (α - β)
$tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha tan \beta }$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}$

Simplify the denominator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5\sqrt{3}}{24})}$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the numerator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$
$tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the fraction
$tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})$
$tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}$

7 0

2 years ago

Riley has collected surveys for her final thesis project. One one question, 46.1% of respondents said that conditions were impro

ira [324]

Answer:

The maximum value of the confidence interval for this set of survey results is 51.73%.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

These bounds depend on the sample proportion and on the margin of error.

The lower bound is the sample proportion subtracted by the margin of error.

The upper bound is the margin of error added to the sample proportion.

In this question:

Sample proportion: 46.1%

Margin of error: 5.63%.

Maximum value is the upper bound:

46.1+5.63 = 51.73

The maximum value of the confidence interval for this set of survey results is 51.73%.

5 0

3 years ago

A hospital recorded the weight of babies born at the hospital during one week on a line plot. How many more pounds was the baby

lbvjy [14]

greatest weight 20 lowest weight 5

3 0

2 years ago

I’m a little confused with this? Can someone walk me through this?

mina [271]

Answer:

A. 5.8

Step-by-step explanation:

From the given graph d has two coordinates;

the first coordinates of d = (0, 0)

the second coordinate of d = (-3 , -5), that is x = -3 when traced up and y = -5 when traced horizontal

The distance between the two coordinates = distance of d;

$distance \ between \ two \ coordinates = \sqrt{(x_2-x_1)^2 \ + \ (y_2-y_1)^2} \\\\d = \sqrt{(-3-0)^2 \ + \ (-5-0)^2}\\\\d = \sqrt{9 \ + \ 25} \\\\d = \sqrt{34} \\\\d = 5.83\\\\d = 5.8$

Option A is correct

6 0

3 years ago